Ratio and fractions

Quick answer

Ratios show how parts relate to each other, and fractions show how parts relate to the whole. You can convert between them by thinking of ratios as fractions of a total group.

Learning outcome

By the end of this page, you will be able to understand how part-to-part ratios connect to part-of-whole fractions, and use this to solve simple problems in everyday life.

• You can describe a ratio like 3:2 using a fraction like 3/5 of the group.
• You can find the fraction of a group that a part of a ratio represents.
• You can match ratios to the correct fractions when given a real-life situation.
• You can use ratios and fractions together to solve simple problems like sharing sweets or sorting toys.

Why this matters

Understanding ratios and fractions helps you solve problems in everyday life. When you share snacks with friends, divide a pizza, or sort your toys, you're using ratios and fractions without even realising it. This skill helps you think more clearly about how things are shared, how parts fit together, and how to make fair decisions.

In school, this connects to more advanced maths like percentages, decimals, and scaling. In games and sports, it helps you understand how scores work, how many players are on each team, or how to split up a group.

How it works

Let’s think of a simple example. Imagine you have a bag of 10 marbles. 6 are red, and 4 are blue. This is a part-to-part ratio of red to blue: 6:4.

But if you want to know what fraction of the bag is red, you look at the whole group. There are 10 marbles total, and 6 are red. So the fraction of red marbles is 6/10.

So, the ratio 6:4 becomes the fraction 6/10 when we look at how many red marbles there are compared to the total number of marbles.

Let’s break this down step by step:

1. First, count the parts in the ratio. 6 red + 4 blue = 10 total marbles.
2. Then, make a fraction with the part you want (red) over the total (10).
3. So, red marbles = 6/10 of the bag.

Examples you can see

Let’s try a few more examples to make this clearer.

Example 1: Coloured pencils

You have a box of 12 pencils. 5 are red, 7 are blue.

The ratio of red to blue is 5:7.

But what fraction of the pencils are red?

Red pencils = 5 out of 12 total pencils.

So, the fraction is 5/12.

Example 2: Fruit salad

Your mum makes a fruit salad with 3 apples, 4 bananas, and 5 oranges.

The ratio of apples to bananas to oranges is 3:4:5.

How many parts are there in total?

3 + 4 + 5 = 12 parts.

So, the fraction of apples is 3/12.

The fraction of bananas is 4/12.

The fraction of oranges is 5/12.

Example 3: Your toys

You have 8 toy cars. 3 are red, 5 are blue.

The ratio of red to blue cars is 3:5.

What fraction of your cars are red?

Red cars = 3 out of 8 total cars.

So, the fraction is 3/8.

Try it as a mini adventure

Adventure: The Magic Toy Box

You find a magic toy box that splits your toys into groups. You have 15 toys in total. 6 are cars, 9 are dolls.

1st time: What is the ratio of cars to dolls?

Answer: 6:9

2nd time: What fraction of the toys are cars?

Answer: 6/15

3rd time: If you share the dolls equally among 3 friends, how many dolls does each friend get?

Answer: 9 ÷ 3 = 3 dolls each

4th time: What is the ratio of dolls to total toys?

Answer: 9:15

5th time: What fraction of the toys are dolls?

Answer: 9/15

6th time: If you take away 2 cars, what is the new ratio of cars to dolls?

Answer: (6 - 2):9 = 4:9

7th time: What fraction of the new total toys are cars?

Answer: 4 out of 13 = 4/13

Common mistakes

• Mistake: Thinking the ratio 3:4 means 3/4 of the whole.
• Why it happens: Confusing part-to-part with part-of-whole.
• Fix: Always add the parts together to find the whole before making the fraction.

• Mistake: Not simplifying fractions like 6/12 to 1/2.
• Why it happens: Not knowing how to reduce fractions.
• Fix: Find the biggest number that divides both top and bottom (like 6 divides both 6 and 12).

• Mistake: Using the wrong part when making a fraction.
• Why it happens: Not reading the question carefully.
• Fix: Underline or circle what part you're looking for before making the fraction.

Parent and carer guide

Help your child by:

1. Using everyday examples like sharing food or sorting toys to show ratios and fractions.
2. Encouraging them to draw pictures or use physical objects to understand the relationship.
3. Practising together by asking questions like, "If you have 10 sweets and 3 are red, what fraction are red?"
4. Checking if they understand that ratios compare parts to parts, while fractions compare parts to the whole.
5. Letting them make mistakes and learn from them without pressure.

Don’t worry if they struggle at first. These ideas take time to understand. Keep the learning fun and connected to real life!

Practice questions

1. There are 12 birds. 5 are blue, 7 are green. What is the ratio of blue to green birds?
2. What fraction of the birds are blue?
3. There are 10 animals. 4 are cats, 6 are dogs. What is the ratio of cats to dogs?
4. What fraction of the animals are dogs?
5. There are 15 crayons. 6 are red, 5 are yellow, 4 are blue. What is the ratio of red to yellow to blue?
6. What fraction of the crayons are yellow?
7. There are 8 fish. 3 are gold, 5 are silver. What is the ratio of gold to silver fish?
8. What fraction of the fish are silver?
9. There are 20 stickers. 7 are stars, 8 are hearts, 5 are moons. What is the ratio of stars to hearts to moons?
10. What fraction of the stickers are hearts?

Answers:

1. 5:7
2. 5/12
3. 4:6
4. 6/10 or 3/5
5. 6:5:4
6. 5/15 or 1/3
7. 3:5
8. 5/8
9. 7:8:5
10. 8/20 or 2/5

FAQ

What is the difference between a ratio and a fraction?

A ratio compares parts to other parts (like 3 red toys to 2 blue toys). A fraction compares a part to the whole (like 3 red toys out of 5 total toys).

Can I turn any ratio into a fraction?

Yes! Just add all the parts together to get the whole, then write the part you're interested in as the numerator and the total as the denominator.

Why do we need to know ratios and fractions?

They help us share things fairly, understand how parts fit together, and solve problems in cooking, sports, art, and daily life.

How do I simplify a fraction?

Find the biggest number that divides both the top and bottom. For example, 6/12 can be simplified to 1/2 because 6 goes into both 6 and 12.

Can ratios be more than 2 parts?

Yes! Ratios can compare 3 or more parts, like 2:3:5 for red, blue, and green marbles.