Fractions, decimals & percentages
Equivalent Fractions: Simplifying, Comparing & Ordering
Year 3 · Year 4 · Year 5 · Year 6
- ✓By the end of this lesson students will be able to recognise and identify equivalent fractions.
- ✓By the end of this lesson students will be able to create equivalent fractions using multiplication and division.
- ✓By the end of this lesson students will be able to simplify fractions to their simplest form.
- ✓By the end of this lesson students will be able to compare and order fractions by finding common denominators.
Key concepts
Equivalent fractions are fractions that look different but represent the same value or amount. Imagine you have a delicious chocolate bar. If you cut it into 2 equal pieces and eat 1 piece, you've eaten 1/2 of the bar. Now, imagine you cut the *same* chocolate bar into 4 equal pieces and eat 2 pieces. You've eaten 2/4 of the bar. Even though the fractions look different (1/2 and 2/4), you've eaten the exact same amount of chocolate! This means 1/2 and 2/4 are equivalent fractions. To find an equivalent fraction, you must multiply or divide both the numerator and the denominator by the same non-zero number.
The numerator is the top number in a fraction. It tells you how many parts of the whole you are considering or have.
The denominator is the bottom number in a fraction. It tells you the total number of equal parts the whole has been divided into.
Simplifying a fraction (also known as reducing a fraction) means finding an equivalent fraction where the numerator and denominator are as small as possible. A fraction is in its simplest form when the only common factor of the numerator and denominator is 1. To simplify a fraction, you divide both the numerator and the denominator by their highest common factor (HCF).
A common denominator is a shared denominator for two or more fractions. When fractions have the same denominator, it makes them much easier to compare, order, add, or subtract. To find a common denominator, you can find the lowest common multiple (LCM) of the original denominators.
Key facts to remember
- 1Equivalent fractions represent the same amount or value, even if they look different.
- 2To find an equivalent fraction, you must multiply or divide both the numerator and the denominator by the same non-zero number.
- 3Simplifying a fraction means writing it in its simplest form, where the numerator and denominator have no common factors other than 1.
- 4To simplify, divide both the numerator and denominator by their highest common factor (HCF).
- 5To compare or order fractions, it is usually easiest to convert them to equivalent fractions with a common denominator.
- 6The numerator is the top number of a fraction; the denominator is the bottom number.
- 7The larger the denominator (for the same numerator), the smaller the fraction (e.g., 1/4 is smaller than 1/3).
Worked examples
Example 1
Find two equivalent fractions for 3/4.
Answer
Two equivalent fractions for 3/4 are 6/8 and 9/12.
You can multiply by any whole number (except zero) to find an equivalent fraction.
Example 2
Simplify 12/18 to its simplest form.
Answer
The simplest form of 12/18 is 2/3.
You could also find the Highest Common Factor (HCF) of 12 and 18, which is 6, and divide both by 6 in one step: 12 ÷ 6 = 2, 18 ÷ 6 = 3.
Example 3
Which fraction is larger: 2/3 or 3/5?
Answer
2/3 is larger than 3/5.
Always find a common denominator before comparing or ordering fractions.
Common mistakes
- ✗Only multiplying or dividing the numerator or the denominator, but not both, when finding equivalent fractions.
- ✗Not simplifying a fraction fully (e.g., simplifying 12/18 to 6/9 instead of 2/3).
- ✗Incorrectly comparing fractions without first finding a common denominator (e.g., thinking 1/3 is smaller than 1/4 because 3 is smaller than 4).
- ✗Forgetting that the number you multiply or divide by must be a whole number (and not zero).
Exam tips
- ★Always show your working when finding equivalent fractions or simplifying, especially in exams.
- ★Use your multiplication tables to help you find common factors for simplifying and common multiples for finding common denominators.
- ★If you are unsure, draw diagrams (like fraction walls or shaded shapes) to visualise equivalent fractions.
- ★When comparing or ordering fractions, always convert them to a common denominator first to avoid errors.
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