What is a fraction?
A fraction describes a part of a whole that has been divided into equal parts.
In the fraction 3/4:
the bottom number, the denominator (4), tells you how many equal parts the whole is divided into,
the top number, the numerator (3), tells you how many of those parts you are taking.
So 3/4 of a chocolate bar means: cut it into 4 equal pieces and take 3 of them.
The parts must be equal. Cutting a roti into 4 pieces of different sizes does not give you quarters.
Types of fractions
Type | Meaning | Examples |
|---|---|---|
Proper | numerator smaller than denominator, so less than 1 | 2/5, 7/9 |
Improper | numerator equal to or bigger than denominator | 7/4, 5/5 |
Mixed | a whole number and a proper fraction | 1¾, 2⅓ |
Like | same denominator | 2/7, 5/7 |
Unlike | different denominators | 1/3, 2/5 |
To turn the improper fraction 7/4 into a mixed fraction, divide: 7 ÷ 4 = 1 remainder 3, so 7/4 = 1¾. To go back, multiply and add: 1¾ = (1 × 4 + 3)/4 = 7/4.
Equivalent fractions
Fractions that show the same amount are equivalent. 1/2, 2/4 and 4/8 all describe half of something.
You get an equivalent fraction by multiplying (or dividing) the numerator and the denominator by the same number:
2/3 = (2 × 4)/(3 × 4) = 8/12
To check whether two fractions are equivalent, cross-multiply. 2/3 and 8/12 are equivalent because 2 × 12 = 3 × 8 = 24.
Simplest form
A fraction is in its simplest form (lowest terms) when the numerator and denominator have no common factor except 1. Divide both by their HCF.
Example. Simplify 18/24. The HCF of 18 and 24 is 6, so 18/24 = 3/4.
Comparing fractions
Same denominator: the bigger numerator is the bigger fraction. 5/9 > 2/9.
Same numerator: the smaller denominator is the bigger fraction, because the pieces are bigger. 3/5 > 3/8.
Different both: change them to equivalent fractions with the same denominator (use the LCM).
Example. Which is bigger, 2/3 or 3/5? The LCM of 3 and 5 is 15. 2/3 = 10/15 and 3/5 = 9/15, so 2/3 is bigger.
Adding and subtracting fractions
Like fractions: add or subtract the numerators and keep the denominator.
2/7 + 3/7 = 5/7, and 5/8 − 1/8 = 4/8 = 1/2
Unlike fractions: first rewrite them with a common denominator (the LCM of the denominators), then add or subtract.
Example. 1/4 + 2/3. The LCM of 4 and 3 is 12, so 1/4 = 3/12 and 2/3 = 8/12. The sum is 3/12 + 8/12 = 11/12.
Example. Riya had 3/4 of a litre of milk and used 1/6 of a litre. How much is left?
3/4 − 1/6 = 9/12 − 2/12 = 7/12 litre.
Common mistakes
Adding the denominators: 1/2 + 1/3 is not 2/5. Use a common denominator: 3/6 + 2/6 = 5/6.
Forgetting to simplify the final answer.
Thinking 1/8 is bigger than 1/5 because 8 > 5. More pieces means smaller pieces.