Multiplication Tips

8/4/2019 Multiplication Tips

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Multiplication Tips

Multiplying by five

Jenny Logwood writes: Here is an easy way to find an answer to a 5times question.

If you are multiplying 5 times an even number: halve the number you aremultiplying by and place a zero after the number. Example: 5 6, half

of6 is 3, add a zero for an answer of 30. Another example: 5 8, half of8

is 4, add a zero for an answer of 40.

If you are multiplying 5 times an odd number: subtract one from the

number you are multiplying, then halve that number and place a 5 afterthe resulting number. Example: 5 7: -1 from 7 is 6, half of 6 is

3, place a 5 at the end of the resulting number to produce the number

35. Another example:5 3: -1 from 3 is 2, half of 2 is 1, place a 5 at theend of this number toproduce 15.

Doug Elliott adds: To square a number that ends in 5, multiply the tensdigit by (itself+1), then append 25. For example: to calculate 25

25, first do 2 3 = 6, then append 25 to this result; the answer is

625. Other examples: 55 x 55; 5 6 = 30, answer is 3025. You can also

square three digit numbers this way, by starting with the the first twodigits:995 x 995; 99 100 = 9900, answer is 990025.

Multiplying by nine

Diana Grinwis says: To multiply by nine on your fingers, hold up tenfingers - if the problem is 9 8 you just put down your 8 finger andthere's your answer: 72. (If the problem is 9 7 just put down your 7

finger: 63.)

Laurie Stryker explains it this way: When you are multiplying by 9, onyour fingers (starting with your thumb) count the number you are

multiplying by and hold down that finger. The number of fingers before

the finger held down is the first digit of the answer and the number of

finger after the finger held down is the second digit of the answer.

Example: 2 9. your index finder is held down, your thumb is before,representing 1, and there are eight fingers after your index finger,

representing 18.

Polly Norris suggests: When you multiply a number times 9, count backone from that number to get the beginning of your product. (5 9: one


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less than 5 is 4).

To get the rest of your answer, just think of the add fact families for 9:

1 + 8 = 9 2 + 7 = 9 3 + 6 = 9 4 + 5 = 9

8 + 1 = 9 7 + 2 = 9 6 + 3 = 9 5 + 4 = 9

5 9 = 4_. Just think to yourself: 4 + _ = 9 because the digits in your

product always add up to 9 when one of the factors is 9. Therefore,4 + 5 =9 and your answer is 45! I use this method to teach the "nines" in

multiplication to my third graders and they learn them in one lesson!

Tamzo explains this a little differently:

1. Take the number you are multiplying 9 by and subtract one. Thatnumber is the first number in the solution.

2. Then subtract that number from nine. That number is the secondnumber of the solution.Examples:

4 * 9 = 36

1. 4-1=32. 9-3=63. solution = 36

8 * 9 = 72

4. 8-1=75. 9-7=26. solution = 72

5 * 9 = 45

7. 5-1=48. 9-4=59. solution = 45

Sergey writes in: Take the one-digit number you are multipling by nine,and insert a zero to its right. Then subtract the original number from it.For example: if the problem is 9 * 6, insert a zero to the right of the six,

then subtract six:

9 * 6 = 60 - 6 = 54

Multiplying a 2-digit number by 11


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A tip sent in by Bill Eldridge: Simply add the first and second digits andplace the result between them.

Here's an example using 24 as the 2-digit number to be multiplied by 11:2

+ 4 = 6 so 24 11 = 264.

This can be done using any 2-digit number. (If the sum is 10 or greater,

don't forget to carry the one.)

Multiplying any number by 11

Lonnie Dennis II writes in:Let's say, for example, you wanted to multiply 54321 by 11. First, let'slook at the problem the long way...

54321

x 11

54321

+ 543210

= 597531

Now let's look at the easy way...

11 54321

= 5 4+5 4+3 3+2 2+1 1

= 597531

Do you see the pattern? In a way, you're simply adding the digit to

whatever comes before it.

But you must work from right to left. The reason I work from right to left

is that if the numbers, when added together, sum to more than 9, then you

have something to carry over.

Let's look at another example...

11 9527136

Well, we know that 6 will be the last number in the answer. So the answer


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now is

???????6.

Calculate the tens place: 6+3=9, so now we know that the product has the

form

??????96.

3+1=4, so now we know that the product has the form

?????496.

1+7=8, so

????8496.

7+2=9, so

???98496.

2+5=7, so

??798496.

5+9=14.

Here's where carrying digits comes in: we fill in the hundred thousands

place with the ones digit of the sum 5+9, and our product has the form

?4798496.

We will carry the extra 10 over to the next (and final) place.

9+0=9, but we need to add the one carried from the previous sum:

9+0+1=10.

So the product is 104798496.

Multiplying by thirteen

Fourth grader Mariam Labib has a trick for multiplication by 13.Put the tens digit on the left, the unit number on the right, add them up

together in the middle. Then add double the number to the previous result.

