Friday Funny! 😂😂😂

Have you ever had a Math book fall on your head?  Who else is there to blame but your shelf?
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Happy Friday, everyone!

What Is My Approximate Annual Salary?

Without performing the messy calculations, is there a quick way to know approximately how much you will earn in a year if you work the entire year and average 40 hours per week?  Many years ago, I learned a trick, and the process remains a valid one today.

Let's take a look at a possible real-world scenario, and understand the benefit of knowing this helpful information.

Mr. Miller works 40 hours each week throughout the year and currently makes an annual salary of $40,000 and would like to find a job that pays more money without working more hours.  He has recently interviewed for a job at the local factory that pays $25 per hour and he is trying to determine which job will earn more money?

Here is the solution:
Traditional Method of calculation:
1.) Multiply $25/hr x 40 hrs/wk x 52 wks/yr.
2.) He will earn $52,000.

Alternate Method of Approximation:
1.) Multiply the hourly wage $25 and double it, which is $50.
2.) Multiply by $1,000 or if you prefer you may add 3 zeros, which is $50,000.

Let's take a closer look at the math operations and gain a better understanding of how this actually works.  If he works 40 hrs per week every week and there are approximately 50 weeks in a year, we can quickly multiply 40 x 50 and know the product is 2,000.  We also know that 2 factors of 2,000 are 2 x 1,000 which enables us to double the hourly wage (utilizing the 2 of both factors) and apply the 3 zeros in 1,000 to the product, which gives us the estimated wage of $50,000.

Some of you may be concerned that the wage varies by $2,000 from the actual calculated amount, and my reasoning for accepting this method of approximation, is that you know you'll make at least $50,000 and it would be wise for Mr. Miller to accept the new job offer if he is ready to make a change in his employment.

One quick note about the variance in the calculations is knowing that the higher the hourly wage, the greater the variance will be between both annual salaries.  Another note about the difference in wages, by underestimating the actual wage, we are offering a layer of financial protection by accounting for 50 of the 52 weeks in the year.

Try a few examples on your own, and you will soon be the expert!  😉😉

Tropical Depression or Tropical Storm?

Since I was a young boy, I have always been fascinated with weather, and particularly watching storms brew.  Living in Indiana most of my life, I've never experienced a Tropical Depression or Tropical Storm, but we've certainly had numerous storms with winds that were in excess of 60 mph, that often produced heavy downpours and often hail.

According to the many weather experts, a Tropical Depression is when a storm delivers sustained winds of 38 mph or less, and if the sustained winds are 39 mph or greater, it becomes a named storm and is changed to a Tropical Storm.

As of today, Tropical Storm Colin will be making a path from the southwest waters in the Gulf of Mexico and will pass over Tampa in a northeasterly direction across Florida and then aim for the east coast.

Be safe everyone, and take this storm very seriously, as extensive flooding may occur.  This storm may produce tornadoes as well.

How Fast Do Greyhounds Run?

Many years ago, I attended a greyhound race, and wondered how fast these fascinating dogs run.  If I were to tell you that some of the faster greyhounds can sprint as fast as 60 feet per second, do you know approximately how many miles per hour they can run?

Let's take a look at an example.

How do you convert feet per second to miles per hour?

Solution:

60 feet         60 seconds           60 minutes           1 mile            216,000
---------   x    -------------   x      -------------   x    -----------   =    ----------   =  approx. 40 miles/hr
second               minute                 hour              5280 feet           5280

To solve this problem, you need to multiply 60 x 60 x 60, which is 216,000.  One more calculation, divide 216,000 by 5280, and arrive at the answer, approximately 40 mph.

There you have it, a greyhound runs as fast as 40mph! 

How Much Water to Fill My Pool?

Do you ever wonder how many gallons of water it would take to fill a medium size above- or below-ground swimming pool?  If you are similar to the average person, you have likely thought about it once or twice in your lifetime, but probably not much more than that.  Perhaps during one of your famous cannonball dives and several gallons are displaced out of the pool, you may have thought about it, in a competitive way!

The formula is fairly simple, especially if you are familiar with a few Math terms.  Let's look at a couple examples.

1.) How many gallons of water does it take to fill a circular swimming pool that measures 20ft across and has an average water depth of 5ft?
Solution:
* Find the area of the surface, which = Pi (3.14) x Radius squared.
3.14 x 24 x 24 = 576 sq.ft.
* Find the volume of the pool by multiplying the top surface area times the depth of the pool, which is 5 ft.
576 sq.ft  x 5ft = 2880 cubic ft.
* Knowing that there are approximately 7.5 gallons of water per cubic foot, you can multiply the volume times the number of gallons of cubic feet to know how many gallons you need.2880 cubic ft.  x  7.5 gallons per cubic ft. = 21,600 gallons!


Take a look at another example, this time the pool is rectangular shape, and measures 16ft x 36ft and is 5ft deep throughout the pool.  How much water does it take to fill the pool?
Solution:
* Find the area of the surface which is 16 x 36 = 576
* Find the volume of the pool by multiplying the top surface area  x  the depth, which is 576 x 5 = 2880 cubic ft.
* Multiply the volume  x 7.5, which is 2880 x 7.5 = 21.600 gallons!

Did you notice something?  Both pools with different shapes and different dimensions require the same number of gallons to be filled!  Next time you are trying to decide which pool to build at your new home, you will know that there is more than one shape of a pool that can have the same overall dimensions and water usage!

For those of you who want to know how many Liters it would take to fill the pools in our examples, you can simply multiply 21,600 gallons x 3.78 L per gallon.  It would take 81,648 L to fill each pool! 

Happy swimming, everyone! 

No Boss Will Ever Say This!

I saw something today, and it caused me to realize once again why I do what I do, but even more importantly, that I truly enjoy being a Math Teacher and helping others learn.

The sign read, "I need to hire employees who can't do Math--said no boss ever!"

Family and friends, it is never too late to learn new skills, or to brush up on the ones that you need to re-learn.  I have created a new blog today helpmedothemath.blogspot.com which is a blog similar to this one, but you can directly ask me a Math question and receive help.

Receive Change Like a Boss!

Do you go to the market or restaurant, and frequently receive a large number of coins and small bills, but wish you knew the trick to receive larger denominations of both?  I remember as a youth watching my mom and dad make purchases at the market and be able to adjust the amount they received in change, quickly knowing how to make an adjustment to the amount they gave the cashier to pay for their groceries.

In my adult life, I have been instructed by a cashier from time to time that it was too late to make an adjustment to the amount that he/she had expected to receive from me, primarily in the form of a whole dollar bill, perhaps a $5, $10, or $20.  I have been told by cashiers also, that they have been advised to provide the exact amount of change that the 'computer told them to give' and to not deviate from it.  The trick and very first step is being confident and ready and to not show the cashier the amount you are paying until he/she is ready to receive your payment.

Let's take a look at a real-world example and see how you can adjust the amount of change you receive.

You are at Dave's Deli and have purchased a turkey sandwich and a large drink.  The total due is $7.36, and you are paying cash for your purchase.  Let's assume you have a $20 bill, a $10 bill, and (3) $1 bills, and the following coins: (3) Quarters, (1) Dime, and (4) Pennies.  There is more than one solution to the amount that you may give Sondra, the deli's ace cashier. 

