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!