For example: 13 22


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Step 1: (2 100) + 2 + [(2 + 2) 10] = 242.Step 2: 22 2 = 44.

Answer: 242 + 44 = 286.

If the two digits sum to more than ten, then you carry the one to add it to

the number on the left and continue.

For example: 13 65

Step 1: (6 100) + 5 + [(6 + 5) 10] = 715.

Step 2: 65 2 = 130.Answer: 715 + 130 = 845.

Multiplying by sixteen

Ibrahim Labib offers a quick way to find an answer when multiplying by16.

First, multiply the number in question by 10. Then multiply half the

number by 10. Then add those two results together with the number itselfto get your final answer.

For example: 16 24

Step 1: 24 10 = 240

Step 2: (24 1/2) 10 = 12 10 = 120

Step 3: add steps 1 and 2 and the number = 240 + 120 + 24 = 384

Multiply Up to 20X20 In Your Head

In just FIVE minutes you should learn to quickly multiply up to 20x20 in your

head. With this trick, you will be able to multiply any two numbers from 11 to 19 in

your head quickly, without the use of a calculator.

I will assume that you know your multiplication table reasonably well up to 10x10.

Try this:

Take 15 x 13 for an example. Always place the larger number of the two on top in your mind. Then draw the shape of Africa mentally so it covers the 15 and the 3 from the

13 below. Those covered numbers are all you need.


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First add 15 + 3 = 18 Add a zero behind it (multiply by 10) to get 180. Multiply the covered lower 3 x the single digit above it the "5" (3x5= 15) Add 180 + 15 = 195.

That is It! Wasn't that easy? Practice it on paper first!

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Want to Learn More?

The one book I recommend

May be out of print

"Super Math-E-Magics"

by V.A. Stephen Lenaghan

It may be available from Amazon.com or one of the other online sellers of used

books

The 11 Rule

You likely all know the 10 rule (to multiply by 10, just add a 0 behind the number)

but do you know the 11 rule? It is as easy! You should be able to do this one in you

head for any two digit number. Practice it on paper first!

To multiply any two digit number by 11:

For this example we will use 54. Separate the two digits in you mind (5__4). Notice the hole between them! Add the 5 and the 4 together (5+4=9)
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Put the resulting 9 in the hole 594. That's it! 11 x 54=594The only thing tricky to remember is that if the result of the addition is greater

than 9, you only put the "ones" digit in the hole and carry the "tens" digit from

the addition. For example 11 x 57 ... 5__7 ... 5+7=12 ... put the 2 in the hole and

add the 1 from the 12 to the 5 in to get 6 for a result of 627 ... 11 x 57 = 627Practice it on paper first!


Finger Math: 9X Rule

To multiply by 9,try this:

(1) Spread your two hands out and place them on a desk or table in front of you.

(2) To multiply by 3, fold down the 3rd finger from the left. To multiply by 4, it

would be the 4th finger and so on.

(3) the answer is 27 ... READ it from the two fingers on the left of the folded down

finger and the 7 fingers on the right of it.

This works for anything up to 9x10!


Square a 2 Digit Number Ending in 5
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For this example we will use 25

Take the "tens" part of the number (the 2 and add 1)=3 Multiply the original "tens" part of the number by the new number (2x3) Take the result (2x3=6) and put 25 behind it. Result the answer 625.

Try a few more 75 squared ... = 7x8=56 ... put 25 behind it is 5625.

55 squared = 5x6=30 ... put 25 behind it ... is 3025. Another easy one! Practice it

on paper first!


Square 2 Digit Number: UP-DOWN Method

Square a 2 Digit Number, for this example 37:

Look for the nearest 10 boundary In this case up 3 from 37 to 40. Since you went UP 3 to 40 go DOWN 3 from 37 to 34. Now mentally multiply 34x40 The way I do it is 34x10=340; Double it mentally to 680 Double it again mentally to 1360 This 1360 is the FIRST interim answer. 37 is "3" away from the 10 boundary 40. Square this "3" distance from 10 boundary. 3x3=9 which is the SECOND interim answer. Add the two interim answers to get the final answer. Answer: 1360 + 9 = 1369

With practice this can easily be done in your head.

Thanks To Ryan

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you can't add to its "neighbor" so just write down 6 below the 6 in the units

col.

For the "tens" place, add the 3 to the its "neighbor" (the 6). Write theanswer: 9 below the 3.

For the "hundreds" place, add the 2 to the its "neighbor" (the 3). Write theanswer: 5 below the 2.

For the "thousands" place, add the 1 to the its "neighbor" (the 2). Write theanswer: 3 below the 1.

For the "ten-thousands" place, add the 5 to the its "neighbor" (the 1). Writethe answer: 6 below the 5.

For the "hundred-thousands" place, add the 0 to the its "neighbor" (the 5).Write the answer: 5 below the 0.

That's it ... 11 X 051236 = 563596

Practice it on paper first!

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Multiplication Tips