Knowing that you don't have the exact change to give, here are some possible scenarios:

a.) Simply give her a $10 bill, forgetting that you have several coins in your pocket, and expect to receive $2.64 in change from Sondra. 
b.) You remember that in addition to the $20, $10 and few $1 bills, you have several coins in your pocket.  You quickly decide to pay her $10.36 and she returns $3 in one dollar bills.
c.) Sondra sees that you have some pennies in your hand, and she asks you to give her one penny in addition to the $10, making the total amount received $10.01.  You are thinking to yourself, "Why is she asking me for an extra penny, when $10 is more than enough to cover your sandwich and drink?"
Sondra, seeing the confused look on your face, quickly explains that instead of returning $2 and $0.64 in coins, by giving her the extra penny, she now owes you change of $2.65 which simplifies the Math, saves her 4 pennies for the next customer, and you don't have to carry around extra coins in your pocket. 
d.) While you were in line to pay for your sandwich and drink, you just remembered that you hadn't purchased gifts for your 5 year old twin nephews' birthday party later in the afternoon.  Not having time to purchase a gift, you decide to give each twin $10 in cash.  How will you handle this transaction?  You're now having one of those "Aha Moments" and know exactly how to masterfully receive the perfect amount of change, to make life simple for Sondra, to decrease the amount of coins in your pocket, and to have enough cash for your birthday gifts. 
* Give Sondra your $20 and (2) $1 in addition to (1) Quarter, (1) Dime, and (1) Penny, which is a total of $22.36.
* Sondra is impressed with your astute Mathematics computation, and she returns a $10 and a $5 bill to you!
You win!  Congratulations!  You have successfully decreased the amount of coins in your pocket, and have made life easy for Sondra, and were able to place $10 in each birthday card for your twin nephews!   

A Little Trick Using the Associative Property of Multiplication

A Little Trick Using Associative Property of Multiplication

Earlier this week, we reviewed the Associative Property of Addition.  The Associative and Commutative Properties were the two properties that I had the most difficult time sorting out, for some reason.

As I teach my students each day, I encourage them to find a special way to memorize certain principles and formulas. 

Let's take a closer look at the Associative Property of Multiplication.  For many of us, we have many activities throughout life and we like to associate with certain friends as we enjoy those activities.  There are those other activities that we enjoy, but we prefer to be with other groups of friends.

The Associative Property works very similarly to our social needs, and let's see how we can apply numbers to gain a better understanding.  This property very simply states that if we are multiplying a few numbers, we can multiply them in groups and it doesn't matter which order we place them, the end result will be the same.

Here's a quick example:
1.)  What is the value of 2 x (3 x 5)?
Solution:
Step 1--Do the parenthesis first, (3 x 5) = 15.
Step 2--Multiply by 2.
Answer: 2 x (3 x 5) = 30.

Now, let's regroup the numbers, using the parentheses around the first two numbers and see if we gain the same result.
2.) What is the value of (2 x 3) x 5?
Solution:
Step 1--Do the parenthesis first, (2 x 3) = 6.
Step 2--Multiply by 5.
Answer: (2 x 3) x 5 = 30.

We can easily create and demonstrate several problems, and the principle remains the same.  As long as we are multiplying all of the numbers, we can reposition and regroup the parenthesis, and the result will be the same! 

Create a few examples on your own, and you'll see how easy it is!  Don't forget to share this great information with a friend!

A Little Trick Using Associative Property of Addition

I remember many years ago trying to memorize the handful of Math Properties, and some of them were easier to learn than others.  The Associative and Commutative Properties were the two properties that I had the most difficult time sorting out, for some reason.

As I teach my students each day, I encourage them to find a special way to memorize certain principles and formulas. 

Let's take a closer look at the Associative Property of Addition.  For many of us, we have many activities throughout life and we like to associate with certain friends as we enjoy those activities.  There are those other activities that we enjoy, but we prefer to be with other groups of friends.

The Associative Property works very similarly to our social needs, and let's see how we can apply numbers to gain a better understanding.  This property very simply states that if we are adding a few numbers, we can add them in groups and it doesn't matter which order we place them, the end result will be the same.

Here's a quick example:
1.)  What is the value of 2 + (3 + 5)?
Solution:
Step 1--Do the parenthesis first, (3 + 5) = 8.
Step 2--Add 2.
Answer: 2 + 8 = 10.

Now, let's regroup the numbers, using the parentheses around the first two numbers and see if we gain the same result.
2.) What is the value of (2 + 3) + 5?
Solution:
Step 1--Do the parenthesis first, (2 + 3) = 5.
Step 2--Add 5.
Answer: 5 + 5 = 10.

We can demonstrate several problems, and the principle remains the same.  As long as we are adding all of the numbers, we can reposition the parenthesis, and the result will be the same! 

Create a few examples on your own, and you'll see how easy it is!  Don't forget to share this great information with a friend!

Which Weighs More? Hint: It's Not the Ton of Bricks! 🤓

Many years ago, a teacher asked us which one weighed more, a ton of bricks or a ton of feathers.  The natural response for most of us was to pick the what seemed like the obvious answer, which was a ton of bricks.  Zooming right past the word 'ton' and focusing on the bricks, we knew, in our finite way of thinking, there was no possible way the feathers could weigh as much, or could they?

Thankfully, we were not on a TV Game Show, and didn't forfeit a life-changing Grand Prize by choosing the wrong answer!

As I reflect on this question and many others throughout my life, it often becomes a great teaching moment, as I once again consider the value of instructing others to think before we speak too quickly.

We know that a ton is a ton, whether we are talking about watermelons, gravel, bricks, or feathers.  The correct answer to this riddle is they weigh the same.

Share this riddle and others with your children to sharpen their ability to think for themselves, and to be courageous and creative in their problem-solving skills.

Have a great day, everyone!
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Is it divisible by 5?

Sometimes you need to know if a number is evenly divisible by another number.  Today's hint is quite simple when determining if a number is divisible by 5.  If the dividend (the number being divided) ends with a 0 or 5, then it is always evenly divisible by 5.

Let's look at some examples.

1.) Is 164 evenly divisible by 5?
Solution:
Step 1--Does the number being divided (164) end with a 0 or 5?  No!
Step 2--It is not evenly divisible by 5.  You can certainly divide it, but you will have a remainder of 4.
The answer is 32.8 or 32 4/5.

2.) Is 90 evenly divisible by 5?
Solution:
Step 1--Does it 90 end with a 0 or 5?  Yes.
Step 2--It is evenly divisible by 5.  For every 100, 5 is divisible 20 times.  Since 90 is 10 less than 100, you can conclude that not only is it evenly divisible, but the quotient (the answer to a division problem) is 2 less than 20, which is 18.

3.) Is 10,495 evenly divisible by 5?
Step 1--Does 10,395 end with a 0 or 5?  Yes.
Step 2--It is evenly divisible by 5.  For every 1,000 being divided, 5 is divisible 200 times.  For 10,000 you can conclude that 10,000 is 10 x 1,000 and the answer to the first part of the solution is 10 x 200 = 2,000.
Step 3--Because we know that we can divide 5 into each 100 exactly 20 times, and 395 is 5 less than 400, we can conclude that 395 divided by 5 is simply 20 x 4 -1 = 79. 
Step 4--Add 2,000 + 79 = 2,079.  

