Age 10 guide to fractions and decimals

Quick answer

By the end of this page, you will understand how fractions and decimals are different ways to show parts of a whole, and how to convert between them. You'll also learn how to compare and order them, and see how they appear in everyday life.

Learning outcome

By the end of this page, you will be able to:

• Understand that fractions and decimals both show parts of a whole
• Convert simple fractions to decimals and vice versa
• Compare and order fractions and decimals
• Use fractions and decimals in real-life situations

Why this matters

Fractions and decimals are everywhere in daily life. You use them when sharing a pizza, measuring ingredients for a recipe, calculating how much money you have, or even when playing games. Understanding them helps you make better decisions and solve problems more easily. In school, fractions and decimals are building blocks for more advanced maths, including percentages, ratios, and algebra.

How it works

Fractions and decimals are two ways to show the same thing – parts of a whole. A fraction is written as numerator/denominator, like 3/4, which means 3 parts out of 4 equal parts. A decimal is a number that uses a decimal point, like 0.75, which means 75 parts out of 100 equal parts. You can think of decimals as fractions where the denominator is a power of 10 (10, 100, 1000, etc.).

Here’s how to convert between them:

1. From fraction to decimal: Divide the numerator by the denominator.
2. From decimal to fraction: Write the decimal as a fraction over a power of 10, then simplify if needed.

Examples you can see

Imagine you are sharing a chocolate bar with your friends. If you cut it into 4 equal pieces and you take 1 piece, you have 1/4 of the bar. This is the same as 0.25 of the bar when written as a decimal.

Let’s try a few examples:

Let’s look at how to change a fraction to a decimal:

• For 1/2, divide 1 by 2 = 0.5
• For 3/4, divide 3 by 4 = 0.75
• For 1/5, divide 1 by 5 = 0.2

Now, how to change a decimal to a fraction:

• 0.5 = 5/10 = 1/2
• 0.25 = 25/100 = 1/4
• 0.7 = 7/10

Try it as a mini adventure

Imagine you are a chef in a kitchen. You need to make a special cake that calls for 1/2 cup of sugar, 3/4 cup of flour, and 0.75 litres of milk. You have measuring cups and a scale. What do you need to do?

First, you need to understand that 1/2 is the same as 0.5, so you need 0.5 cups of sugar.

Then, 3/4 is the same as 0.75, so you need 0.75 cups of flour.

Finally, 0.75 litres of milk is already in decimal form, so you measure 0.75 litres.

Now, let’s play a game! You are at a shop and you have £2.50. You want to buy a toy that costs £1.75. How much money do you have left? You can think of this as: 2.50 - 1.75 = ?

Try to solve it using both fractions and decimals. You might find it easier to work with decimals for money, but fractions can help you understand the parts better.

Common mistakes

• Mistake: Thinking that 0.25 is the same as 1/4 but confusing the decimal point placement.
• Why it happens: Mixing up the place values of decimals.
• Fix: Use visual aids like a number line or a place value chart to show how 0.25 means 2 tenths and 5 hundredths.

• Mistake: Converting 0.3 to 3/100 instead of 3/10.
• Why it happens: Not knowing how many decimal places there are.
• Fix: Count the decimal places: 0.3 has one decimal place, so it's 3/10.

• Mistake: Comparing 0.5 and 1/2 by thinking 0.5 is bigger because it has more digits.
• Why it happens: Not understanding that 0.5 = 1/2.
• Fix: Remember that 0.5 is the same as 1/2, so they are equal.

Parent and carer guide

As a parent or carer, you can help your child by:

• Using real-life examples like cooking, shopping, or splitting a pizza.
• Practising converting between fractions and decimals with simple numbers.
• Encouraging your child to explain their thinking to you.
• Playing games that involve fractions and decimals, like board games or online activities.
• Noticing when your child makes mistakes and helping them understand the correct way, not just saying “wrong”.

Remember to keep the atmosphere fun and encouraging. Fractions and decimals can be tricky, but with practice and real-world connections, your child will get the hang of it!

Practice questions

1. Convert 1/4 to a decimal.
2. Convert 0.6 to a fraction.
3. Which is bigger: 0.3 or 1/3?
4. Convert 7/10 to a decimal.
5. Order these decimals from smallest to largest: 0.2, 0.5, 0.1, 0.8.

Answers:

1. 0.25
2. 3/5
3. 1/3 is bigger (1/3 ≈ 0.333)
4. 0.7
5. 0.1, 0.2, 0.5, 0.8

FAQ

What is the difference between a fraction and a decimal?

A fraction shows parts of a whole using a numerator and denominator, like 3/4. A decimal uses a decimal point to show parts of a whole, like 0.75.

Why do we need to know about fractions and decimals?

Fractions and decimals help us measure, share, and calculate things more precisely. They are used in cooking, shopping, science, and many other areas of life.

How do I know which is bigger: 0.4 or 2/5?

Convert 2/5 to a decimal: 2 ÷ 5 = 0.4. So they are equal!

Can I use a calculator for fractions and decimals?

Yes, calculators can help, but it’s good to understand how to do it by hand first so you know what’s happening.

How can I practice at home?

You can practice by cooking, shopping, or using online games that focus on fractions and decimals. Try to relate them to everyday situations like splitting a pizza or sharing money.