Multiplying fractions by whole numbers

Quick answer

Multiplying a fraction by a whole number means adding the fraction that many times. For example, 3 × 1/4 is the same as 1/4 + 1/4 + 1/4, which equals 3/4.

Learning outcome

By the end of this page, you will be able to multiply a fraction by a whole number using repeated addition and visual models.

• You can show how multiplying a fraction by a whole number is the same as adding the fraction that many times.
• You can draw pictures or use objects to help solve these problems.
• You can solve word problems involving multiplying fractions by whole numbers.
• You can explain your thinking when solving these problems.

Why this matters

Multiplying fractions by whole numbers helps you solve real-life problems like sharing food, measuring ingredients, or working out how much time you spend on activities. For example, if you eat 1/3 of a pizza every day for 5 days, you can figure out how much pizza you've eaten in total. This skill also prepares you for more advanced maths, like multiplying fractions by fractions or decimals.

How it works

Multiplying a fraction by a whole number is really just adding the fraction over and over again. Here's how it works:

1. Start with the fraction you want to multiply, like 1/5.
2. Decide how many times you want to add it, like 3 times.
3. Add the fraction that many times: 1/5 + 1/5 + 1/5.
4. Count the parts: 3 parts of 5 = 3/5.

You can also think of it as having 3 groups of 1/5, and then counting all the parts together.

Examples you can see

Let’s look at some examples you can imagine or draw:

Example 1: 2 × 1/3

Think of this as 1/3 + 1/3.

• You have 2 groups of 1/3.
• Each group is one part out of three.
• So together, you have 2 parts out of 3.
• The answer is 2/3.

Example 2: 4 × 1/6

This is 1/6 + 1/6 + 1/6 + 1/6.

• You have 4 groups of 1/6.
• That’s 4 parts out of 6.
• The answer is 4/6.

Example 3: 3 × 2/5

This is 2/5 + 2/5 + 2/5.

• You have 3 groups of 2/5.
• Each group has 2 parts out of 5.
• So altogether, you have 6 parts out of 5.
• The answer is 6/5.

Try it as a mini adventure

Adventure: The Cake Sharing Challenge

You and your friends are making a big cake for a party. The cake is cut into 8 equal pieces. You decide to give 5 pieces to your friends, but each friend gets the same amount. If you have 3 friends, how much cake does each friend get?

1. You start with 5 pieces of cake.
2. These 5 pieces are shared equally among 3 friends.
3. This is the same as 5 × 1/8 of the cake.
4. That means you’re sharing 5 pieces of a cake that is 8 pieces total.
5. Each friend gets 5/8 of the cake.

Try this: Draw a circle and divide it into 8 equal slices. Colour in 5 slices. Then, imagine splitting those 5 slices among 3 friends. Each friend gets 5/8 of the cake.

Common mistakes

• Mistake: Thinking that multiplying a fraction by a whole number means multiplying both the numerator and denominator by the whole number.
  Why it happens: Confusing this with multiplying fractions by fractions.
  Fix: Remember: only multiply the numerator by the whole number. Keep the denominator the same.
• Mistake: Adding the whole number to the numerator.
  Why it happens: Not understanding what multiplication means.
  Fix: Think of it as repeated addition, not addition with the whole number.
• Mistake: Forgetting to simplify the fraction.
  Why it happens: Not knowing how to reduce fractions.
  Fix: Look for common factors in the numerator and denominator and divide both by the same number.

Parent and carer guide

Helping your child learn this skill is about building understanding, not just memorising steps. Here’s how:

1. Use real objects: Use pizza slices, blocks, or counters to show how fractions work. For example, show 3 groups of 1/4 using 3 pieces of a pizza cut into 4 parts.
2. Draw pictures: Ask your child to draw the fraction and then show the repeated addition. This helps them see the process clearly.
3. Ask questions: Ask, “How many parts are there in total?” or “How many groups are you making?” This builds their thinking.
4. Keep it fun: Make it a game! Try a cooking challenge where they have to measure ingredients using fractions.
5. Don’t rush: Let your child make mistakes and learn from them. It’s part of the learning journey.

Practice questions

1. What is 3 × 1/4?
2. Calculate 2 × 3/5.
3. Find 4 × 1/6.
4. Solve 5 × 2/7.
5. What is 6 × 1/3?

Answers:

1. 3 × 1/4 = 3/4
2. 2 × 3/5 = 6/5
3. 4 × 1/6 = 4/6
4. 5 × 2/7 = 10/7
5. 6 × 1/3 = 6/3

FAQ

What does it mean to multiply a fraction by a whole number?

It means you are adding the fraction that many times. For example, 4 × 1/5 means 1/5 + 1/5 + 1/5 + 1/5 = 4/5.

Can I use a number line to help?

Yes! You can jump along a number line by the fraction, repeating the jump as many times as the whole number.

Why do we only multiply the numerator?

Because the denominator shows how many equal parts the whole is divided into. That doesn’t change when we multiply. Only the number of parts (numerator) changes.

Can I simplify my answer?

Yes! If the numerator and denominator have a common factor, you can divide both by that number to make the fraction smaller.

Is there a shortcut for this?

Yes! You can multiply the numerator by the whole number and keep the denominator the same. For example: 3 × 2/5 = (3 × 2)/5 = 6/5.