By: Alyssa Liegmann and Ealin Ran Mental Math Techniques *Note this only works when multiplying a three or four digit by 11 Multiplying by 11 Multiplying Two Digit Numbers with a Base of 10 Squaring a number between 30 and 70 is easy with this simple trick.

Example: 56 to the power of 2

First, find the difference between your base?????? and 50. (56-50= 6)

Then, add this number to 25. (25+6= 31) These are you first two digits.

After, find the square of the difference between your base and 50.(6 to the power of 2= 36) These are you last two digits.

Your answer is 3136.

*Note: If you are squaring a number less than 50, SUBTRACT the difference from your base and 50 from 25. Squaring a Number between 30-70 This method is only used to quickly multiply two, two digit numbers. *Must has the same first digit and the last 2 digits must multiply to egual 10.(Ex. 98x92,74x76,35x35)

Ex.56x54

Take a look at the first number's first digit. (5)

To find the first part of the final answer, multiply this number with the number that comes after it.4,5,6 (5x6)

The answer to the equation (30) will be the first digits of the final answer.

Then, simply multiply the last digits of both numbers (6,4). This will find you the last digits of the final answer. (6x4=24)

The final answer is 3024! Multiplying two,2

digit numbers with the same first digit Multiplying 2, 3 digit numbers * This method is used to divide number 9.

Ex.221013/9

To begin with, the first digit of the dividend will be the same in the final answer.(2)

Then, add this digit to the next digit in 221013. 2+2=4. Use this answer to add the next digit in 221013. 4+1

Continue to do this until you reach the end.

2 2 1 0 1 3

2 4 5 5 6

Once you reach the final addition equation

which in this case is 3+6, you do not

write 9. This is b/c 9=the divisor.

Since 9 goes into itself once,add

1 to the number closest to the right which is 6.(5+1).

After finding the sum of all these

numbers, the final answer is

24557! Long Division with 9 The strategy is to add pairs of number next to each other, excluding the numbers on the outside.

Example:

627 x 11

First write down the first digit: "6"

Then add the first and second digits: 6+2= 8

Then add the second and third digits: 2+7= 9

Then write down the last digit: "7"

Your answer is 6897

*Note: When there is a sum of more than 9, increase the digit to the left by one (Carry)

Example:

4723 x 11

Write down the first digit: 4

Then add the first and second digits: 4+7= 11, But because the sum is more than 9, make the first digit 5, instead of 4, so far we have 5 and 1 as the first two digits

Then add the second and third digits: 7+2= 9

Then add the third and forth digits: 2+3= 5

Lastly, write down the final digit: 3

Your answer is 51 953 *This technique is used to multiply two,2 digit numbers with a base of 10.

Ex. 12x13

Take a look at the second digit of the second number. In this case, it is 3.

Then, add this number to the first number of the equation:12+3

The answer to this equation will be the first two digits of the final answer. (15)

Then take a look at the second digits of both numbers:2 & 3

Multiply these two numbers. This will be the last digit of the final answer. (6)

The final answer is 156! Multiplying 2, 3 digit numbers is easy with this simple trick 1 2 1

x3 0 2

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36542

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