## Calculation Tips & Tricks

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## Multiplication Tips

Multiplying by five

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

If you are multiplying 5 times an even number: halve the number you are multiplying by and place a zero after the number. Example: 5 × 6, half of 6 is 3, add a zero for an answer of 30. Another example: 5 × 8, half of 8 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 after the 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 the end of this number to produce 15.

• Doug Elliott adds: To square a number that ends in 5, multiply the tens digit 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 two digits: 995 x 995; 99 × 100 = 9900, answer is 990025.
Multiplying by nine

• Diana Grinwis says: To multiply by nine on your fingers, hold up ten fingers - if the problem is 9 × 8 you just put down your 8 finger and there'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, on your 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 back one from that number to get the beginning of your product. (5 × 9: one less than 5 is 4).

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. That number is the first number in the solution.
2. Then subtract that number from nine. That number is the second number of the solution.

Examples:

4 * 9 = 36
1. 4-1=3
2. 9-3=6
3. solution = 36

8 * 9 = 72

1. 8-1=7
2. 9-7=2
3. solution = 72

5 * 9 = 45

1. 5-1=4
2. 9-4=5
3. 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

• A tip sent in by Bill Eldridge: Simply add the first and second digits and place 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's look 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 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
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 by 16.

First, multiply the number in question by 10. Then multiply half the number by 10. Then add those two results together with the number itself to 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