To become experts at mental math, children need considerable practice because mental computation is not done in the same way as pencil-and-paper procedures. There are many ways to add, subtract, multiply, and divide using mental math. As there is no one clear-cut method to use in solving a problem, children need to choose the method that works best for them.

### Addition

It is easy to add tens and hundreds if place-value words are used.

Example: 200 + 300 + 40

Think or say: 2 hundred and 3 hundred is 5 hundred and 40 more is 540.

It can be easier to add hundreds and thousands if the thousands are thought of as hundreds.

Example: 4200 + 500

Think or say: 42 hundred and 5 hundred is 47 hundred.

Begin on the left when using mental math to add numbers.

Example: 24 + 32

Think or say: 20 and 30 is 50. 4 and 2 is 6. 50 and 6 is 56.

Example: 37 + 45

Think or say: 30 and 40 is 70. 7 and 5 is 12. 70 and 12 is 82. OR

37 and 40 is 77. 77 and 5 is 82.

It is easy to add by making one of the numbers a multiple of ten and then compensating. This method works especially well when adding numbers ending in an 8 or 9.

Example: 69 + 18

Think or say: 69 and 1 is 70. 70 and 18 is 88. 88 take off 1 is 87. OR

18 and 2 is 20. 69 and 20 is 89. 89 take off 2 is 87.

Numbers are easier to add when both numbers end in 5.

Example: 65 + 28

Think or say: 28 is 25 and 3. 65 and 25 is 90. 90 and 3 is 93.

Compatible numbers are numbers that go together to make tens or hundreds.

Example: 70 + 20 + 80

Think or say: 20 and 80 is 100. 100 and 70 is 170.

### Subtraction

When children are doing subtraction, they will find it helpful to think addition.

Example: 15 - 7

Think or say: 7 + what equals 15. 8.

Making the number to be subtracted a multiple of ten and then keeping track of how much is added on to that number to get the total is one method of mental math subtraction. Two other methods to solve the same problem will follow.

Example: 53 - 47

Think or say: 47 and 3 is 50 and 3 more is 53. 3 and 3 is 6.

As in addition, you can begin on the left when using mental math to subtract numbers.

Example: 53 - 47

Think or say: 50 - 40 is 10. 10 and 3 is 13. 13 - 7 is 6.

It is easy to subtract by making tens with the number to be subtracted and then compensating.

Example: 53 - 47

Think or say: 53 - 40 is 13. 13 - 7 is 6.

Use compensation when you subtract numbers ending in 8 or 9.

Example: 53 - 19

Think or say: 19 + 1 is 20. 53 - 20 is 33. 33 + 1 is 34.

Larger numbers can be handled easier by dropping common zeros. Caution: These zeros must be added back on to get the right place value in the answer.

Example: 800 - 400

Think or say: 8 - 4 is 4. Then add back the zeros to get 400.

Example: 840 - 400

Think or say: 84 - 40 is 44. Then add back the missing zero to get 440. OR

8 - 4 is 4. Add back the missing zeros to get 400 then add 40 more. 440.

You can drop the ending digits if they are the same in both numbers just like in dropping common zeros. However, you must remember to add zeros to get the correct place value.

Example: 846 - 446

Think or say: 8 - 4 is 4. Add two zeros to get the correct place value 400.

### Multiplication

Numbers that have many zeros are easy to multiply. You multiply the nonzero numbers first and then add on the zeros. Caution: You must understand the relationship between the zeros and place value. One zero represents tens, two zeros represents hundreds, three zeros represents thousands, and so on.

Example: 7 x 300

Think or say: 7 x 3 is 21. Add on two zeros. 2100. OR

7 x 3 is 21. Use place value. 21 hundred. 2100.

Go from left to right when multiplying large numbers. Multiply the large number first and then add in the little parts.

Example: 74 x 8

Think or say: 8 x 70 is 560. 8 x 4 is 32. 560 and 32 is 592.

When multiplying very large numbers, break the number into parts that are easy to handle.

Example: 524 x 3

Think or say: 3 x 500 is 1500. 3 x 24 is 72. 1500 and 72 is 1572. OR

3 x 500 is 1500. 3 x 20 is 60. 3 x 4 is 12. 1500 and 60 and 12 is 1572.

To multiply numbers ending in 8 or 9, use the next higher multiple of 10 and then compensate. This is especially helpful when dealing with money.

Example: 6 x 49

Think or say: 6 x 50 is 300. 6 x 1 is 6. 300 take back 6 is 294.

Example: 6 x $4.98

Think or say: 6 x $5.00 is $30.00 less 6 x 2 cents. $30.00 less $.12 is $29.88.

Some numbers are easier to multiply if you halve one number and double the other.

Example: 8 x 15

Think or say: Half of 8 is 4 and double 15 is 30. 4 x 30 is 120.

Example: 8 x 16

Think or say: Halve and double more than once. 4 x 32. Then 2 x 64 is 128.

Rearrange one or both numbers to make mental multiplication easier.

Example: 16 x 25

Think or say: 16 x 25 is 4 x 4 x 25. 4 x 25 is 100. 100 x 4 is 400.

### Division

When using mental math to do division, think multiplication just as in pencil-and-paper problems.

Example: 56 ÷ 8

Think or say: What times 8 is 56. 7.

When the number to be divided has zeros, cut off the zeros, divide, and then put the zeros back.

Example: 2400 ÷ 8

Think or say: Cut off the zeros. 8 times what is 24. 3. Then add back the zeros to get 300. OR

Cut off the zeros. 24 divided by 8 is 3. Then add back the zeros to get 300.

When both the number to be divided and the divisor have zeros, cancel the common zeros.

Example: 600 ÷ 300

Think or say: 3 times what is 6. 2. OR 6 divided by 3 is 2.

Example: 600 ÷ 30

Think or say: 3 times what is 60. 20. OR 60 divided by 3 is 20.

Start at the left. Break the number to be divided into parts to make division easier.

Example: 240 ÷ 4

Think or say: 240 is 200 and 40. 200 ÷ 4 is 50. 40 ÷ 4 is 10. 50 and 10 is 60.

Change the number to be divided so it is rearranged into multiples of the divisor.

Example: 136 ÷ 8

Think or say: 136 can be changed to 80 plus 56. 80 8 is 10. 56 8 is 7. 10 and 7 is 17.

Change both the number to be divided and the divisor in the same way.

Example: 700 ÷ 25

Think or say: Multiply both numbers by 4. 700 x 4 is 2800. 25 x 4 is 100. 2800 ÷ 100 is 28.

### More about mental math

Years of practice are essential to gaining mental math skills. Children should begin learning how to do mental math in first grade and keep practicing these skills through at least eighth grade. To find more mental math activities, look in your children's math textbooks. Also, Dale Seymour Publications has Mental Math books for the primary grades, middle grades, and junior high offer children more practice in using mental math. In addition, children can learn how to do lightning quick calculation and amazing number tricks in the book, *Secrets of Mental Math* by Arthur Benjamin and Michael Shermer.