Today's tip is easy to understand, and very practical if you need to divide a number by 5 without a remainder.  Create and practice a few examples on your own and share this helpful tip with a friend! 😄

A Late-Night Laugh! 😂

I've often heard mathematicians proclaim that there are only 10 types of people in this world--those who understand binary, and those who don't!
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Awesome Trick with Percents!

As a child, someone told me that those who are quick with their basic math skills, make successful negotiators.  Whether we realize it or not, we negotiate deals many times throughout our lives.  As I have experienced life, I realize more now than ever before, those words are great advice!
Today's tip relates to learning how to make quick mental calculations of percents that might otherwise require a calculator.

Take a look at this great information!

Suppose you need to calculate 12% of 50.  Of course you can use the decimal form of 12%, which is 0.12, then multiply times 50.  Doing the math, we know the answer is 6.

Here's an alternative way for you to calculate the product of these two numbers much quicker:
Step 1--Instead of calculating 12% of 50, switch the order of the numbers and trade the symbols, also.
Step 2--Calculate 50% of 12.  We all know that 50% of any number is the same as dividing that number by 2.  Very quickly, we know that 50% of 12 is 6.  Same answer, but I'll bet you calculated it much quicker and with great ease!

Consider this real-world example:
Francine's Fashions is celebrating their 48th Anniversary this week, and has reduced all items in the store by 48%.   (To find the savings, you need to know how to find 48% of $25.)
Step 1--Switch the numbers and the signs.  Re-word the question to read, "What is 25% of 48?"
Step 2--Calculate 25% of 48.  We know that 25% of any number is 1/4 of that number.  We also know that we can multiply 48 x 1/4 to get the answer or divide 48/4.
Either way, you can quickly find the answer question without a calculator or paper and pencil!  The answer is 12.

Try it, you'll quickly trade this method for the one you have been using!  Don't forget to share this tip with a family member or friend!  😃

Friday Funny--Gone Without a Tres!

The other day, I watched a magician who was famous for his amazing skills.  He was very confident that he could do something very incredible that night, and he insisted that he could make himself disappear before the count of three, right in front of the audience.
Without hesitation, he began his routine.
"Uno," he said.  Nothing happened.
"Dos," he counted, and poof!  He was gone!
That's right, he disappeared without a tres!
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Math jokes--you should never have to explain them!

Have you ever told a joke, only to receive the response that someone doesn't understand the punchline?  After several embarrassing situations where I have cracked jokes that were truly hilarious, and the response was just the opposite, I have learned to refrain from cracking intellectual jokes until I know the academic understanding of my audience.

When the audience has an appropriate understanding of academic humor, the response you typically receive from them is a joke that they've been dying to share with someone, but just could find the audience to listen.

Go ahead, crack some jokes!  Good, clean, intellectual jokes are the best!  Take time to laugh each day!  😄😂😄😂

Multiplying by 9?

As a young student, I was required to learn the multiplication table beginning with 0 all the way to 12 x 12, which is 144.  As I teach my students each day, I am aware that there are some numbers in the multiplication table that are more difficult for them to learn than others.

Let's take a look at the number 9, and learn a basic trick.

9 x 1  =  09
9 x 2  =  18
9 x 3  =  27
9 x 4  =  36
9 x 5  =  45
9 x 6  =  54
9 x 7  =  63
9 x 8. =  72
9 x 9  =  81
9 x 10 = 90

Notice in the first column, containing all of the numbers highlighted in yellow, we begin counting with 0 and end with 9.  In the second column, highlighted in mauve, we begin with 9 and count down to 0.
Although the 0 in front of the 9 is absent mathematically in the first calculation of 9 x 1, I have included it for illustrative purposes.

That's the trick!  If you know someone who has difficulty mastering the multiplication of 9, please show them this practical tip!


           

Doggone decimal getting you down?

Have you ever needed to multiply two numbers and one of them contained a decimal?  Without a calculator in hand, what was your immediate response? Did you panic? 😬

I have great news! 😀 There is hope for everyone!  Know that our number system is based on a power of 10, and learn a few quick tricks, and you'll never panic again! 👍🏼

Let's take a look at an example, and learn about this nifty trick.

There are 10 children in the Schmidt family, and they have just received news that each of them will receive 1/10 of their grandmother's estate worth $445,000.  What is the value of each child's inheritance?

Solution:

Step 1: Convert 1/10 to a decimal, which is 0.1

Step 2: Multiply $445,000 x 1.  (That is not a typo.  Multiply it times 1.)

Step 3: Apply the decimal to your calculation.  You need to move the place value 1 position to the left only 1 place, since we are multiplying times 0.1.  

The answer is $445,000 x 0.1 which is $44,500.  

Each child will receive $44,500.

We'll look at a few more examples in upcoming posts.  Don't forget to share this tip with a friend!  👌🏼

Here's an average way of doin' it!

Have you ever been asked to find the average of two numbers, and wanted to know a simple way to find the solution without a calculator or paper and pencil?  There is a very easy remedy, and most of us probably never realized how basic this process is.

Let's look at an example or two, and even use a real-world situation to illustrate.

John went bowling last night and wanted to know the average score of his first two games.  He bowled a 242 in his first game, and earned a better score in his 2nd game, tallying an impressive 278!  What was John's average so far?

Solution:
Step 1: Find the difference between the scores of the two games. 278 - 242 = 36.
Step 2: Divide 36 by 2, which is 18.
Step 3: Add 18 to the smaller number, which is 242 + 18 = 260.
All set!  The average of 242 and 278 is 260.

Let's try another one.

Freddy cut grass for 2 of his neighbors today, and was paid $15 and $19.  He wants to know the average earnings per lawn he mows, so he can estimate how many more he needs to cut to save enough money for his new bicycle.

Solution:
Step 1: Find the difference between $15 and $19, which is 4.
Step 2: Divide 4 by 2 = 2
Step 3: Add 2 to the smaller number, which is simply $15 + $2 = $17.
We have solved it rather quickly!  The average of $15 and $19 = $17.

Additional Information:
To find the average of two numbers, you are merely finding the midpoint between those two numbers.
The midpoint between 7 and 9 is 8.

Look how easy this method is!  Create a few more scenarios of your own, and don't forget to share this practical tip with a friend.

Cut one number in 1/2 and double the other for easy multiplication!

Have you wondered if there is a trick to multiplying 2 numbers, especially if one number is much larger than the other?  There is a neat trick that you can use every time, especially if one of the numbers has a factor of 2 multiplied several times.  The only skill you need to know is how to cut one number in 1/2 and double the other number.  You may need to repeat this step several times.

Let's take a quick look at a possible scenario.

Multiply 24 x 125.  No need for paper and pencil or a calculator on this one!  Check it out!
Step 1: Reduce 24 to 12 and Double 125 to 250.
Step 2: Reduce 12 to 6 and Double 250 to 500.
Step 3: Reduce 6 to 3 and Double 500 to 1,000.
We all know that 3 x 1,000 = 3,000.  That's correct!  3 x 1,000 = 24 x 125

Here's another one!

After a great month at the sales office, Sales Manager, Ronald agreed to pay each of his 16 employees a $750 bonus!  Let's see how easy this one will compute.
Step 1: Reduce 16 to 8 and Double $750 to $1,500.
Step 2: Reduce 8 to 4 and Double $1,500 to $3,000.
Step 3: Reduce 4 to 2 and Double $3,000 to $6,000.

