Exam-Style Questions on Fractions

1.	IGCSE Core

Without using your calculator, work out the value of the following calculations giving each answer as a fraction in its lowest terms. You must show all your working.

(a)

$$1\frac{5}{12} - \frac58$$

(b)

$$\frac49 ÷ 6\frac23$$

Worked Solution

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2.	IGCSE Extended

In January, a supermarket sold 12 624 boxes of breakfast cereal.

(a) The cost of a box of cereal was £2.15 . Calculate the amount received from the sale of the 12 624 boxes. Give your answer correct to the nearest hundred pounds.

(b) The number of boxes sold in February was 13% more than the number sold in January. Calculate the number of boxes sold in February.

(c) There were 3 different types of cereal. The number of boxes sold of each type every month was in the ratio Riceflakes : Cornflakes : Branflakes = 4 : 5 : 3. The total number of boxes sold was 12 624. Calculate the number of boxes of Branflakes sold.

(d) How may more boxes of Cornflakes than Riceflakes were sold in February?

(e) \(\frac{5}{6}\) of the 12 624 bottles sold in January are included in a special promotion. Calculate the number of boxes that are included in that promotion.

Worked Solution

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3.	GCSE Higher

Find the product of the two numbers below giving your answer as a mixed number in its simplest form.

$$ 3 \frac{2}{3} $$

$$ 4 \frac{2}{5} $$

Worked Solution

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4.	GCSE Higher

Unit fractions have numerators equal to 1, for example \(\dfrac12\),\(\dfrac19\) and \(\dfrac{1}{36}\).

Unit fractions can be written as the sum of two different unit fractions, for example

$$\frac12 = \frac13 + \frac16$$

Write each of the following unit fractions as the sum of two different unit fractions.

(a) \(\dfrac14\)

(b) \(\dfrac16\)

(c) \(\dfrac19\)

Worked Solution

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5.	IB Analysis and Approaches

Express the following algebraic fractions as the sum of two partial fractions:

(a)

$$ \dfrac{10x+29}{x^2+3x-10} $$

(b)

$$ \dfrac{10x+1}{2x^2-5x+2} $$

(c) Hence or otherwise simplify the following:

$$ \dfrac{10x+29}{x^2+3x-10} - \dfrac{10x+1}{2x^2-5x+2}$$

Worked Solution

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