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Multiplying by any 2-Digit number

Example 1. Find 48 × 23.
Solution.
Step 1. Multiply by the Step 2. Multiply by the Step 3. Add the products.
ones. tens.

H T O H T O Th H T O
4 8 4 8 4 8
× 2 3 20 + 3 × 2 3 20 + 3 × 2 3

1 4 4 48 × 3 1 4 4 1 4 4

+ 9 6 0 48 × 20 + 9 6 0
1 1 0 4
Therefore, 48 × 23 = 1104.
Alternative Method
×
Step 1. Expand each of the two numbers, i.e., 48 into 20 40 8
40 and 8, and 23 into 20 and 3. 3

Step 2. Write the expanded form of 48 and 23 along
different blocks as shown. × 40 8
Step 3. Multiply 40 and 8 by 20 and write the products 20 800 160
as shown. 3

Step 4. Multiply 40 and 8 by 3 and write the products × 40 8
as shown. 20 800 160
Step 5. Now, add the products. 3 120 24
920 184
Therefore, 48 x 23 = 1104. 920 + 184 = 1104

Example 2. Multiply 532 by 38.

Solution.
Step 1. Multiply by the Step 2. Multiply by the Step 3. Add the products.
ones. tens.

Th H T O TTh Th H T O TTh Th H T O

5 3 2 5 3 2 5 3 2
× 3 8 30 + 8 × 3 8 30 + 8 × 3 8
4 2 5 6 532 × 8 4 2 5 6 4 2 5 6

+ 1 5 9 6 0 532 × 30 + 1 5 9 6 0

2 0 2 1 6

Therefore, 532 × 38 = 20216.

48 Mathematics 4