Multiply 2 x $6,000 = $12,000.  That's right!  Ronald owes his employees $12,000 and they are so excited! 

Multiply or Divide? Your Choice!

Is it easier for you to multiply or divide?  Your answer to that question may change depending on the facts in the problem you need to solve.

Let's take a look at a couple scenarios, and you select which math operation you prefer to use.

1.) Sharon picked 48 ears of corn from her garden and wants to make enough equal portions so she will have 3 meals for her family.  How many ears of corn will she be able to serve for each meal?
Option 1:
Solve by Division: 48/3 = 16.

Option 2:
Solve by Multiplication: 48 x 1/3 = 16.
* To solve, we multiplied by the reciprocal of 3, which is 1/3, and yields the same results as dividing by 3.

2.)  Leonardo pumped 64 gallons of water into his new swimming pool, which took 4 minutes.  How many gallons of water per minute did he pump?
Option 1:
Solve by Division: 64/4 = 16.

Option 2:
Solve by Multiplication: 64 x 1/4 = 16.
* Once again, we multiplied by the reciprocal instead of dividing.  The reciprocal of 4 is 1/4, and as you can see, it yielded the same results.  Leonard pumped 16 gallons of water into his pool each minute.

Create and solve a few examples on your own, and share this great tip with a friend!  😀

Reciprocals are everywhere! How do you find them?

A reciprocal is indeed very valuable in many math calculations!  Before we can properly use it, however, we must understand what it is.  

A reciprocal is simply 1 divided that number.  For example, the reciprocal of 2 is 1 divided by 2, or 1/2.  The reciprocal of 4 is 1/4.  The reciprocal of 25 is 1/25.  Notice how dividing by 1 to find the reciprocal actually flips that number, so it is now on the bottom.

Negative numbers also have reciprocals and are calculated the same way.  For example, the reciprocal of -6 = -1/6.  The reciprocal of -9 = -1/9.

Every number has a reciprocal except 0.  We know that it is not possible to divide any number by 0.  1/0 is undefined.

In our next post, we will see how reciprocals can be used to simplify our calculations!  😀

Need a pinch? A smidgen? A dash?

What in the world is a pinch?  A dash?  How about a smidgen?  All of these measurements pertain to very small amounts of a fine powder or granular substance.  Dry and liquid substances can vary, but will never differ by more than double, depending on the substance.

Here are the dry measurements of each:
Smidgen = 1/32 teaspoon
Pinch = 1/16 teaspoon
Dash = 1/8 teaspoon
Tad = 1/4 teaspoon

It is understood that the universal measurement for a pinch is simply the amount of a substance that you can pinch between your index finger and your thumb.  Although some people argue that a pinch is not an exact measurement, it has been accepted that the amount of a pinch is equivalent to1/16 teaspoon.

Over the years, I've heard people request a smidgen when ordering a slice of cake or pie.  If they only knew that a smidgen is 1/32nd of a teaspoon, that is hardly enough to taste!  Why bother?! 😂

In some cookbooks, I've seen recipes listing a dash of salt or other seasoning.  Doing some quick math, we can conclude that a dash, 1/8 teaspoon, is equivalent to 2 pinches.

A tad, which is 1/4 teaspoon, would equate to approximately 2 dashes or 4 pinches.  When serving guests at my home, I've heard them ask for a tad of mashed potatoes and gravy.  If they had known that one tad = 1/4 teaspoon, they would likely request a dollop, which is most definitely a more reasonable portion to eat!  A dollop is a scoop or other mass that has no regular shape or form.  I'll take a dollop of ice cream any day!

Would you like your own set of measuring spoons?  You may order them at the link below.
If you are a regular Anazon customer,  please save this link for your other purchases as well.
All prices and privileges are the same as other Amazon links.

www.astore.amazon.com/iwanttolovema-20

I hope you enjoyed this great tip!  Remember, if you come to my home for dinner, I'll gladly serve you more than a smidgen of ice cream for dessert!  I'll certainly top it with more than a tad of chocolate syrup!

Friday Funny! Swiss Flag

People sometimes ask me if I were to move to another country, which one would it be.  As a Math Teacher, this is very easy to answer!  Of course, I choose Switzerland!  The delightful, scenic mountains and scrumptious chocolates are two good reasons, but take a look at that beautiful Swiss flag!  It is definitely a big plus!  😄😄😄😄😄





Happy Friday, everyone!

Multiplying Identical Digits?

Have you been given identical digits to multiply, and wondered if there could be a tip to make it a bit easier?  To clarify, identical digits are digits that repeat, such as 77, or 55, or 888, or 222, or 9999, and the list goes on and on. The tip is to always place the number with the identical digits on the bottom, which will simplify the process.

Let's take a look at 2 methods to multiply such numbers, and see which one you prefer.

Multiply 44 x 72.

Method 1:  (Multiply the numbers in the order they were given to you.)
     44
  x 72
     88
 308  
 3168
Note: In this step, you need to multiply 44 x 2, then multiply 44 x 7.  This is not difficult, but there is a better way, which is shown in Method 2.

Method 2:  (Make 44, the number with the repeating digits, the multiplier, which is on the bottom.)
     72
  x 44
   288
 288  
 3168
Note: In this step, you multiply 72 x 4, which is 288, then you simply write the same number on the next line, because you are multiplying 72 x 4 once again.  This tip becomes extremely beneficial if we were to calculate by hand 569 x 3333 and other such numbers. 

You may not need to use this tip often, but it is certainly a great tip to keep in your mind for those times when you may need it.  I guarantee that you will drastically reduce the time to perform the calculation and also will also reduce your risk of computational errors! 

Try it a few times, and you will see.  To become the expert, show this to a friend! 
 

Take the Grover Cleveland bill, or a Penny Doubled 25 times?

If you were offered one Grover Cleveland bill ($1,000) or the value of an Abraham Lincoln coin (penny) which was doubled 20 times, which one would you choose?






Let's do the math!

Option 1 = $1,000
Option 2 =
$0.01 x 2 = $0.02
$0.02 x 2 = $0.04
$0.04 x 2 = $0.08
$0.08 x 2 = $0.16
$0.16 x 2 = $0.32
$0.32 x 2 = $0.64
$0.64 x 2 = $1.28
$1.28 x 2 = $2.56
$2.56 x 2 = $5.12
$5.12 x 2 = $10.24
After doubling the penny 10 times, it sure does look like Option 1 was the way to go, doesn't it?  Not so quick!  Let's keep going...
$10.24 x 2 = $20.48
$20.48 x 2 = $40.96
$40.96 x 2 = $81.92
$81.92 x 2 = $163.84
$163.84 x 2 = $327.68
$327.68 x 2 = $655.36
$655.36 x 2 = $1,310.72
$1,310.72 x 2 = $2,621.44
$2,621.44 x 2 = $5,242.88
$5,242.88 x 2 = $10,485.76
Sure does prove the value of compounded money!  If you are ever offered these 2 choices, you would be wise to choose Option 2.  After the penny is doubled 17 times, it is worth more than the $1,000 bill by more than $300! 
Just for fun, let's keep going and see if we can break $1M!
$10,485.76 x 2 = $20,971.52
$20,971.52 x 2 = $41,943.04
$41,943.04 x 2 = $83,886.08
$83,886.08 x 2 = $167,772.16
$167,772.16 x 2 = $335,544.32
$335,544.32 x 2 = $671,088.64
$671,088.64 x 2 = $1,342,177.28
$1,342,177.28 x 2 = $2,684,354.56
$2,684,354.56 x 2 = $5,368,709.12
$5,368,709.12 x 2 = $10,737,418.20
That's correct!  A penny doubled 30 times, which is every day for one month, will be worth over $10.7M! 

