## MENTAL CALCULATION STRATEGIES

an x am, where n + m = 10
A strategy to multiply any two two-digit-numbers that have the same first digit (tens) and their second digits (units) add up to 10.

## Example 1

38 x 32 = 1216
How we got 1216

Step 1: Multiply «the first digit» by «itself plus one». This forms the first part of our answer.
3 x (3 + 1) = 12

Step 2: Multiply the last two digits to get the second part of our answer.
8 x 2 = 16

## Example 2

17 x 13 = 221
How we got 221

Step 1: Multiply «the first digit» by «itself plus one». This forms the first part of our answer.
1 x (1 + 1) = 2

Step 2: Multiply the last two digits to get the second part of our answer.
7 x 3 = 21

## Example 3

25 x 25 = 625
How we got 625

Step 1: Multiply «the first digit» by «itself plus one». This forms the first part of our answer.
2 x (2 + 1) = 6

Step 2: Multiply the last two digits to get the second part of our answer.
5 x 5 = 25

## Example 4

62 x 68 = 4216
How we got 4216

Step 1: Multiply «the first digit» by «itself plus one». This forms the first part of our answer.
6 x (6 + 1) = 42

Step 2: Multiply the last two digits to get the second part of our answer.
2 x 8 = 16

## Example 5

96 x 94 = 9024
How we got 9024

Step 1: Multiply «the first digit» by «itself plus one». This forms the first part of our answer.
9 x (9 + 1) = 90

Step 2: Multiply the last two digits to get the second part of our answer.
6 x 4 = 24

## Example 6

41 x 49 = 2009
How we got 2009

Step 1: Multiply «the first digit» by «itself plus one». This forms the first part of our answer.
4 x (4 + 1) = 20

Step 2: Multiply the last two digits to get the second part of our answer.
1 x 9 = 09
Note that we add an extra zero if the product is less than 10. Here the answer is 2009 and not 209.

## Example 7

39 x 31 = 1209
How we got 1209

Step 1: Multiply «the first digit» by «itself plus one». This forms the first part of our answer.
3 x (3 + 1) = 12

Step 2: Multiply the last two digits to get the second part of our answer.
9 x 1 = 09
Note that we add an extra zero if the product is less than 10. Here the answer is 1209 and not 129.