Last reviewed: 10 November 2026
Updated November 2026. These Grade 8 fractions notes cover reciprocals and combined operations on fractions. The reciprocal of a fraction is the fraction turned upside down: the reciprocal of 3/5 is 5/3. In combined operations, work brackets first, then “of”, division and multiplication, then addition and subtraction.
All examples are original practice for Kenyan junior school learners. For the other topics, see our Grade 8 mathematics revision guide and the Grade 8 notes hub.
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What the Grade 8 Curriculum Covers
Fractions is a sub-strand under Numbers in the Kenya Institute of Curriculum Development’s Grade 8 Mathematics design. Learners work out reciprocals of fractions and carry out combined operations on fractions in different situations. The design is listed on the KICD Grade Eight curriculum designs page. Fraction rules are also explained in OpenStax Prealgebra 2e.
Reciprocals
Two numbers are reciprocals if they multiply to give 1. 2/7 × 7/2 = 1.
- Reciprocal of 4/9 is 9/4 (or 2¼).
- Reciprocal of a whole number 6 (= 6/1) is 1/6.
- For a mixed number, change it to an improper fraction first: 1½ = 3/2, so its reciprocal is 2/3.
- Zero has no reciprocal.
Reciprocals are used in division: dividing by a fraction is the same as multiplying by its reciprocal. 3/4 ÷ 3/8 = 3/4 × 8/3 = 2.
Order of Operations With Fractions
Use BODMAS: Brackets, Of, Division, Multiplication, Addition, Subtraction. “Of” means multiply: 2/3 of 12 = 8.
Example. Work out 1/2 + 2/3 × 3/4.
Multiply first: 2/3 × 3/4 = 1/2. Then 1/2 + 1/2 = 1.
Example. Work out (3/4 − 1/2) ÷ 1/8.
Bracket: 3/4 − 2/4 = 1/4. Then 1/4 ÷ 1/8 = 1/4 × 8 = 2.
Example. Work out 2/5 of (1¼ + 3/4) − 1/2.
Bracket: 1¼ + ¾ = 2. Of: 2/5 × 2 = 4/5. Subtract: 4/5 − 1/2 = 8/10 − 5/10 = 3/10.
Fractions in Real Life
A farmer plants 2/5 of a shamba with maize and 1/3 with beans. The rest is for vegetables. Fraction planted = 2/5 + 1/3 = 6/15 + 5/15 = 11/15. Vegetables = 1 − 11/15 = 4/15 of the shamba.
Original Practice Questions With Worked Answers
- Write the reciprocal of 2⅓.
Answer: 2⅓ = 7/3, so the reciprocal is 3/7. - Work out 5/6 ÷ 5/12.
Answer: 5/6 × 12/5 = 2. - Work out 3/4 − 1/4 × 2/3.
Answer: 1/4 × 2/3 = 1/6; 3/4 − 1/6 = 9/12 − 2/12 = 7/12. - Work out 1/3 of 3/5 + 1/5.
Answer: 1/3 × 3/5 = 1/5; 1/5 + 1/5 = 2/5. - Amina spends 1/4 of her pocket money on fare and 2/3 of the remainder on lunch. What fraction is left?
Answer: remainder after fare = 3/4. Lunch = 2/3 × 3/4 = 1/2. Left = 3/4 − 1/2 = 1/4.
Decimals follow on in our Grade 8 decimals notes.
For daily practice across subjects, a Day Pass (KSh 20) or Monthly Pass (KSh 500) opens the full question bank.
Frequently Asked Questions
What is the reciprocal of a fraction?
It is the fraction turned upside down, so that the two multiply to give 1. The reciprocal of 3/5 is 5/3.
What does “of” mean in fractions?
“Of” means multiply. 2/3 of 12 is 2/3 × 12 = 8.
Which operation comes first with fractions?
Follow BODMAS: brackets, then “of”, division and multiplication, then addition and subtraction.
Does zero have a reciprocal?
No. No number multiplied by zero gives 1, so zero has no reciprocal.
Ten-minute check: try the free Grade 8 CBC Challenge. It has 10 questions, each marked on the spot with the working, and it shows which topics to practise next.