I learned this tip many years ago in elementary school.  As a young student, we all picked the large bill, and who wouldn't do the same?  Most adults would have chosen the large bill, but it definitely does not outperform the penny which is doubled at least 17 times! 

Enjoy this valuable information, and share it with your family and friends!  They'll be impressed! 

"Are we there yet?"-- A short lesson in ratios

How often are we driving on the interstate highway in our vehicle and have asked ourselves how hours or minutes remain until we reach our destination?  It's a very practical question that we all can solve with great ease if we know how far we've traveled so far and how long it took.

Here's a scenario to consider.

Jim and his wife, Kim, left their home 2 hours ago and have driven 130 miles.  If they continue driving at their current average speed, how long will it take them to drive the remaining 390 miles from Indianapolis to Milwaukee?

Solution:

Setup a ratio and solve.  

2hrs.                 x

------       =     ------

130 mi.         390 mi.      

Cross-multiply 2 x 390  = 780.

Divide 780/130 to calculate the value for x.

780/130 =  6

It will take 6 hrs to drive the remaining 390 miles until they reach their destination and arrive in Milwaukee.  Watch your speed, and have a safe journey, Jim and Kim!  

Math humor--a quick joke for your day!

Students often tell me that my classroom is chilly.  My response to them remains the same each time. With a big smile on my face, I instruct them to stand in the corner where it is 90 degrees!
😂😂😂😂😂😂

Round 'em all...as fast as you can!

In our last tip, we reviewed a very specific example containing only numbers that were just a penny or two below the dollar, and it was very easy to round all numbers up to the nearest whole dollar.  It won't always be so easy, and you may need to combine a couple numbers, or possibly 3 or more numbers prior to rounding 'em up.

Let s look at another example, once again assisting Jim with his trip to the market, and helping him to decide if he has enough money to pay cash for the items in his cart.  He has $25 cash to purchase the following items: 1 box Yummy O's $3.49, 3lb bag of apples $2.59, 5 lb bag of potatoes $3.39, 1 pkg of celery $1.49, 3 boxes of cake mix $1.29 each, 3 cans of soup $1.69 each, 1/2 lb roasted turkey breast from the deli $4.99.
Time to round 'em up!  Does he have enough cash?
$3.49 + $2.59 + 3.39 + $1.49 + $1.29 + $1.29 + $1.29 + $1.69 + $1.69 + $1.69 = ?
Solution:
Step 1: $3.49 + $1.49 = $3.50 + $1.50 = $5.00 (when rounded up).
Step 2: $2.59 + $3.39 = $2.60 + $3.40 = $6.00 (when rounded up).
Step 3: $1.29 + $1.69 = $1.30 + $1.70 = $3.00 (when rounded up).  There are a total of 3 pairs of $1.29 + $1.69, so after the pair is rounded to $3.00, we must multiply x 3 to account for all 6 items.  Step 3 Total = $3.00 x 3 = $9.00.
Step 4: $4.99--round up to $5.00.
Step 5:  Add Steps 1 through 4.  $5 + $6 + $9 + $5 = $25.

Congratulations!  Once again, Jim has achieved a successful trip to the market!  👍🏼
Unfortunately for Jim, however, he doesn't have enough extra money to buy a candy bar to eat on the way home!  Maybe next time, Jim.  😩

What a practical tip once again today!  I know Jim appreciates this information as well!  Don't forget to use this tip each time you shop, and also remember to share this great advice with a friend!  😄

Round 'em up!

Doing quick math in your head doesn't need to be difficult!  In today's world, when you shop for groceries and other items, such as clothing and household goods, the price may end with .95, .97, .98, and commonly .99, which has been used for many years.

Best news of the day if you need to get a quick subtotal for the items you are getting ready to purchase....round 'em up!

Here's a practical example to consider.

Jim went to the store to purchase a few last-minute items to make homemade pizza for his family, and wants to know if the money in his pocket, $10, will be enough to pay for the items.  Here are the items: pizza sauce $0.99, sausage $3.97, cheese $2.99, and mushrooms $1.98.

Solution:  Round each item up to the nearest whole dollar, since they are all have ending digits more than $.90.
Pizza Sauce = $1.00
Sausage = $4.00
Cheese = $3.00
Mushrooms = $2.00
We know that 1 + 4 + 3 + 2 = 10.  Because each item was rounded up, and there is no sales tax for grocery sales, we know that Jim has enough money.  By knowing how to quickly round 'em up, Jim knew that he had no extra money to purchase a small candy bar to eat on the way home.  Maybe next time!

Don't forget to use this great tip, and share it with a friend!  😃

What was today? 4/8/16

In the past month, we have celebrated National Pi Day (3/14/16) and National Square Root Day earlier this week (4/4/16).  What was today?  Did anyone celebrate its significance?  Days that had similar mathematical significance that should have been worthy of celebration, or at least acknowledgment were 1/2/04, 2/4/08, 3/6/12, and now 4/8/16.  

Do you see the pattern?  Each successive digit is 2x the previous digit.  We won't have another similar day until 5/10/20, then 6/12/24, 7/14/28, 8/16/32, and so forth.  

We have 1493 days until next time, 5/10/20.  It sounds like we have plenty of time to name this day, and to also print t-shirts and do what we can to increase awareness of this soon-to-be special day worthy of mathematical awareness. 

Sounds like a great idea to me!  😃  

Cut it in half first!

My students are always looking for the easiest way to multiply numbers, especially since I don't allow them to depend on calculators.  Recently while learning how to find the area of triangles, I taught them to take advantage of the 1/2 in the formula, A = 1/2 x b x h.

Here's an example to consider.

Find the area of a triangle that has a base = 7, height = 18.  

Solution: A = 1/2 x b x h.  Plugging in the numbers, we see that A = 1/2 x 7 x 18.  Basic properties of math allow us to multiply the numbers in any order. 

Step 1: Multiply 18 x 1/2, or simply divide 18 by 2, which is 9.

Step 2:  Multiply 9 x 7, which = 63.

Done!  That was much easier than multiplying 7 x 18, then taking that product x 1/2!  Most people don't readily know that 7 x 18 = 126.  On the other hand, because we have learned our multiplication tables up to 10 x 10, we know that 7 x 9 = 63.

Let's try one more.

What is the product of 1/2 x 10 x 32?

Solution:  We have a choice to cut 10 or 32 in half, before multiplying the remaining number.  Which do you prefer?  Let's cut the 32 in half, so we can multiply the first product x 10.

Step 1:  Multiply 32 x 1/2 = 16.

Step 2: Multiply 16 x 10, which = 160.  All set!  We know that 1/2 x 10 x 32 = 160.

That was much easier than multiplying 1/2 x 10 = 5, then multiplying 5 x 32.

