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Split and combine to multiply worksheets

15 × 18 is 15 × 10 plus 15 × 8, and 37 × 6 + 63 × 6 is simply 100 × 6. These free printable worksheets practise the distributive property in both directions — splitting a product apart and combining two into one — for grades 3 to 5.

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Split and combine to multiply
Split and combine to multiply worksheet — Split and combine, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

Splitting turns a two-digit multiplication into two easy ones. 15 × 18 becomes 15 × 10 + 15 × 8 = 150 + 120 = 270. The tens part is always a times-ten fact, so the only real work is the ones part and one addition.

Why this sheet works

Combining runs the same rule backwards, and it is where the property surprises children. 37 × 6 + 63 × 6 has the same 6 in both products, so it is (37 + 63) × 6 = 100 × 6 = 600 — two multiplications that never need doing. The difference works the same way: 86 × 7 − 36 × 7 = 50 × 7 = 350.

How this one works

45 × 17

45 × 17=45 × 10 + 45 × 7
45 × 10 + 45 × 7=450 + 315
450 + 315=765
  1. Split the second number into tens and ones, multiply each part, then add.
  2. Work out the easy part first: 45 × 10 + 45 × 7 = 450 + 315.
  3. Then finish: 450 + 315 = 765.

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