Last reviewed: 25 October 2026
Fractions are one of the topics Grade 6 learners most often lose marks on, not because the ideas are hard but because small steps get skipped. This guide walks through every fraction skill an upper primary learner needs, with a worked example for each, so a parent can sit with a child and check the method rather than just the answer. Fractions are a sub-strand of Numbers in KICD’s Grade 6 Mathematics curriculum design.
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What a Fraction Means
A fraction shows part of a whole. In 3/4, the bottom number (the denominator) tells you the whole was cut into 4 equal parts, and the top number (the numerator) tells you 3 of those parts are being counted. A proper fraction has a smaller numerator than denominator, like 3/4. An improper fraction has a numerator equal to or larger than the denominator, like 7/4. A mixed number combines a whole number and a fraction, like 1 3/4, which is the same amount as 7/4.
Converting: to turn 2 2/5 into an improper fraction, multiply the whole number by the denominator and add the numerator: 2 × 5 + 2 = 12, so 2 2/5 = 12/5. To go back, divide: 12 ÷ 5 = 2 remainder 2, so 12/5 = 2 2/5.
Equivalent Fractions and Simplifying
Equivalent fractions name the same amount. Multiply or divide the top and bottom by the same number: 2/3 = 4/6 = 8/12. To simplify, divide both by their highest common factor. For 18/24, the highest common factor is 6, so 18/24 = 3/4. Examiners expect answers in their simplest form, so make simplifying the last step of every question.
Comparing and Ordering Fractions
When denominators are the same, the larger numerator is the larger fraction. When they differ, rewrite them with a common denominator. To compare 3/5 and 2/3, use 15: 3/5 = 9/15 and 2/3 = 10/15, so 2/3 is larger. Ordering a list works the same way: change every fraction to the lowest common denominator, then arrange the numerators.
Adding and Subtracting Fractions
You can only add or subtract fractions with the same denominator. Find the lowest common multiple of the denominators first.
- Example: 1/4 + 2/3. The LCM of 4 and 3 is 12. 1/4 = 3/12 and 2/3 = 8/12, so the sum is 11/12.
- Mixed numbers: 3 1/2 − 1 2/3. Change to improper fractions: 7/2 − 5/3 = 21/6 − 10/6 = 11/6 = 1 5/6.
The common mistake is adding the denominators (1/4 + 2/3 = 3/7 is wrong). A quick check: the answer to an addition must be bigger than each fraction you started with.
Multiplying Fractions
Multiply the numerators together and the denominators together, then simplify. 2/3 × 3/5 = 6/15 = 2/5. With a whole number, treat it as a fraction over 1: 4 × 3/8 = 12/8 = 1 1/2. You can cancel before multiplying to keep numbers small: in 2/3 × 3/5, the 3s cancel, leaving 2/5 straight away. “Of” means multiply, so 3/4 of 20 = 15.
Dividing Fractions
To divide by a fraction, multiply by its reciprocal (turn the second fraction upside down). 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 1 1/2. This makes sense: there are one and a half halves in three quarters. With mixed numbers, convert to improper fractions first, then flip only the second fraction.
Word Problems
Most exam fraction marks come from short stories. Read for the whole first, then the part.
- A farmer planted maize on 2/5 of a 30-acre farm. How many acres? 2/5 × 30 = 12 acres.
- Wanjiru spent 1/3 of her money on books and 1/4 on fare. What fraction is left? 1/3 + 1/4 = 7/12 spent, so 5/12 is left.
- A 3/4 litre bottle fills cups of 1/8 litre. How many cups? 3/4 ÷ 1/8 = 6 cups.
Encourage your child to write one line per step. In a multiple-choice paper, wrong options are often the answers you get from a skipped step, so neat working protects marks.
A Ten-Minute Daily Routine
Do three questions a day: one adding or subtracting, one multiplying or dividing, and one word problem. Mark them together and talk through any mistake. The exam countdown gives five free questions a day, and after a practice paper the What to Revise report shows whether fractions are still a weak area. For more, see the Grade 6 hub and Grade 6 Mathematics revision papers.
The first questions of every paper are free. Full timed papers with worked answers are in the Monthly Pass (KSh 500 by M-Pesa), and printed practice is available in our KPSEA Grade 6 revision books. Questions are checked by a teacher before they go live.
Ten-minute check: try the free Grade 6 CBC Challenge. It has 10 questions, each marked on the spot with the working, and it shows which topics to practise next.