MATHS SHORTCUTS ## MULTIPLICATION

Doing quick multiplication is must in exams. Please read the shortcuts again and again. Practice more....
Learning Tables 1 to 30 is mandatory.

## MULTIPLY BY 11

It easy to multiply by 11.

Let's see an example,
Take 72 x 11,

Leave a space between 7_2....
72 x 11 = 7_2
Just add 7 and 2 and put the result in the space.
So, 72 * 11 =7 9 2.

Some more examples:
1) 45 * 11 = 4 (4+5) 5 = 495.
2) 95 * 11 = 9 (9+5) 5 = 9 14 5 = here carry over 1 to next number, so(9+1) = 10 4 5 = 1045.
3) 52 * 11 = 5 (5+2) 2 = 572.

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## MULTIPLY ANY 2 THREE DIGIT NUMBERS

Say  23 x 45

2    3
x        4    5

STEP 1:   Multiply last two numbers 3 x 5 is 15, put 5, carry over 1
5

STEP 2:  Then cross multiply 2x5="10" & 3x4="12, " add 12+10+1 = 23, carry over 2, put 3.
3    5

STEP 3:  Multiply first two numbers 2 x 4 is 8, add 8 + 2 put 10
10    3     5

So, 2 3 X 4 5 = 1035.

Try various examples and keep on practicing, you will find it more easy and faster...

## MULTIPLY ANY 2 THREE DIGIT NUMBERS

Say 123 x 456,

1     2    3
x     4     5    6

STEP 1:      Multiply last two numbers 3 x 6 is 18, put 8, carry over 1
8

STEP 2:     Then cross multiply 2x6="12" & 3x5="15, " add 12+15+1 = 28, carry over 2, put 8.
8    8

STEP 3:      Then cross multiply,
1x6=6, 2x5="10" & 3x4="12,

carry over 3, put 0.
0     8    8

STEP 4:      Then cross multiply 1x5="5" & 2x4="8, " add 5+8+3 = 16, carry over 1, put 6.
6    0     8    8

STEP 5:      Multiply first two numbers 1 x 4 is 4