Fractions (operations, mixed numbers) — KCSE Mathematics

KCSE Mathematics · 90 practice questions · 4 syllabus objectives

35 easy34 medium21 hard

What You'll Learn

Key learning outcomes for this topic, aligned to the KNEC KCSE syllabus.

Add, subtract, multiply and divide fractions and mixed numbers, expressing answers in their simplest form

Convert between improper fractions and mixed numbers; compare and order fractions on a number line

Apply operations on fractions to solve problems involving proportional sharing, ratios and rates

Fractions (operations, mixed numbers)

Sample Questions

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1
easySHORT ANSWER3 marks

A shop sells 3/4 of a box of chocolates. If a customer buys 1/2 of what is left in the box, what fraction of the original box of chocolates does the customer buy? (3 marks)

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Part (a) — 3 marks
Calculate remaining chocolates: 1 - 3/4 = 1/4 (1 mk)
Calculate amount bought by customer: 1/2 × 1/4 = 1/8 (1 mk)
Identify that the customer bought 1/8 of the original box (1 mk)
2
easySHORT ANSWER3 marks

State which of the two fractions 4/7 and 3/5 is larger and explain your reasoning. (3 marks)

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Part (a) — 3 marks
Convert both fractions to have a common denominator, which is 35 (1 mk)
Rewrite 4/7 as 20/35 and 3/5 as 21/35 (1 mk)
State that 21/35 is larger than 20/35, thus 3/5 is larger than 4/7 (1 mk)
3
easySHORT ANSWER3 marks

Evaluate: 3/4 × 2/5 ÷ 1/2, giving your answer as a fraction in simplest form. (3 marks)

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Part (b) — 3 marks
Multiply 3/4 by 2/5: 3/4 × 2/5 = 6/20 (1 mk)
Divide by 1/2: 6/20 ÷ 1/2 = 6/20 × 2/1 = 12/20 (1 mk)
Simplify 12/20 to 3/5 (1 mk)
4

Calculate the value of 2⅓ + 1⅔ - 1/2, expressing your answer as a mixed number in its simplest form. (3 marks)

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