# Multiplying, dividing and order of operations · Years 5–6

> Multiplying, dividing and order of operations, Years 5–6: Dividing and more. Explanation, worked examples and free practice for the national curriculum in England.

In Multiplying, dividing and order of operations (Years 5–6) you practise 7 skills: Multiplying · Thinking about products · Dividing · Thinking about quotients · Divisibility by 3, 6 and 9 · Order of operations · Word problems.

To multiply a two digit number, split it into tens and units and multiply each part: 23 × 4 = 20 × 4 + 3 × 4 = 80 + 12 = 92.

You can work out a product from one close to it: 49 × 8 is 50 × 8 take away 8, which is 400 − 8 = 392.

You can split when you divide too: split the number being divided into parts that each divide exactly. So 1,536 ÷ 3 = (1,500 + 30 + 6) ÷ 3 = 500 + 10 + 2 = 512.

You cannot divide by 0: no number times 0 gives a number that is not 0.

**Tip:** Before you work it out, estimate: which products or quotients of whole tens is the answer between? That makes a mistake easy to spot.

## What you learn

### Multiplying

- Example: Work out: 25 × 3
- Answer: 75
- Solution: Split the first number by place value and multiply each part: 25 × 3 = 20 × 3 + 5 × 3 20 × 3 = 60 5 × 3 = 15 60 + 15 = 75

### Thinking about products

- Example: Work out: 30 × 9
- Answer: 270
- Solution: 3 tens times 9 is 27 tens: 30 × 9 = 270

### Dividing

- Example: Work out: 27 ÷ 9
- Answer: 3
- Solution: Take multiples of 9 away from 27, largest first: 9 × 3 = 27 27 − 27 = 0 The quotient is 3, with no remainder. Check: 3 × 9 = 27

### Thinking about quotients

- Example: Work out: 15,000 ÷ 3
- Answer: 5000
- Solution: 15 thousands divided by 3 is 5 thousands: 15,000 ÷ 3 = 5,000

### Divisibility by 3, 6 and 9

- Example: Is 22 divisible by 3?
- Options: No · Yes
- Answer: No
- Solution: The sum of the digits: 2 + 2 = 4 4 is not divisible by 3. So 22 is not divisible by 3. The answer: no.

### Order of operations

- Example: Work out: 20 ÷ 5 + 54
- Answer: 58
- Solution: Each line does one operation: 20 ÷ 5 + 54 = 4 + 54 4 + 54 = 58

### Word problems

- Example: The school hall has 63 rows of chairs, with 8 chairs in each row. How many chairs are there in the hall?
- Answer: 504
- Solution: 63 × 8 = 504

The exercises are made by rules and the answers are worked out in code. The topic follows the national curriculum in England: mathematics (key stages 3 and 4).

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