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MulTiPliCATion By 3-DiGiT nuMBErS

Multiplying by a 3-Digit number Ending with Two 0s

Let us learn how to multiply a number by a 3-digit number ending with two 0s (100,
200, 300, ...). Observe the results of the following examples.

a. 57 × 100 = 5700 b. 438 × 100 = 43800
c. 48 × 200 = (48 × 2) × 100 = 9600 d. 164 × 300 = (164 × 3) × 100 = 49200

e. 205 × 400 = (205 × 4) × 100 = 82000 f. 105 × 800 = (105 × 8) × 100 = 84000

To multiply a number by a 3-digit number ending with two 0s, we write two 0s (00)
at the end and multiply the number by the digit in the hundreds place.

Multiplying by any 3-Digit number

Example 1. Find 276 × 234.

Solution.

Step 1. Multiply by the ones digit.
276 × 4 = 1104 TTh Th H T O

Step 2. Multiply by the tens digit. 2 7 6
× 2 3 4 200 + 30 + 4
276 × 30 = 8280
Step 3. Multiply by the hundreds digit. 1 1 0 4 276 × 4
8 2 8 0 276 × 30
276 × 200 = 55200
+ 5 5 2 0 0 276 × 200
Step 4. Add the products.
6 4 5 8 4 276 × 234
1104 + 8280 + 55200 = 64584

Therefore, 276 × 234 = 64584.

Example 2. Find 137 × 506.

Solution. TTh Th H T O TTh Th H T O
1 3 7 1 3 7

× 5 0 6 500 + 0 + 6 × 5 0 6 500 + 0 + 6

8 2 2 137 × 6 Or 8 2 2 137 × 6
0 0 0 137 × 0 + 6 8 5 0 0 137 × 500
+ 6 8 5 0 0 137 × 500 6 9 3 2 2

6 9 3 2 2

Therefore, 137 × 506 = 69322.

50 Mathematics 4