X Tables
multiplication

Using known facts to find unknown facts

Use facts like 5 × 8 to solve 6 × 8 or 4 × 8.

Quick answer

You can use what you already know to work out what you don’t know. If you know that 5 × 8 = 40, then you can use that to work out 6 × 8 or 4 × 8.

Learning outcome

By the end of this page, you will be able to use a known multiplication fact to find an unknown multiplication fact. Success signs:
  • You can find 6 × 8 if you know 5 × 8 = 40
  • You can find 4 × 8 if you know 5 × 8 = 40
  • You can explain how you used one fact to find another
  • You can solve a multiplication problem using a known fact

Why this matters

Knowing how to use what you already know helps you solve multiplication problems more quickly and easily. This skill is useful in school, when you're solving word problems, and in real life when you're sharing things, counting groups, or working out how much something costs. It also helps you become more confident with numbers and makes learning new multiplication facts easier.

How it works

You can use a known multiplication fact to work out another one by:
  1. Looking at the difference between the numbers you're multiplying
  2. Adding or subtracting that difference from your known fact
  3. Checking your answer makes sense
Let’s look at a simple example. If you know that 5 × 8 = 40, you can find 6 × 8 by adding one more group of 8 to 40. That means 6 × 8 = 40 + 8 = 48. Or, if you know 5 × 8 = 40, you can find 4 × 8 by taking away one group of 8 from 40. That means 4 × 8 = 40 – 8 = 32.

Examples you can see

Let’s try some examples using what we know to find what we don’t know. Example 1: Using 5 × 8 = 40 to find 6 × 8
  • We know that 5 × 8 = 40
  • 6 × 8 means 5 × 8 + 1 × 8
  • So 6 × 8 = 40 + 8 = 48
Example 2: Using 5 × 8 = 40 to find 4 × 8
  • We know that 5 × 8 = 40
  • 4 × 8 means 5 × 8 – 1 × 8
  • So 4 × 8 = 40 – 8 = 32
Example 3: Using 10 × 6 = 60 to find 9 × 6
  • We know that 10 × 6 = 60
  • 9 × 6 means 10 × 6 – 1 × 6
  • So 9 × 6 = 60 – 6 = 54
Example 4: Using 7 × 5 = 35 to find 8 × 5
  • We know that 7 × 5 = 35
  • 8 × 5 means 7 × 5 + 1 × 5
  • So 8 × 5 = 35 + 5 = 40

Try it as a mini adventure

Adventure: The Magic Multiplication Shop You are a shopkeeper at a magical multiplication shop. You know that 5 × 8 = 40, and you want to help your customers find out other facts quickly. You have 5 groups of 8 magical coins each. You can use these to show how to find 6 × 8 or 4 × 8.
  1. First, you show 5 groups of 8 coins. Count them together: 5 × 8 = 40 coins
  2. Then, you add one more group of 8 coins to find 6 × 8: 40 + 8 = 48 coins
  3. Next, you take away one group of 8 coins to find 4 × 8: 40 – 8 = 32 coins
  4. Finally, you ask a customer to find 7 × 8 using what you know
This is like a puzzle! You can use what you already know to solve new problems.

Common mistakes

  • Mistake: Forgetting to add or subtract the right amount. For example, if you know 5 × 8 = 40, you might think 6 × 8 = 40 + 6 = 46 instead of 40 + 8 = 48.
  • Why it happens: Confusing how many groups you’re adding or subtracting.
  • Fix: Remember that you are adding or subtracting one group of the number you’re multiplying by.
  • Mistake: Thinking that 4 × 8 = 40 – 8 = 32, when it should be 40 – 32 = 8.
  • Why it happens: Mixing up which number is the total and which is the group size.
  • Fix: Double-check that you are subtracting the right amount – one group of 8, not 32.
  • Mistake: Not using a known fact at all and trying to count everything from scratch.
  • Why it happens: Not understanding that using known facts saves time.
  • Fix: Practice using known facts to find new ones, even if it seems simple at first.

Parent and carer guide

This skill helps children build confidence in math and improves their mental maths. As a parent or carer, you can support your child by:
  • Practising with them at home using simple facts they know
  • Asking them to explain how they used one fact to find another
  • Using everyday examples like sharing snacks or counting toys
  • Encouraging them to try different methods, not just one way
  • Not pushing too hard – let them make mistakes and learn from them
You can also ask questions like:
  • “How did you work out 6 × 8 if you know 5 × 8?”
  • “Can you show me how to find 9 × 6 using 10 × 6?”
It’s okay if they don’t get it right away. Practice makes progress!

Practice questions

  1. If you know 5 × 7 = 35, what is 6 × 7?
  2. If you know 8 × 4 = 32, what is 7 × 4?
  3. If you know 9 × 3 = 27, what is 10 × 3?
  4. If you know 6 × 5 = 30, what is 4 × 5?
  5. If you know 11 × 2 = 22, what is 12 × 2?
Answers:
  1. 6 × 7 = 35 + 7 = 42
  2. 7 × 4 = 32 – 4 = 28
  3. 10 × 3 = 27 + 3 = 30
  4. 4 × 5 = 30 – 5 = 25
  5. 12 × 2 = 22 + 2 = 24

FAQ

What does "using known facts to find unknown facts" mean?

It means using a multiplication fact you already know to work out a new one. For example, if you know 5 × 8 = 40, you can use that to find 6 × 8 or 4 × 8.

Why is this useful?

This skill helps you solve problems faster and builds your confidence with numbers. It also helps you understand how multiplication works better.

Can I use this with any multiplication fact?

Yes! You can use it with any multiplication fact, as long as you know one fact and are trying to find a nearby one.

What if I don’t know the first fact?

If you don’t know a fact, try to find a simpler one you do know. For example, if you don’t know 6 × 7, you might know 5 × 7 = 35, and then use that to find 6 × 7.

How can I practice this at home?

You can practice by asking questions like, “If 4 × 6 = 24, what is 5 × 6?” or by using objects like counters or toys to show groups and add or remove them.