Multiplication Tips and Tricks

Some Tips and Tricks

Here are some tips and tricks to help you with multiplication.

Everyone thinks differently, so just ignore any tricks that don't make sense to you.

Math Trainer

First of all: Memory is your best friend! With the whole table in your memory you will just know that 3×15=15, 6×8=48 etc. Memory is fast, too.

Math Trainer - Multiplication is designed to
help you remember your tables.

The Best Trick

Every multiplication has a twin, which may be easier to remember.

For example if you forget 8×2, you might remember 2×8=16. This way, you only have to remember half the table.

multiplication table symmetry

Tricks by Number

2

add the number to itself (in other words, double it)
Example 2×9 = 9+9 = 18

4

double, then double again
Example 4×9: double 9 is 18, double 18 is 36

5

Cut in half, then times 10
Example: 5x6: Cut 6 in half to get 3, then times 10 for 30

Or times 10 then cut in half
Example: 5x9: 9 times 10 is 90, then cut in half for 45

Also the last digit goes 5, 0, 5, 0, ... like this: 5, 10, 15, 20, ...

6

when you multiply 6 by an even number, they both end in the same digit.
Examples: 6×2=12, 6×4=24, 6×6=36, etc

7×8

Think "5,6,7,8": 56=7×8

8

Double, double, double!
Example: 8×6: double 6 is 12, double 12 is 24, double 24 is 48

9

is 10× the number minus the number.
Example: 9×6 = 10×66 = 60−6 = 54

the ones digit goes 9, 8, 7, 6, ...: 9, 18, 27, 36, 45, ...
  the tens digit goes  0, 1, 2, 3, ...: 9, 18, 27, 36, 45, ...

subtract one to get the tens digit, and the tens and ones digit together make 9
Example: 9×5: tens digit is 4, 4 and 5 make 9, so 45
Example: 9×8: tens digit is 7, 7 and 2 make 9, so 72

fingers multiply 9


your hands can help! Example: to multiply 9 by 8, hold your 8th finger down, and count "7" and "2", the answer is 72


10

put a zero after it
Example: 10×2 = 20

11

up to 11x9: just repeat the digit. Example: 11x4 = 44

for 11×10 to 11×18: write the sum of the digits between the digits
Example: 11×15 = 1(1+5)5 = 165

Note: this works for any two-digit number, but when the sum of the digits is more than 9, we need to"carry the one". Example: 11×75 = 7(7+5)5 = 7(12)5 = 825.

12

is 10× plus 2×
Example: 12×4 = 40+8 = 48

15

multiply by 10, then add half again
Example: 15×4 = 40+20 = 60
Example: 15×9 = 90+45 = 135

20

multiply by 10, then double
Example: 20×4 = 40+40 = 80
Example: 20×7 = 70+70 = 140

Remembering Squares Can Help

This may not work for you, but it worked for me. I like remembering the squares (where you multiply a number by itself):

1×1=1 2×2=4 3×3=9 4×4=16 5×5=25 6×6=36
           
7×7=49 8×8=64 9×9=81 10×10=100 11×11=121 12×12=144

And this gives us one more trick. When the numbers we are multiplying are separated by 2 (example 7 and 5), then multiply the number in the middle by itself and subtract one. See this:

5×5 = 25 is just one bigger than 6×4 = 24
6×6 = 36 is just one bigger than 7×5 = 35
7×7 = 49 is just one bigger than 8×6 = 48
8×8 = 64 is just one bigger than 9×7 = 63
etc ...