Multiplying

Multiplying puts equal groups together. Once numbers get bigger than the times tables, we split them into parts and multiply each part: the grid method, short multiplication and long multiplication.

Key facts

  • Multiplying adds equal groups: 4 groups of 3 is 4 × 3 = 12.
  • You can multiply in any order: 3 × 4 = 4 × 3.
  • To multiply by a multiple of 10, use a times table fact, then make it 10 times bigger: 6 × 4 = 24, so 6 × 40 = 240.
  • Grid method: split both numbers into tens and ones, multiply each pair, then add.
  • Short multiplication: multiply each digit by the single digit, starting with the ones, and carry.
  • Long multiplication: multiply by the ones digit, then by the tens (put a 0 first), then add the rows.
  • Estimate first by rounding each number; if your answer is far from the estimate, check your working.

Worked examples

Example 1

There are 4 plates with 3 cakes on each plate. How many cakes are there?

  1. 4 equal groups of 3. 3 + 3 + 3 + 3 = 12
  2. So 4 × 3 = 12.

Answer: 12

Example 2

A box of chocolates has 3 rows with 5 chocolates in each row. How many chocolates are in the box?

  1. Each row has 5. Count in 5s, once for each row. 5, 10, 15

Answer: 15

Example 3

A tricycle has 3 wheels. How many wheels do 6 tricycles have?

  1. Count in 3s, once for each tricycle. 3, 6, 9, 12, 15, 18

Answer: 18

Example 4

24 × 3

  1. Split 24 into tens and ones, then multiply each. 20 × 3 = 60, 4 × 3 = 12
  2. Add them. 60 + 12 = 72

Answer: 72

Example 5

A spider has 8 legs. How many legs do 7 spiders have?

  1. 7 lots of 8 is 7 × 8. 7 × 8 = 56

Answer: 56

Example 6

Work out 6 × 40.

  1. Work out 6 × 4 first. 6 × 4 = 24
  2. 40 is 10 times 4, so the answer is 10 times bigger. 6 × 40 = 240

Answer: 240

Example 7

367 × 4

  1. Ones: 7 × 4 = 28. Write 8, carry 2.
  2. Tens: 6 × 4 + 2 = 26. Write 6, carry 2.
  3. Hundreds: 3 × 4 + 2 = 14.
  4. Answer: 1,468

Answer: 1,468

Example 8

46 × 23

  1. Split: 46 = 40 + 6 and 23 = 20 + 3.
  2. Multiply each pair, then add. 800 + 120 + 120 + 18 = 1,058

Answer: 1,058

Example 9

Work out 326 × 47.

  1. Multiply by the ones digit. 326 × 7 = 2,282
  2. Multiply by the tens: put a 0 first, then multiply by 4. 326 × 40 = 13,040
  3. Add the two rows. 2,282 + 13,040 = 15,322

Answer: 15,322

Example 10

A theatre has 46 rows with 28 seats in each row. Every seat is sold for 15 shows. How many tickets is that?

  1. Find the number of seats. 46 × 28 = 1,288
  2. Multiply by the number of shows. 1,288 × 15 = 19,320

Answer: 19,320 tickets

Example 11

Estimate, then work out 4,906 × 38.

  1. Estimate: round each number. 5,000 × 40 = 200,000
  2. Multiply by the ones digit. 4,906 × 8 = 39,248
  3. Multiply by the tens. 4,906 × 30 = 147,180
  4. Add the two rows, and compare with the estimate. 39,248 + 147,180 = 186,428

Answer: 186,428