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Fractions are one of the most important topics on the SET 11+ maths papers. You need to understand what fractions mean, how to simplify them, how to compare them, and how to add, subtract, multiply, and divide them. This lesson takes you through each skill with clear worked examples.
A fraction represents a part of a whole. It is written as two numbers separated by a line:
For example, 3/4 means 3 out of 4 equal parts.
Two fractions are equivalent if they represent the same amount. You create equivalent fractions by multiplying or dividing the numerator and denominator by the same number.
Top Tip: Equivalent fractions are the key to comparing fractions and adding fractions with different denominators.
To simplify a fraction, divide the numerator and denominator by their Highest Common Factor (HCF).
Simplify 18/24.
The HCF of 18 and 24 is 6. Divide both by 6:
18 ÷ 6 = 3, and 24 ÷ 6 = 4.
Answer: 3/4
To compare fractions with different denominators, convert them to equivalent fractions with the same denominator (the Lowest Common Multiple of the two denominators).
Which is larger: 3/5 or 5/8?
LCM of 5 and 8 = 40.
25/40 > 24/40, so 5/8 is larger.
Step 1: Find a common denominator. Step 2: Convert each fraction. Step 3: Add or subtract the numerators. Step 4: Simplify if possible.
Calculate 2/3 + 1/4.
LCM of 3 and 4 = 12.
8/12 + 3/12 = 11/12
Calculate 5/6 - 1/4.
LCM of 6 and 4 = 12.
10/12 - 3/12 = 7/12
Answer: 7/12
A mixed number has a whole-number part and a fraction part, such as 2 3/4.
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