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example 2. Multiply 2457 by 28.

Solution.

Step 1. Break up the multiplier. 28 = 20 + 8 TTh Th H T O

Step 2. Multiply by the ones. 2457 × 8 = 19656 2 4 5 7

Step 3. Multiply by the tens. × 2 8 20 + 8

2457 × 20 = 49140 1 9 6 5 6 2457 × 8
Step 4. Add the two partial products. + 4 9 1 4 0 2457 × 20

19656 + 49140 = 68796 6 8 7 9 6
Thus, 2457 × 28 = 68796.

example 3. Multiply 562 by 409.

Solution.

Step 1. Break up the multiplier. 409 = 400 + 0 + 9 L TTh Th H T O

Step 2. Multiply by the ones. 562 × 9 = 5058 5 6 2

Step 3. Multiply by the tens. 562 × 0 = 0 × 4 0 9 400 + 0 + 9

Step 4. Multiply by the hundreds. 5 0 5 8 562 × 9
562 × 400 = 224800 0 0 0 0 562 × 0

Step 5. Add all the partial products. + 2 2 4 8 0 0 562 × 400

5058 + 0 + 224800 = 229858
2 2 9 8 5 8
Thus, 562 × 409 = 229858.

example 4. Multiply 6172 by 435. Multiplication
by 0 tens can
Solution. be skipped.

Step 1. Break up the multiplier.
TL L TTh Th H T O
435 = 400 + 30 + 5
6 1 7 2
Step 2. Multiply by the ones.
× 4 3 5 400 + 30 + 5
6172 × 5 = 30860

Step 3. Multiply by the tens. 3 0 8 6 0 6172 × 5

6172 × 30 = 185160 1 8 5 1 6 0 6172 × 30

Step 4. Multiply by the hundreds. + 2 4 6 8 8 0 0 6172 × 400

6172 × 400 = 2468800 2 6 8 4 8 2 0

44 Mathematics 5