GCSELearning PackNumberFractions

Fractions Learning Pack

GCSE explanations, worked examples and practice for Fractions, covering Fractions meaning, Fractions representations, Fractions methods.

Resource

Work through the content for this resource.

Learning Pack

Fractions

1. Understand

Connect real objects, bar models and number lines

2. Build

Use equivalence to compare and calculate

3. Practise

Move from supported questions to mixed problems

4. Check

Reveal answers and identify the next skill to revisit

What you will learn

Understand fractions as parts of a whole, positions on a number line and division
Use equivalent fractions to compare, simplify and calculate accurately
Solve fluency and problem-solving questions involving fractions

Before you start

Know times tables and common factors
Understand numerator and denominator
Use multiplication and division accurately
Recognise halves, quarters, fifths, tenths and hundredths

A fraction compares a part with a whole. The denominator tells you how many equal parts the whole is split into, and the numerator tells you how many of those parts are being used.

1. Fractions of real objects

Fractions often start with real objects. If a cake is cut into 2 equal pieces, one piece is 12. If a pizza is cut into 3 equal slices, one slice is 13.

The pieces must be equal size
12 means 1 out of 2 equal parts
13 means 1 out of 3 equal parts

A round cake cut into two equal halves with one half highlighted

12 of the cake is shaded

A pizza cut into three equal slices with one third highlighted

13 of the pizza is shaded

2. What a fraction represents

Start by seeing the whole as equal parts. In 35, the whole is split into 5 equal parts and 3 parts are selected.

The denominator names the number of equal parts
The numerator counts how many parts are selected
The parts must be equal size

35 of the whole is shaded

Numerator: 3 selected parts

Denominator: 5 equal parts

3. Equivalent fractions

Equivalent fractions look different but have the same value. You make them by multiplying or dividing the numerator and denominator by the same number.

12, 24 and 48 cover the same amount
The value stays the same because the whole has been split into smaller equal parts
Equivalent fractions help with comparing, adding and subtracting

4. Fractions on a number line

A fraction is also a position between whole numbers. To place 34, split the distance from 0 to 1 into 4 equal jumps, then count 3 jumps.

The denominator tells you how many equal intervals to make
The numerator tells you how many intervals to count along
This helps with ordering fractions

5. Adding fractions

Fractions can only be added directly when the parts are the same size. If the denominators are different, rewrite one or both fractions using a common denominator.

14 is the same as 28
28 + 38 = 58
Only add the numerators once the denominators match

14 = 28

28 + 38 = 58

6. Fractions of amounts

To find a fraction of an amount, divide by the denominator to find one equal part, then multiply by the numerator to find the required number of parts.

For 35 of 20, divide 20 by 5 first
One fifth of 20 is 4
Three fifths of 20 is 3 × 4 = 12

35 of 20 = 12

Each row shows one fifth of the amount

7. Multiplying fractions

An area model shows why multiplying fractions means finding a fraction of another fraction. In the model, 23 of 34 is the overlapping region.

Multiply the numerators
Multiply the denominators
Simplify the answer where possible

3/42/3overlap

23 × 34 = 612 = 12

8. Improper fractions and mixed numbers

A mixed number combines whole ones and a fraction. An improper fraction records the same amount using only equal fractional parts.

One whole is the same as 44
1 34 is the same as 74
Convert mixed numbers before multiplying or dividing

one whole = 44

three more quarters = 34

1 34 = 74

Key vocabulary

numerator
denominator
equivalent
simplify
improper fraction
mixed number
common denominator
reciprocal

Key facts and methods

Equivalent fractions have the same value but use different numerators and denominators
To simplify a fraction, divide the numerator and denominator by the same common factor
To add or subtract fractions, use a common denominator first
To multiply fractions, multiply the numerators and multiply the denominators
To divide by a fraction, multiply by its reciprocal
A fraction of an amount can be found by dividing by the denominator, then multiplying by the numerator

Learning route

Decide whether the question is asking you to compare, simplify, calculate or find a fraction of an amount
Check whether the denominators are already the same
Use equivalent fractions when the denominators need to match
Simplify the final answer where possible
Check whether the answer should be written as a fraction, mixed number or whole number

Worked example 1

Simplify 1824

1. Find a common factor of 18 and 24

2. Both numbers divide by 6

3. 1824 = 34

Answer: 34

Worked example 2

Calculate 23 + 512

1. Use 12 as a common denominator

2. 23 = 812

3. 812 + 512 = 1312

4. 1312 = 1 112

Answer: 1 112

Worked example 3

Find 35 of 40

1. Divide 40 by the denominator: 40 / 5 = 8

2. Multiply by the numerator: 8 times 3 = 24

3. So 35 of 40 is 24

Answer: 24

Practice 1

Start here

Check the core ideas before moving into calculations.

Question 1

Write 35 as an equivalent fraction with denominator 20

Reveal answer

1220

Question 2

Simplify 1435

Reveal answer

Question 3

Write 1 34 as an improper fraction

Reveal answer

Practice 2

Build fluency

Choose the correct calculation method and simplify each answer.

Question 1

Calculate 14 + 38

Reveal answer

Question 2

Calculate 45 - 13

Reveal answer

715

Question 3

Calculate 38 × 49

Reveal answer

Question 4

Calculate 56 / 23

Reveal answer

54 or 1 14

Practice 3

Apply the idea

Use fractions in context and explain your reasoning.

Question 1

A recipe uses 34 kg of flour. Sam makes 23 of the recipe. How much flour does Sam use

Reveal answer

12 kg

Question 2

A tank is 58 full. 12 litres are added and it becomes 78 full. Find the capacity of the tank

Reveal answer

48 litres

Question 3

A student says 23 + 14 = 37. Explain the mistake and give the correct answer

Reveal answer

The denominators must match before adding. 23 + 14 = 812 + 312 = 1112

Common misconceptions

Adding denominators as well as numerators
Simplifying by subtracting instead of dividing
Forgetting to convert mixed numbers before multiplying or dividing
Using a common denominator for multiplication when it is not needed
Leaving an answer unsimplified when the question asks for simplest form

Check understanding

Why does multiplying the numerator and denominator by the same number keep the value the same
When do fractions need a common denominator
What is the reciprocal of 35
How can you check that 1824 and 34 are equivalent
Which operation is needed to find 23 of 45

Ready to move on?

I can simplify fractions using common factors
I can find equivalent fractions with a chosen denominator
I can add and subtract fractions using common denominators
I can multiply and divide fractions
I can find a fraction of an amount
I can decide whether to leave an answer as an improper fraction or mixed number