Remember that multiplying any number x 1/2 gives the same result as dividing that same number by 2..  There are many examples other than the finding area of triangles where you can use this helpful tip!  

Double it, and double it again!

Multiplying a number times 4 in your head, but just can't do it quickly?  Most everyone can double a number (multiply it times 2) without paper and pencil, so here's the tip.  We know that 2 x 2 = 4, so you can quickly and easily double it, and double it again instead of multiplying by 4.

Here's an example.

What is 23 x 4?
Solution:  23 x 2 = 46, and multiply x 2 again, which = 92.  Done!

Let's try another one.
What is 214 x 4?
Solution:  214 x 2 = 428, and multiply x 2 again, we know that 428 x 2 = 856.  214 x 4 = 856.

What a simple, but neat little trick to simplify a calculation!  Create a few examples on your own, and remember to share this with a friend.  😀

Simply add a zero!

Need to multiply a whole number or integer by 10?  It doesn't get much easier than this!  Simply place a 0 at the end of that number.

Here are a few examples to consider.

What is the product of 12 x 10?
Solution: Place a zero at the end of 12.  120 is our answer.

Let's look at a practical real-world problem to solve.
For the next 10 days, Ashley will make $25 per day helping her mother with household chores.  How much will she make?
Solution: Place a 0 at the end of 25.  Ashley will make $250.

This process also works for Integers, which contain negative numbers.

Here's another practical problem to solve.

On his way to the office each day, Charlie spends exactly $3 at the local convenience store buying a fountain drink and a bag of chips.  After 10 visits to the store, how much did he spend?
Solution:  Spending money is a reduction in his account.  We must multiply -$3 x 10 to solve our problem.  We know that -3 x 10 = -30.  Charlie spent $30.

Create your own example, and share this practical tip with a friend!

Is it divisible by 4?

Here's another number that boasts a little trick!  How do you know if a number is divisible by 4?  There are two simple rules to follow.  If the number being divided ends with 2 zeros, it is divisible by 4.  Also, if the last 2 digits of the number being divided are divisible by 4, then the number being divided is also divisible by 4.  It is important to understand that other numbers are divisible by 4 as well, but these two tricks are additional ways to quickly know the divisibility of 4.

Let's try a few examples.  Is 700 divisible by 4?
Solution: The last two digits of 700 are 00, which means that 4 evenly divides into 700.  We also know that 100/4 = 25 and 700 is a multiple of 100, which helps us to not only know that 4 is divisible, but we can quickly multiply 25 x 7 to get our answer, 175.

Here's another one to try.  Is 563,724 divisible by 4?
Solution:  The last 2 digits of 563,724 are 24.  We know that 24 is evenly divisible by 4.  We conclude that 563,724 can be evenly divided by 4 and will not have a remainder.  Doing the calculation, we find the solution 563,724/4 = 140,931.

It works every time!  Do a few more of these and you will be the expert!  Share this neat little tip with a friend!

Happy Square Root Day!

Did you know that today is National Square Root Day?  Today is 4/4/16.  The square root of 16 is 4.
We've only had 3 other square root days since 2000.  We've celebrated this day on 1/1/01, and 2/2/04, and 3/3/09.
The next square root day won't be until 5/5/25, which is more than 9 years from now!  I hope you had a great day celebrating!
Tomorrow's tip will be dedicated to the number 4.  Join us for some great information!

Is it divisible by 2?

When we divide numbers, we often need to know if they are evenly divisible by other numbers.  It is very helpful if we know if they can be evenly divided by another number without a remainder.
If we need to know whether a number is divisible by 2, the number being divided must end with a 2, 4, 6, 8, or 0.  Let's take a look at a couple examples.

Is 24 divisible by 2?
Solution:  The ending digit in 24 is a 4, and it is definitely divisible by 2.

Is 347 divisible by 2?
Solution:  The last digit is 7, which is not 2, 4, 6, 8, or 0.  We can quickly conclude that 347 is not divisible by 7.

Today's tip is something that I learned at a very young age, but I know there are many people who are not aware of this great information.  Use it, and explain this tip to a friend today.

Treat it like money!

We have already learned a few tips on how to quickly add numbers.  Here is another great tip to use, especially when adding 3-digit or 4-digit numbers!

Here is our first example.
What is the sum of 413 + 769?  If we treat it like money, we are breaking it into two separate usable parts.  Rewrite it and solve it as the sum of $4.13 + $7.69.
Step 1--Add the numbers to the left of the decimal, or what we think of as the number of dollars.  We know that 7 + 4 = 11.
Step 2--Add the numbers to the right of the decimal, or more simply, the value of the cents or coins.  13 + 69 = 82.
Step 3--Combine the answers from Step 1 and Step 2.  The solution is $11.82, but since the question was not asking for dollars and cents, we must remove the decimal.  413 + 769 = 1182.
Done!

Let's try another one.
Bob is donating bottled waters for 2 upcoming charity events.  Each person will receive one bottle of water at the entrance.  Last year the attendance at each event was 1142 and 1217.  If the attendance this year is expected to be the same as last year, how many bottles should Bob purchase?

Solution:
Rewrite the problem as $11.42 + $12.17.
Step 1--Add 11 + 12, which is 23.
Step 2--Add  42 + 17, which is 59.
Step 3--Combine the answers for our solution.  $11.42 + $12.17 = $23.59, but we must remove the decimal and $.  1142 + 1217 = 2359!

Cases of bottled waters commonly have 24 bottles.  If Bob wants to round the amount to 2400, he quickly knows that he should buy 100 cases.

Practice a few more of your own examples, and remember to teach this practical tip to a friend!

Adding two numbers? Break them into usable parts.

Have you ever needed to add two numbers, but for some reason you were not able to add them in your head?  Today's tip will show us how we can break apart two numbers into more user-friendly parts so we can quickly add them with great ease!

Let's look at our first example.  

You are at the dealership getting your oil changed and the technician reminded you that it is time to have tires rotated.  The oil change is $37 and if they rotate your tires, it will cost an additional $29.  How much will you owe if they do both jobs?  

Solution:  

Step 1--Break down $37 to $30 + $7 and $29 to $20 + $9.  

Step 2--Add $30 + $20 = $50.  

Step 3--Add 7 + $9 = $16. 

Step 4--Add $50 + $16 = $66.

Done!  😃

Heres another one to try.

What is 68 + 38?

Step 1--Break down 68 to 60 + 8 and 38 to 30 + 8.

Step 2--Add 60 + 30 = 90.

Step 3--Add 8 + 8 = 16.

Step 4--Add 90 + 16 = 106.

As we can see, this is a very practical way to add two numbers.  Try a few on your own, and remember to show this tip to a friend!  

Use multiplication to add numbers

What an interesting thought, isn't it?  How do you use multiplication to simplify addition of several numbers?  Let's take a look at some practical examples that will clarify why it is beneficial to multiply while adding.

Suppose you are given the following numbers to add:
7 + 5 + 4 + 7 + 6 + 7.  There is certainly nothing wrong with adding all 6 numbers in the order that were listed.  On the other hand, if we multiply 3 x 7 = 21, we have quickly added half of the list of numbers that were given.  To add the remaining numbers, 5 + 4 + 6 = 15.  We know that 21 + 15 = 36.

