# Multiplication Shortcut Part- 1

**Change Order**

Numbers may be multiplied in any orders. You can take advantage of this fact by multiplying whatever order is easiest for you.

Example:

25 × 937 × 4= 25 × 4 × 937= 100 × 937= 93700

**Splitting Number**

You can simplify multiplication by splitting a number into smaller parts by units (ones), tens, hundreds etc.

Example:

87 × 9= (80 + 7) × 9 = (80 × 9) + (7 × 9) = 720 + 63 = 783;

213 × 8 = (200 + 13) × 8 = (200 × 8) + (13 × 8) = 1600 + (10 + 3) × 8 = 1600 + 80 + 24 = 1704

**Doubling and Halving**

We can simplify some multiplication problems by doubling one factor and halving the other factor.

Example:

35 × 28 = 70 × 14 = 140 × 7 = (100 + 40) × 7= 700 + 280 = 980;

45 × 48= 90 × 24= 180 × 12= 360 × 6 = (300 + 60 ) × 6= 1800 + 360= 2160;

750 × 24 = 1500 × 12 =3000 × 6= 18000.

In the above examples we simplify these multiplication by doubling first number and halving the other number.

**10- Level Number**

You can made numbers near 10-level such as 9, 11, 19, 21, 29, 31… etc into easy multipliers by changing them into numbers ending in zero.

Example:

45 × 19= 45 × (20 – 1)= 45 × 20 – 45= 900 – 45= 855;

31 × 29 = (30 + 1) × (30 – 1) = 900 – 1= 899; [(a + b)(a – b)= a^2 – b^2];

99 × 97 = (100 – 1) ) × 97 = 9700 – 97 = 9700 – 100 + 3 = 9603

** ****One Number Has All Digits Alike**

If the digits of a number in multiplication are all the same, you can simplify the multiplication by making the number as multiplier.

Example:

**No Carry Multiplication**

Multiplication can be done without carrying wither from left to right or right to left. The zeros in the partial products help to make the addition easier.

Example: