Multiplication facts: 6, 7, 8 & 9
Theory
Multiplication facts for 6, 7, 8 and 9 are a Year 4 maths skill. Instead of learning every fact by heart, you can work them out with strategies: double a known fact, use ten-times then take one group away for the nines, turn a fact around with the commutative property, and use fact families to link multiplication and division. Curriculum: VC2M4A02 / AC9M4A02.
A multiplication fact is a times-table answer, like \(9 \times 4 = 36\). The first number tells how many equal groups there are, and the second tells how many are in each group. So \(6 \times 7\) means six groups of seven.
You do not have to memorise every fact. A strategy lets you build a harder fact from an easier one you already know. For the sixes and eights you can double a smaller fact, and for the nines you can use ten-times then take one group away.
The commutative property means the order does not change the answer, so \(7 \times 8 = 8 \times 7\). A fact family links a multiplication fact to its division facts: \(8 \times 4 = 32\) also gives \(32 \div 4 = 8\).
These strategies help you build the 6, 7, 8 and 9 facts from facts you already know.
How to work out a tricky times-table fact
- Pick a strategy. For a 6 or 8 fact, double a smaller fact. For a 9 fact, use ten-times then take one group away.
- Start from a fact you know. Work out the easy fact first, like \(3 \times 5 = 15\) or \(10 \times 4 = 40\).
- Finish the step. Double the answer, or take away one group, to reach the fact you need.
- Check it. Turn the fact around, or add the digits for a nine fact, to make sure the answer is right.
Sevens. Split the 7 into 5 and 2, then add the two parts: \(7 \times 3 = 5 \times 3 + 2 \times 3 = 15 + 6 = 21\).
Missing numbers and sharing. Use the fact family. For \(\square \times 8 = 40\), ask which number times 8 makes 40: it is 5, so \(40 \div 8 = 5\). The same fact tells you how many boxes of 8 hold 40 things.
| \(4\text{ jumps of }7\) | \(=\) | \(28\) |
| \(4 \times 7\) | \(=\) | \(28\) |
The jumps match \(4 \times 7 = 28\).
| \(4 \times 3\) | \(=\) | \(12\) |
| \(8\text{ is double }4\) | \(\to\) | \(12 + 12\) |
| \(8 \times 3\) | \(=\) | \(24\) |
So \(8 \times 3 = 24\).
| \(10 \times 8\) | \(=\) | \(80\) |
| \(80 - 8\) | \(=\) | \(72\) |
| \(9 \times 8\) | \(=\) | \(72\) |
Check: \(7 + 2 = 9\), so \(9 \times 8 = 72\).
| \(49 \div 7\) | \(=\) | \(7\) |
| \(7 \times 7\) | \(=\) | \(49\) |
The missing number is \(7\).
Common pitfalls
Frequently asked questions
How do you work out the 6 times tables?
Double a three-times fact, because 6 is double 3. For \(6 \times 5\), work out \(3 \times 5 = 15\), then double it: \(15 + 15 = 30\), so \(6 \times 5 = 30\).
What is the easiest way to remember the 9 times tables?
Use ten-times then take one group away. For \(9 \times 4\), work out \(10 \times 4 = 40\), then take away one \(4\): \(40 - 4 = 36\). You can also check that the two digits add to 9, because \(3 + 6 = 9\).
What is a fact family?
A fact family is a group of multiplication and division facts that use the same three numbers. From \(8 \times 4 = 32\) you also get \(4 \times 8 = 32\), \(32 \div 4 = 8\) and \(32 \div 8 = 4\).
Does 9 times 4 equal 4 times 9?
Yes. The commutative property means you can turn the numbers around and the answer stays the same. Both \(9 \times 4\) and \(4 \times 9\) equal \(36\), so learning one fact gives you the other.
How do you use doubling to multiply?
Because 6 is double 3 and 8 is double 4, you can work out a hard fact by doubling an easier one. For \(8 \times 4\), double \(4 \times 4 = 16\): \(16 + 16 = 32\). Double only one of the numbers, not both.
How do you work out a 7 fact?
Split the 7 into 5 and 2. For \(7 \times 4\), work out \(5 \times 4 = 20\) and \(2 \times 4 = 8\), then add: \(20 + 8 = 28\), so \(7 \times 4 = 28\).