Non-unit fractions

Quick answer

Non-unit fractions are fractions where the numerator (top number) is more than 1, such as 3/4 or 5/6. You can think of them as 3 parts of 4 equal parts or 5 parts of 6 equal parts. They are made by adding together unit fractions (like 1/4 + 1/4 + 1/4).

Learning outcome

By the end of this page, you will understand how to make and read non-unit fractions by adding unit fractions together, and you will be able to see them in everyday situations like sharing food or dividing up playtime.

• You can explain what a non-unit fraction means
• You can show how to build a non-unit fraction from unit fractions
• You can identify non-unit fractions in real life
• You can use visual models to show non-unit fractions

Why this matters

Fractions help you share things fairly, measure ingredients, understand time, and solve problems. Non-unit fractions are important because they show parts of a whole that are more than one piece. For example, if you eat 3 slices of a pizza that has been cut into 8 slices, you have eaten 3/8 of the pizza. Understanding this helps you in cooking, sharing, games, and even telling time!

How it works

Let's start with a simple idea: a unit fraction is a fraction where the top number (numerator) is 1, like 1/3 or 1/5. A non-unit fraction has a numerator that is more than 1, like 2/3 or 4/5.

1. Think of a whole object, like a pizza or a chocolate bar
2. Divide it into equal parts
3. Take more than one of those parts to make a non-unit fraction
4. Count how many parts you took and how many parts the whole was divided into

For example, if you have a pizza cut into 6 pieces and you eat 3 pieces, you have eaten 3/6 of the pizza. This is a non-unit fraction because 3 is more than 1.

Examples you can see

Let's look at how we can build non-unit fractions using unit fractions.

Let’s imagine you are sharing a chocolate bar that is divided into 4 equal pieces. If you eat 3 pieces, you have eaten 3/4 of the bar. That’s a non-unit fraction because you took 3 parts out of 4.

Here’s how to draw it:

• Draw a rectangle to represent the chocolate bar
• Divide it into 4 equal parts
• Shade 3 of the 4 parts
• Write the fraction as 3/4

Try it as a mini adventure

Adventure: The Fraction Bakery

You are a baker helping your grandpa in his bakery. He has a large cake that he cuts into 8 equal pieces. You need to make sure each customer gets exactly the right amount.

1. Customer 1 wants 2 pieces. What fraction is that?
2. Customer 2 wants 5 pieces. What fraction is that?
3. Customer 3 wants 3 pieces. What fraction is that?
4. Customer 4 wants 7 pieces. What fraction is that?

Now, let's think: how many pieces did you give away in total? If the cake had 8 pieces and you gave away 2 + 5 + 3 + 7 = 17 pieces, how many pieces are left? That’s not possible! So, you must have made more cakes or shared fewer pieces. This is a fun way to see how fractions work in real life!

Common mistakes

• Mistake: Thinking that 3/4 means 3 parts out of 4 parts, but confusing which parts are the whole.
• Why it happens: Not seeing that the denominator tells you how many equal parts the whole is divided into.
• Fix: Always check that the denominator shows how many equal parts the whole is split into, and the numerator shows how many parts you are using.

• Mistake: Counting the parts wrong when drawing a fraction.
• Why it happens: Not dividing the shape into equal parts or not counting carefully.
• Fix: Use a ruler or fold paper carefully to make sure parts are equal. Count them again!

• Mistake: Mixing up unit fractions and non-unit fractions.
• Why it happens: Not knowing that a unit fraction has 1 on top.
• Fix: Remember that unit fractions always have 1 on top, like 1/2, 1/3, 1/4. Non-unit fractions have more than 1 on top.

Parent and carer guide

Helping your child understand non-unit fractions is easy and fun!

• Use everyday examples: Share a pizza, a chocolate bar, or a cake to show how fractions work.
• Draw it out: Let your child draw shapes and shade parts to make fractions.
• Ask questions: “If we split this cake into 6 pieces and you eat 4, what fraction did you eat?”
• Play games: Use fraction cards or fraction games online to practice.
• Don’t rush: Take time to make sure they understand the idea of equal parts before moving on.

What to say: “You’re doing great! Let’s look at this together.”

What not to worry about: It’s okay if they make a mistake. Mistakes help us learn!

Practice questions

1. What is 1/6 + 1/6 + 1/6?
2. If a pie is cut into 5 equal pieces and you eat 3 pieces, what fraction did you eat?
3. How can you write 4/9 as a sum of unit fractions?
4. Draw a rectangle divided into 8 equal parts and shade 5 of them. What fraction is that?
5. What is 1/3 + 1/3 + 1/3?

Answers:

1. 3/6
2. 3/5
3. 1/9 + 1/9 + 1/9 + 1/9
4. 5/8
5. 3/3 = 1 whole

FAQ

What is a non-unit fraction?

A non-unit fraction is a fraction where the numerator (top number) is more than 1, like 2/3, 4/5, or 7/8.

How do I make a non-unit fraction?

You can make a non-unit fraction by adding together unit fractions. For example, 3/5 = 1/5 + 1/5 + 1/5.

Why are non-unit fractions important?

They help you share things fairly, measure ingredients, and understand parts of a whole in daily life.

Can I use non-unit fractions to make a whole?

Yes! For example, if you have 4/4, that equals 1 whole.

How can I practice non-unit fractions at home?

You can use food, drawings, or games. Try sharing a pizza or cutting a chocolate bar into equal parts and counting how many pieces you take.