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.
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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!