You are viewing a free preview of this lesson.
Subscribe to unlock all 10 lessons in this course and every other course on LearningBro.
This lesson covers DfE content statements L1.8, L1.9 and L1.16 — reading, writing, ordering and comparing fractions; finding fractions of quantities; and understanding equivalences between common fractions, decimals and percentages.
A fraction describes a part of a whole. It has two numbers:
graph TD
A["3/4"] --> B["3 = Numerator (how many parts you have)"]
A --> C["4 = Denominator (how many equal parts the whole is split into)"]
Everyday example: If a pizza is cut into 4 equal slices and you eat 3 of them, you have eaten 3/4 of the pizza.
| Type | Description | Example |
|---|---|---|
| Proper fraction | Numerator is smaller than denominator | 3/4, 2/5 |
| Improper fraction | Numerator is larger than (or equal to) denominator | 7/4, 5/3 |
| Mixed number | A whole number and a fraction together | 1 3/4, 2 1/3 |
Improper → Mixed: Divide the numerator by the denominator.
Mixed → Improper: Multiply the whole number by the denominator, then add the numerator.
Equivalent fractions look different but have the same value. You create them by multiplying (or dividing) the numerator and denominator by the same number.
| Original | × 2 | × 3 | × 4 |
|---|---|---|---|
| 1/2 | 2/4 | 3/6 | 4/8 |
| 1/3 | 2/6 | 3/9 | 4/12 |
| 3/4 | 6/8 | 9/12 | 12/16 |
| 2/5 | 4/10 | 6/15 | 8/20 |
To simplify (or reduce) a fraction, divide the numerator and denominator by their highest common factor (HCF).
Example: Simplify 8/12.
Scenario: A box contains 20 chocolates. 15 are milk chocolate. What fraction are milk chocolate? Give your answer in its simplest form.
15/20 → divide both by 5 → 3/4
To compare fractions with different denominators, you need to give them the same denominator (a common denominator).
Scenario: Which is larger: 2/3 or 3/5?
Step 1: Find a common denominator. The lowest common multiple of 3 and 5 is 15. Step 2: Convert both fractions:
It is often quicker to compare fractions to a known benchmark like 1/2.
Exam Tip: If you need to order several fractions, convert them all to the same denominator first. Write the converted fractions clearly — the examiner can follow your reasoning and award method marks even if you make a slip.
This is one of the most common exam questions. The method is always the same:
To find a fraction of an amount:
| Fraction | Method | Example: Fraction of £120 |
|---|---|---|
| 1/2 | ÷ 2 | £60 |
| 1/4 | ÷ 4 | £30 |
| 3/4 | ÷ 4, then × 3 | £90 |
| 1/3 | ÷ 3 | £40 |
| 2/3 | ÷ 3, then × 2 | £80 |
| 1/5 | ÷ 5 | £24 |
| 1/10 | ÷ 10 | £12 |
Scenario: A factory has 240 workers. 3/4 of them work full-time. How many work full-time?
Step 1: 240 ÷ 4 = 60 Step 2: 60 × 3 = 180 Answer: 180 workers work full-time.
Scenario: A recipe for 4 people needs 600 g of mince. You want to make it for 2 people — that is half the amount. How much mince do you need?
1/2 of 600 g = 600 ÷ 2 = 300 g
Subscribe to continue reading
Get full access to this lesson and all 10 lessons in this course.