Fractions with different denominators
Add and subtract fractions when the denominators differ, and simplify your answer. Read one step, play with it, then tap “I understand this”.
Make the denominators the same
You can only add pieces of the same size. To do 13 + 16, first turn 13 into sixths: 13 = 26.
The fraction machine
Choose the denominators and numerators. The middle strip shows the new, equal pieces.
If one denominator is a multiple of the other, multiply the smaller denominator (and its numerator) until they match.
29 is smaller than 13 on its own! When you add something, the answer can’t get smaller. The pieces are different sizes, so first change the thirds into sixths: 13 = 26, and 26 + 16 = 36.
Subtracting with different denominators
34 − 38 = 68 − 38 = 38
Do not subtract the denominators: 34 − 38 is not 04. Make the denominators equal first.
In the fraction machine in step 1 you can choose minus too.
Simplify your answer
Divide the numerator and denominator by the biggest number that divides into both. 68 = 34 (both ÷ 2).
Simplify
Choose the simplest form.
Correct: 068 and 34 are exactly the same amount. Simplifying gives the same amount in the fewest, biggest pieces, and that is easier to read and compare.
Mixed numbers
Add the wholes and the fractions separately. If the fractions make more than 1 together, move one whole across.
234 + 112 = 3 + 34 + 24 = 3 + 54 = 414
A fraction of an amount
Divide by the denominator, multiply by the numerator: 35 of R40 = R40 ÷ 5 × 3 = R24.
“Of” means multiply: 35 of 40 = 35 × 40.
3 groups of 4 is 3 × 4. In the same way, 35 of 40 is “35 of a group of 40”, so 35 × 40. Dividing by 5 gives one fifth; multiplying by 3 gives three fifths.
Fractions, decimals and percentages
| Fraction | Decimal | % |
|---|---|---|
| 12 | 0,5 | 50% |
| 14 | 0,25 | 25% |
| 34 | 0,75 | 75% |
| 15 | 0,2 | 20% |
| 110 | 0,1 | 10% |
Percent means “out of 100”. Make the denominator 100, and the numerator is the percentage.
Check yourself
- Different denominators? Make them the same first (use the LCM).
- Simplify: divide top and bottom by the HCF.
- Mixed numbers: add the wholes and the fractions separately.
- “Of” means multiply: 35 of 40 = 40 ÷ 5 × 3 = 24.
- Percent is out of 100: 34 = 75100 = 75%.
Write these points in your maths book. Read them again the night before the test.
Quick questions
Tap an answer. If you get one wrong, read why and go back to that step. You get new questions every time.
You ticked all 6 steps! Now you are ready for the quiz.- Practice sheet for this classQuestions + memo · 2 A4 pagesPractice sheet
- Numbers16 pages · PDFPaperMemo
Ready for more? The Grade 6 fractions quiz gives you new questions every time.
- One step a day is enough. Ten calm minutes work better than an hour the night before the test.
- Bake together: a recipe for 4 people must be halved for 2. “34 cup of flour divided by 2?” Fractions then make sense.
- Ask your child to tell you the rule in their own words. If they can explain it, they understand it.
- The ticks (“I understand this”) are saved on this device only. We never ask for names or emails.
Follows CAPS for Grade 6 Maths. Always check your teacher’s notes and textbook too.