Here's a practical example to consider.
Betty bought 20 pairs of socks for her grandchildren, and they were on sale for $2 per pair.  How much did she spend?
Solution:  Is it easier to add $2 twenty times, or use multiplication?  Let's use multiplication!  We quickly know that 20 x 2 = 40.  Betty spent $40 (before tax) on her purchase today.

As we can see, there is more than one way to add a list of numbers.  Use this great tip to simplify your life, and remember to share it with a friend!

Adding a series of sequential numbers...the easy way!

Have you ever had to add a series of sequential numbers?  For example, if you need to add the numbers 1 through 10.  Can you do it?  Can you do it without adding 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9? 
Let's solve this one with today's tip. 
Step 1: Add the first and last number in the sequence.  1 + 9 = 10.
Step 2: Divide that total of Step 1 by 2.  10/2 = 5.
Step 3: Multiply the answer in Step 2 times the number of numbers in the sequence.  In this example, it is 9.  9 x 5 = 45.
You solved it!  The total of 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45.

Here's another one to try.
What is the total of the sequence of numbers from 10 to 14?
Step 1: Add the first and last number in the sequence.  10 + 14 = 24.
Step 2: Divide the total of Step 1 by 2.  24/2 = 12.
Step 3: Multiply the answer in Step 2 times the number of number in the sequence.  12 x 5 = 60.
You're right!  The total of 10 + 11 + 12 + 13+ 14 = 60!

This practical tip works every time, and will simplify your life, especially if you have a long list of sequential numbers to add.  Try it, and share this with a friend! 

Adding numbers? Regroup them for quicker calculations

Have you ever been given several numbers to add and didn't know where to begin?  Did you think there must be a tip or other shortcut, but somehow in the busyness of life you have somehow forgotten it?  For some of us, we struggle with adding numbers without a calculator, and especially without using paper and a pencil.
Here is a practical tip that just may simplify your life at the perfect time!

When adding numbers, group them so they can be quickly added to other numbers in your list.

Here's an example of grouping numbers.
You are given the following numbers to add, and have only 3 to 5 seconds to add them.
Find the sum of 34 + 63 + 16 + 27.
Solution: Group two pairs of numbers (34 + 16) and (63 + 27).
34 + 16 = 50 and 63 + 27 = 90.
Add the sum of both groups, and you have quickly concluded the solution is 140.

Let's try another one.
Find the sum of 12 + 91 + 9.
In this scenario, there is only one group that needs to be formed, which is (91 + 9).  You can see very quickly that 100 + 12 = 112.

I know you will find this tip to be practical, and can find many ways to simplify your life by utilizing this short-cut.  Please remember to share this with a co-worker or friend!

Shall I multiply or divide?

Being a full-time teacher, I instruct my students to become better problem solvers.  When offering assistance, my question to them always inquires whether they need to add, subtract, multiply, or divide.  Given a choice to multiply or divide, which one will you choose?

Let's take a look at a couple examples, then you decide.
Mr. Johnson is cutting a 48 inch board into 4 equal pieces.  How long will each board be when he is done?
Solution: Your choices are to multiply or divide.  To solve it using division, setup the problem as 48/4 = 12.  You can also multiply 48 x 1/4, which is also 12.  Which math operation do you prefer to use?

Here's another example.
There are 150 students who are attending a field trip today to the local zoo.  There are 3 buses taking the students.  How many students can ride on each bus?
Solution: Using division, the solution is 150/3 = 50.  To solve the problem using multiplication, you can multiply 150 x 1/3, which equals 50.

Math often allows flexibility to solve problems.  Sometimes you may prefer to multiply, other times you may divide. 

Don't forget to share today's tip with a friend!
  

Multiplication of two numbers made easy

Have you been at the market, or home improvement center, or perhaps were in the process of purchasing tickets for the upcoming big game, and you were confronted with another dreaded multiplication problem?  You have no calculator nearby, and now you must make a quick decision whether or not to make the purchase.  Relax, take a deep breath, and learn a new tip today that will simplify your life and increase your confidence!
Here is a scenario for our consideration.  The cost of each concert ticket is $28 and you need to purchase 5 tickets to take your family on Friday evening.  What is the total cost before taxes and other fees?
Reduce $28 to $14, but at the same time, we must double the 5 to make it 10.  Instead of multiplying 5 x 28 in our head, we can work with 10 x 14.  Given both scenarios, we can choose the 2nd alternative instead of guessing and hoping we are correct, or perhaps not performing the calculation, and ultimately not having enough money to make the purchase.  We conclude that 28 x 5 = 10 x 14, which is 140. 
Let's try another one.  To paint your new office, you need to purchase 12 gallons that are $15 per gallon on sale.  What is the total cost of the paint before sales tax?
Some of us may already know that 12 x 15 = 180.  For the rest of us, let us reduce 12 to 6, which is cutting it in half, and also doubling 15 to 30.  We now have the choice to multiply 12 x 15, or 6 x 30.  We all know that 6 x 3 = 18, therefore 6 x 30 = 180.
Try this new tip today and share this great information with a friend!  They will certainly appreciate you! 

  

Simplifying numbers for easy subtraction calculations

Have you needed to add or subtract two numbers very quickly, and didn't have a calculator nearby, or felt too tired to compute the sum or difference in your head?  There are many techniques that can be used that are especially helpful for those who need a helping hand!

Let's work a couple examples.
What is the solution of 147 - 93?  There are a few people that can quickly compute this within a second or two.  The easiest way to simplify this calculation is to add 7 to 93, which bumps it to 100.   If we add 7 to the one number, we must add 7 to the other number, increasing it from 147 to 154.
Now, what is the difference of 154 + 100?  That's right!  It is 54!  What is 147 - 93?  It is also 54, because we have maintained the same relationship between both numbers by adding the same number!

Here's another one to try.  What is 83 - 36?  You can increase 36 to 40 by adding 4, and also increase 83 by 4, which is 87.  The difference is 47.

Many of us refrain from subtracting 2-digit numbers in our head, because we don't have experience, or we prefer to write it on paper where we can see it, but also feel more confident that we won't make a mistake when we can see it in writing.
Practice this tip a few times, and don't forget to show this to a friend or co-worker.

Simplifying numbers for easy addition calculations

Have you needed to add or subtract two numbers very quickly, and didn't have a calculator nearby, or felt too tired to compute the sum or difference in your head?  There are many techniques that can be used that are especially helpful for those who need a helping hand!

Let's work a couple examples.
What is the sum of 121 + 98?  There are a few people that can quickly compute this within a second or two.  The easiest way to simplify this calculation is to add 2 to 98, which bumps it to 100.  If we add 2 to the one number, we must subtract 2 from the other number, decreasing it from 121 to 119.
Now, what is the sum of 119 + 100?  That's right!  It is 219.

Here's another one to try.  What is the sum of 77 + 36?  You can increase 77 to 80 by adding 3, and also decrease 36 by 3, which is 33.  The sum is 113.

We could have easily adjusted the 36 to 40 by adding 4, and decreasing 77 by 4 to 73.  40 + 73 = 113.

Many of us refrain from adding numbers in our head, because we don't have experience, or we prefer to write it on paper where we can see it, but also feel more confident that we won't make a mistake.
This is just one of many tips and shortcuts that I will share with you as you continue in your quest to love math!

How do you square 2-digit numbers that end with a 0?

