Multiplying, dividing and order of operations · Years 5–6
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
For example: Work out: 25 × 3
Answer and solution
The answer: 75
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
For example: Work out: 30 × 9
Answer and solution
The answer: 270
3 tens times 9 is 27 tens: 30 × 9 = 270
Dividing
For example: Work out: 27 ÷ 9
Answer and solution
The answer: 3
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
For example: Work out: 15,000 ÷ 3
Answer and solution
The answer: 5000
15 thousands divided by 3 is 5 thousands: 15,000 ÷ 3 = 5,000
Divisibility by 3, 6 and 9
For example: Is 22 divisible by 3?
- No
- Yes
Answer and solution
The answer: No
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
For example: Work out: 20 ÷ 5 + 54
Answer and solution
The answer: 58
Each line does one operation: 20 ÷ 5 + 54 = 4 + 54 4 + 54 = 58
Word problems
For example: The school hall has 63 rows of chairs, with 8 chairs in each row. How many chairs are there in the hall?
Answer and solution
The answer: 504
63 × 8 = 504
The exercises are made by rules and the answers are worked out in code, so there are new exercises every time. The topic follows the national curriculum in England: mathematics (key stages 3 and 4).