operations · Year 4 · AC9M4A02

Partial products (distributive property)

To multiply a bigger number, split it into parts that are easy to multiply, multiply every part, then add the answers. 7 × 36 = 7 × 30 + 7 × 6 = 210 + 42 = 252. An area model shows why: the rectangle is split into two smaller rectangles. A number just below a round number can be done as round number minus a bit: 6 × 49 = 6 × 50 − 6 × 1.

Sample questions

6 × 19 = 6 × 10 + 6 × 9 = ?

10966 × 106 × 9
  1. Split 19 into 10 + 9.
  2. 6 × 10 = 60 and 6 × 9 = 54.
  3. 60 + 54 = 114.

Answer: 114

8 × 71 = 8 × 70 + 8 × 1 = ?

70188 × 708 × 1
  1. Split 71 into 70 + 1.
  2. 8 × 70 = 560 and 8 × 1 = 8.
  3. 560 + 8 = 568.

Answer: 568

5 × 36 = 5 × 30 + 5 × 6 = ?

30655 × 305 × 6
  1. Split 36 into 30 + 6.
  2. 5 × 30 = 150 and 5 × 6 = 30.
  3. 150 + 30 = 180.

Answer: 180

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