Of all the 2-digit numbers that you may need to square, this is certainly the easiest!
Let's try one!  How quickly can you square 40?
To multiply 40 x 40, multiply 4 x 4, then place 2 zeros after the product of 4 x 4.  Very simply, 40 x 40 = 1600.
Here is another one.  What is 70 x 70?  7 x 7 = 49.  Insert both zeros after 49.  70 x 70 = 4900.
The squaring of 2-digit numbers that end in 0 may be a calculation that you will use more often than squaring other numbers.
Use this tip often, and remember to share this with a friend!

How do you square 2-digit numbers that end with a 1?

For the next several days, we will see how to square 2-digit numbers ending in 1 to 9, using quick, easy tips and tricks.  How do you square a number that ends with a 1?  As a quick review of vocabulary, to square a number simply means to multiply a number by itself.  Squaring 21 means to multiply 21 x 21, and squaring 61 is multiplying 61 x 61.
What is the quickest way to square 2 numbers that end with a 1?  Let's try 31 x 31.
Step 1, reduce the number to the nearest 10, which means that we will subtract 1 from 31 to make it 30.
Step 2, multiply 30 x 30, which is 900.
Step 3, add 30 + 30 to 900, which is 960.
Step 4, add 1, which is 961.
Done!

Let's try another one!  What is the square of 51?
Step 1, reduce 51 to 50.
Step 2, multiply 50 x 50, which is 2500.
Step 3, add 50 + 50 to 2500, which is 2600.
Step 4, add 1, which is 2601.
That's it!  😃
It is a very simple process, and I know you will gain much confidence as you practice a few of these. Don't forget to share this tip with a friend!

Squaring 2-digit numbers--Why is this important?

What is the importance of knowing how to square two numbers?  Unless you are a full-time student, or an educator, you may be wondering why it is beneficial to know this information.  Certainly anyone working in landscaping, engineering, and construction-related fields knows the value of computing numbers quickly.  If you are a do-it-yourself type of person and own a home, there are many practical applications around the home, such as painting, flooring, and other remodeling jobs where quick calculations can save you time and money.

If you are installing ceramic tiles or hardwood flooring in your newly-remodeled kitchen or bathroom, and you know the dimensions of the room, you can purchase the right amount of supplies on your first trip to the home improvement store.  How unfortunate it would be if you miscalculated and purchased the wrong amount of a certain tile that was on clearance, and when you completed your job a few weeks later, you were unable to find additional matching tiles. 

Follow my blog each day as we continue to add tips and tricks to use Math in a practical way.  Don't forget to share with a friend!

What is the sale price?

How often do you shop in a retail store and see sale signs everywhere, but have no idea how 30% off equates to dollars and cents?

There is more than one way to determine the net amount you will pay after the savings are deducted from the original price.  Savings of 30%, simply means that you are paying 70% of the retail price.

Think about it for a moment.  100% - 30% = 70%.  Instead of calculating the savings, then deducting that amount from the retail price, you can multiply the retail price by 70%, and you will quickly know the sale price.

One more thing you need to know is 70% has the same value as 0.70, or 0.7 in simplest decimal form.  We know this, because 70% is 70/100, which is 0.70.

Let's try one.  A shirt has a retail price of $29.99 and it is on sale for 30% off.  How much is the sale price?  Prior to doing the calculation, you should round up the price from $29.99 to $30 to simplify the calculation.  Very simply, $30 x 70% = 30 x .70 = $21.

Try another one.  The hat is $20 and is on sale for 25% off.  What is the sale price?  Converting 25% to a decimal = 0.25, which is also 1/4.  Because we readily know that 1/4 of $20 = $5, we can subtract $5 from $20, which is $15.  For many of us, it may have been easier to calculate the savings, then deduct the amount instead of multiplying $20 x .75 like we did in the first example.

Enjoy the savings, but more importantly, enjoy these new tips and share them with someone you love!

How do you know if a number is divisible by 9?

Do you ever wonder if a number is divisible by other numbers?  How do you know if a number is divisible by 9?  Like the Divisibility Rule for 3 that we learned earlier this week, simply add the digits of a number, and if the sum of those digits is divisible by 9, the number is divisible by 9 as well. 
Is 792 divisible by 9?  The sum of the digits 7 + 9 + 2 = 18.  18 is divisible by 9, and you can conclude that 792 is also divisible by 9.
Let's try another one that you know is divisible by 9.  Is 99 divisible by 9?  The sum of the digits 9 + 9 = 18, and 18 is divisible by 9, therefore 99 is divisible by 9.  
Another neat fact about the Divisibility of 9, you can accurately conclude that when a number is divisible by 9, it is also divisible by 3, because 3 is a factor of 9.  Try this simple rule each and every time you need to divide a number by three or nine, and it works like magic!
Practice a few more examples on your own, and share this tip with a friend!

Happy Pi Day, Everyone!

Today is Pi Day!  How will you celebrate?

Subtraction of numbers made easy!

Have you ever wondered if it is possible to subtract a number without the messy borrowing and regrouping of values?  We all know that traditional methods of subtraction can be complicated, and therefore lead to possible mistakes.

Here is a quick glimpse of the traditional method of subtraction.  Notice that you must borrow a 1 from 70, making the 0 a 10, which then allows you to subtract 6 from 10, resulting in a 4.  The next step requires no regrouping, and most of us know fairly quickly that 69-53=16.  We conclude that 700-536=164, which is correct.

69 1

 70^0

-53 6

 164

Let's try this again, but using a simple trick.  Reduce both numbers by 1 before applying the operation of subtraction.  

 699

-535

 164

Notice that no borrowing nor regrouping of numbers was required to perform the operation, yet we have the same answer!  By reducing both numbers by 1, we didn't change the relationship between those numbers, and our answer is the same.  

Time for one more?

 303

-169

   ?

To solve this problem with great ease, reduce both numbers by 4.

 299

-165

 134

Try this trick, and share it with others!  

How do you know if a number is divisible by 3?

Do you ever wonder if a number is divisible by other numbers?  How do you know if a number is divisible by 3?  Simply add the digits of a number, and if the sum of those digits is divisible by 3, the number is divisible by 3 as well.
Is 891 divisible by 3?  The sum of the digits 8 + 9 + 1 = 18.  18 is divisible by 3, and you can conclude that 891 is divisible by 3.
Let's try another one that you know is divisible by 3.  Is 66 divisible by 3?  The sum of the digits 6 + 6 = 12, and 12 is divisible by 3, therefore 66 is divisible by 3.
Try this simple rule each and every time you need to divide a number by three, and it works like magic!

How to square 2-digit numbers ending in a 5

Looking for a quick, easy way to multiply 2 identical 2-digit numbers that end with a 5?
How do you multiply 25 x 25?  Very simply, multiply 2 x (2+1), then place a 25 on the end.  Solution = 2 x 3= 6, then place 25 after the 6.  25 x 25 = 625.
Let's try one more.  What is 65 x 65?  Multiply 6 x (6+1), then place a 25 on the end.  65 x 65 = 4,225.
This tip works well squaring all 2-digit numbers ending in a 5 from 15 x 15 to 95 x 95.
Practice a few, then you'll be one step closer to enjoying Math!
Share this tip with someone today!

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Welcome to I Want to Love Math!  I will share daily tips, tricks, and ideas to entice you to love Math.