6 — Multi-Digit Multiplication

Multi-Digit Multiplication

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Multi-digit multiplication is like breaking a big job into smaller, easier pieces! Instead of trying to multiply large numbers all at once, we multiply by each digit separately and then add up all our partial products. It's the same multiplication skills you already know, just organized in a smart way.

Tip

Key Rule: When multiplying by the tens digit, add one zero placeholder. When multiplying by the hundreds digit, add two zero placeholders. This keeps your place values correct!

Multi-Digit Multiplication · 1:54

Worked Example

Problem

Find 35 × 12

Solution

420

Solution

Explanation

  1. 1Multiply 35 × 2 (the ones digit). 35 × 2 = 70.
  2. 2Multiply 35 × 10 (the tens digit). 35 × 1 = 35, but since we're multiplying by the tens place, we add one zero: 350.
  3. 3Add the partial products. 70 + 350 = 420.

Worked Example

Problem

Calculate 142 × 23

Solution

3,266

Solution

Explanation

  1. 1Multiply 142 × 3 (ones digit). 142 × 3 = 426.
  2. 2Multiply 142 × 20 (tens digit). 142 × 2 = 284, then add one zero for the tens place: 2,840.
  3. 3Add the partial products. 426 + 2,840 = 3,266.

Question

24 × 13

Show Answer
312
Show Solution
Solution
  1. 1Multiply 24 × 3 (ones digit). 4 × 3 = 12, write 2 and carry 1. 2 × 3 = 6, plus carried 1 = 7. So 24 × 3 = 72.
  2. 2Multiply 24 × 10 (tens digit). 24 × 1 = 24, add one zero for tens place: 240.
  3. 3Add partial products. 72 + 240 = 312.

Question

32 × 15

Show Answer
480
Show Solution
Solution
  1. 1Multiply 32 × 5 (ones digit). 2 × 5 = 10, write 0 and carry 1. 3 × 5 = 15, plus carried 1 = 16. So 32 × 5 = 160.
  2. 2Multiply 32 × 10 (tens digit). 32 × 1 = 32, add one zero for tens place: 320.
  3. 3Add partial products. 160 + 320 = 480.

Question

58 × 24

Show Answer
1,392
Show Solution
Solution
  1. 1Multiply 58 × 4 (ones digit). 8 × 4 = 32, write 2 and carry 3. 5 × 4 = 20, plus carried 3 = 23. So 58 × 4 = 232.
  2. 2Multiply 58 × 20 (tens digit). 58 × 2 = 116, add one zero for tens place: 1,160.
  3. 3Add partial products. 232 + 1,160 = 1,392.

Question

67 × 89

Show Answer
5,963
Show Solution
Solution
  1. 1Multiply 67 × 9 (ones digit). 7 × 9 = 63, write 3 and carry 6. 6 × 9 = 54, plus carried 6 = 60. So 67 × 9 = 603.
  2. 2Multiply 67 × 80 (tens digit). 67 × 8 = 536, add one zero for tens place: 5,360.
  3. 3Add partial products. 603 + 5,360 = 5,963.

Question

156 × 47

Show Answer
7,332
Show Solution
Solution
  1. 1Multiply 156 × 7 (ones digit). 6 × 7 = 42, write 2 carry 4. 5 × 7 = 35, plus 4 = 39, write 9 carry 3. 1 × 7 = 7, plus 3 = 10. So 156 × 7 = 1,092.
  2. 2Multiply 156 × 40 (tens digit). 156 × 4 = 624, add one zero: 6,240.
  3. 3Add partial products. 1,092 + 6,240 = 7,332.

Question

284 × 135

Show Answer
38,340
Show Solution
Solution
  1. 1Multiply 284 × 5 = 1,420.
  2. 2Multiply 284 × 30. 284 × 3 = 852, add one zero: 8,520.
  3. 3Multiply 284 × 100. 284 × 1 = 284, add two zeros: 28,400.
  4. 4Add all partial products. 1,420 + 8,520 + 28,400 = 38,340.

Question

307 × 246

Show Answer
75,522
Show Solution
Solution
  1. 1Multiply 307 × 6 = 1,842.
  2. 2Multiply 307 × 40. 307 × 4 = 1,228, add one zero: 12,280.
  3. 3Multiply 307 × 200. 307 × 2 = 614, add two zeros: 61,400.
  4. 4Add all partial products. 1,842 + 12,280 + 61,400 = 75,522.

Tip

Remember: Multi-digit multiplication is just single-digit multiplication done multiple times! Break it into parts, use placeholder zeros to keep your place values straight, and always add up your partial products carefully.