X Tables
multiplication

Doubling and halving strategy

Make products easier by doubling one factor and halving the other.

Quick answer

Doubling and halving is a helpful strategy to make multiplication easier. You take one number and double it, then take the other number and halve it. The answer stays the same!

Learning outcome

By the end of this page, you will be able to use the doubling and halving strategy to solve multiplication problems quickly and easily. Success signs:
  • You can double one number and halve another to make multiplication easier
  • You can solve multiplication problems using this strategy
  • You can explain why doubling one number and halving another gives the same answer
  • You can use this strategy with numbers up to 20

Why this matters

Doubling and halving helps you solve multiplication problems faster, especially when one number is even. It's a smart trick that makes big multiplication problems feel easier. You'll use this strategy when you're shopping, cooking, playing games, or even sharing snacks with friends. In school, this strategy helps you solve problems more quickly. It also helps you understand how multiplication works. The more ways you have to think about numbers, the better you'll get at maths.

How it works

The doubling and halving strategy works like this:
  1. Look at your multiplication problem
  2. Find which number is even (can be shared in two equal parts)
  3. Double the even number
  4. Halve the other number
  5. Multiply the new numbers together
Let's look at an example: If you have 6 × 8, you can double 6 to make 12, and halve 8 to make 4. Now you have 12 × 4, which is easier to work out. 12 × 4 = 48 This is the same as 6 × 8 = 48.

Examples you can see

Let's try some examples together. Example 1: 4 × 6
  • 4 is even, so we double it to 8
  • 6 is halved to 3
  • New problem: 8 × 3 = 24
  • Check: 4 × 6 = 24 ✓
Example 2: 8 × 5
  • 8 is even, so we double it to 16
  • 5 is halved to 2.5
  • New problem: 16 × 2.5 = 40
  • Check: 8 × 5 = 40 ✓
Example 3: 3 × 10
  • 10 is even, so we double it to 20
  • 3 is halved to 1.5
  • New problem: 20 × 1.5 = 30
  • Check: 3 × 10 = 30 ✓
Here's a table showing the doubling and halving strategy for 1 to 12:
Original Doubled Halved Answer
1 × 6 2 3 6
2 × 6 4 3 12
3 × 6 6 3 18
4 × 6 8 3 24
5 × 6 10 3 30
6 × 6 12 3 36
7 × 6 14 3 42
8 × 6 16 3 48
9 × 6 18 3 54
10 × 6 20 3 60
11 × 6 22 3 66
12 × 6 24 3 72

Try it as a mini adventure

Adventure: The Treasure Hunt You are on a treasure hunt! You need to find a hidden chest. The clue says: "If you want to find the treasure, you must solve this problem: There are 8 pirates, and each pirate found 4 gold coins. How many gold coins did they find in total?" You can solve this with 8 × 4. Now use the doubling and halving strategy:
  • Which number is even? 8 is even
  • Double 8 to make 16
  • Halve 4 to make 2
  • New problem: 16 × 2 = 32
So the pirates found 32 gold coins in total! Let's try another clue: "The treasure is hidden under a tree that is 12 steps away from the big rock. If you take 5 steps at a time, how many steps will you take?" This is 12 × 5.
  • 12 is even, so we double it to 24
  • 5 is halved to 2.5
  • New problem: 24 × 2.5 = 60
You will take 60 steps to reach the treasure!

Common mistakes

  • Mistake: Forgetting to halve the number that was doubled
    Why it happens: It's easy to get confused when changing numbers
    Fix: Always check that you doubled one number and halved the other
  • Mistake: Using the strategy with odd numbers
    Why it happens: Some people think it works with all numbers
    Fix: Only use this strategy when one number is even
  • Mistake: Not checking if the answer is correct
    Why it happens: People get excited and forget to double-check
    Fix: Always solve the original problem and the new problem to make sure they match
  • Mistake: Thinking the strategy changes the answer
    Why it happens: Confusion about how numbers work
    Fix: Remember, the answer stays the same, only the numbers change

Parent and carer guide

Parents and carers can help children learn this strategy by:
  • Practicing with simple examples like 2 × 6, 4 × 8, and 6 × 4
  • Using real-life situations like sharing cookies or counting wheels on cars
  • Encouraging children to explain their thinking
  • Checking that the original and new problems give the same answer
  • Playing games where you double and halve numbers together
Here are some tips for helping at home:
  • Start with simple problems where one number is even
  • Use objects like counters or blocks to show the doubling and halving
  • Ask your child to explain why the strategy works
  • Make it fun with games or stories
  • Don't worry if it takes time to learn - it's a new way of thinking!

Practice questions

  1. Use the doubling and halving strategy to solve 4 × 8
  2. Solve 6 × 6 using doubling and halving
  3. What is 10 × 4 using this strategy?
  4. Try 12 × 3 with doubling and halving
  5. Use the strategy to find 8 × 7
  6. Solve 2 × 10 using doubling and halving
  7. What is 6 × 8 with this method?
  8. Try 14 × 5 with doubling and halving
  9. Solve 3 × 12 using the strategy
  10. Find 16 × 2 using doubling and halving
Answers:
  1. 4 × 8 = 32 (double 4 to 8, halve 8 to 4, 8 × 4 = 32)
  2. 6 × 6 = 36 (double 6 to 12, halve 6 to 3, 12 × 3 = 36)
  3. 10 × 4 = 40 (double 10 to 20, halve 4 to 2, 20 × 2 = 40)
  4. 12 × 3 = 36 (double 12 to 24, halve 3 to 1.5, 24 × 1.5 = 36)
  5. 8 × 7 = 56 (double 8 to 16, halve 7 to 3.5, 16 × 3.5 = 56)
  6. 2 × 10 = 20 (double 2 to 4, halve 10 to 5, 4 × 5 = 20)
  7. 6 × 8 = 48 (double 6 to 12, halve 8 to 4, 12 × 4 = 48)
  8. 14 × 5 = 70 (double 14 to 28, halve 5 to 2.5, 28 × 2.5 = 70)
  9. 3 × 12 = 36 (double 12 to 24, halve 3 to 1.5, 24 × 1.5 = 36)
  10. 16 × 2 = 32 (double 16 to 32, halve 2 to 1, 32 × 1 = 32)

FAQ

What is the doubling and halving strategy?

The doubling and halving strategy is a way to make multiplication easier by doubling one number and halving another number. The answer stays the same, but the problem becomes easier to solve.

When can I use this strategy?

You can use this strategy when one of the numbers in your multiplication problem is even. It makes the problem simpler because you're working with smaller, friendlier numbers.

Does this work with all numbers?

No, this strategy only works when one number is even. If both numbers are odd, it won't work as well. You can still use it with decimals, but it's easier with whole numbers.

Why does this strategy work?

This strategy works because when you double one number and halve the other, you're not changing the total amount. It's like having 4 groups of 6 items, or 6 groups of 4 items - the total is the same, just arranged differently.

Can I use this strategy with larger numbers?

Yes! You can use this strategy with larger numbers too. For example, 20 × 8 becomes 40 × 4, which is easier to work out. The key is that one number must be even.