Dividing fractions by whole numbers
Share a fraction into equal smaller parts.
Quick answer
To divide a fraction by a whole number, you multiply the denominator (bottom number) of the fraction by the whole number. This makes the parts smaller and creates a new fraction that is the answer.
Learning outcome
By the end of this page, you will understand how to divide a fraction by a whole number and be able to solve problems like 1/4 ÷ 2 or 3/5 ÷ 3.
Success signs:
- You can explain what happens when you divide a fraction by a whole number
- You can solve simple division problems with fractions and whole numbers
- You can draw or use objects to show how dividing a fraction works
- You can check your answer by multiplying it back
Why this matters
Dividing fractions by whole numbers is useful in everyday life! Imagine you have 1/2 a pizza and want to share it equally between 3 friends. You need to divide 1/2 by 3 to find out how much each friend gets. This helps you share fairly and understand how much of something you have left.
This skill also helps in cooking, measuring ingredients, splitting money, and planning projects. When you learn this, you're getting ready for more advanced maths like dividing fractions by fractions and solving real-world problems.
How it works
Let's break it down step by step:
- Start with a fraction – like 1/3
- Divide it by a whole number – like 2
- Multiply the bottom number (denominator) by the whole number – so 3 × 2 = 6
- Keep the top number (numerator) the same – so 1/6
So 1/3 ÷ 2 = 1/6.
This makes sense because you are splitting 1/3 into 2 equal parts, so each part is now 1/6 of the whole.
Examples you can see
Example 1: Sharing Pizza
Imagine you have 1/4 of a pizza and want to share it equally between 2 people.
- You start with 1/4
- You divide it by 2
- You multiply the bottom number: 4 × 2 = 8
- Your answer is 1/8
So each person gets 1/8 of the whole pizza.
Example 2: Baking Cookies
You have 3/4 of a cookie recipe and want to split it into 3 equal parts for your family.
- You start with 3/4
- You divide it by 3
- You multiply the bottom number: 4 × 3 = 12
- Your answer is 3/12
So each family member gets 3/12 of the original recipe. (This can be simplified to 1/4, but we're focusing on the dividing step here.)
Example 3: Drawing Fractions
Draw a rectangle and shade 1/5 of it. Now, if you split that shaded part into 2 equal parts, what fraction of the whole rectangle is each part?
- Start with 1/5
- Divide by 2
- Multiply the bottom: 5 × 2 = 10
- Answer: 1/10
Each small part is 1/10 of the whole rectangle.
Try it as a mini adventure
The Fraction Fairy’s Challenge
Once upon a time, there was a Fraction Fairy who lived in a magical kitchen. She had 2/3 of a cake and wanted to split it equally among 4 friends. But the fairy needed your help!
Task: Help the Fraction Fairy find out how much cake each friend gets.
- Start with 2/3
- Divide by 4
- Multiply the bottom number: 3 × 4 = 12
- Keep the top number: 2/12
So each friend gets 2/12 of the cake. That’s the same as 1/6 when simplified!
Mini challenge: If the fairy had 3/4 of a cake and split it among 3 friends, how much would each get?
- Start with 3/4
- Divide by 3
- Multiply the bottom: 4 × 3 = 12
- Keep the top number: 3/12
Each friend gets 3/12, or 1/4 of the cake.
Common mistakes
- Mistake: Dividing the numerator (top number) instead of the denominator (bottom number).
Why it happens: Children might think they need to split the whole number into the fraction parts.
Fix: Remember: only the bottom number changes when dividing a fraction by a whole number. - Mistake: Thinking that 1/2 ÷ 2 = 1/4 is the same as 1/2 ÷ 2 = 2/4.
Why it happens: Confusion between multiplication and division of fractions.
Fix: Use the rule: multiply the denominator by the whole number. - Mistake: Forgetting to simplify the final answer.
Why it happens: Kids might be excited to finish and forget to check if fractions can be simplified.
Fix: Always check if the fraction can be simplified by dividing both top and bottom by the same number.
Parent and carer guide
Helping your child learn to divide fractions by whole numbers can be fun and easy!
- Use real-life examples – like sharing food or dividing a cake.
- Draw or use objects – Use pizza slices, blocks, or drawings to show the fraction being split.
- Ask questions – “What happens to the size of the pieces when we split them more?”
- Encourage checking – Have them multiply their answer by the whole number to see if they get back to the original fraction.
- Keep it light – Don’t pressure them to get it perfect straight away. Mistakes are part of learning!
Remember: 1/4 ÷ 2 = 1/8 – the pieces get smaller when you divide them more.
Practice questions
- What is 1/3 ÷ 3?
Answer: 1/9 - What is 2/5 ÷ 2?
Answer: 2/10 (or 1/5 simplified) - What is 3/8 ÷ 4?
Answer: 3/32 - What is 1/6 ÷ 3?
Answer: 1/18 - What is 4/7 ÷ 2?
Answer: 4/14 (or 2/7 simplified)
FAQ
How do I divide a fraction by a whole number?
You multiply the denominator (bottom number) of the fraction by the whole number, and keep the numerator (top number) the same.
Can I use a visual to help me?
Yes! Drawing pictures or using objects like blocks or pizza slices helps you see how the fraction gets smaller when divided.
Why does dividing by a whole number make the fraction smaller?
Because you're splitting the fraction into more equal parts, so each part becomes smaller.
Do I always need to simplify my answer?
It's good practice to simplify if possible, but not always required. If the fraction is already in its simplest form, you're done!
What if the numerator is 1?
If the numerator is 1, like 1/5 ÷ 2, the answer is 1/10. The top stays 1, and the bottom multiplies by 2.