Multiplying and dividing fractions
See why fraction × fraction gets smaller, and divide by a fraction with “keep, change, flip”. Read one step, play with it, then tap “I understand this”.
Fraction times fraction
Multiply the numerators and multiply the denominators: 23 × 34 = 612 = 12. “×” means “of” here: 23 of 34.
The area model
Change the two fractions. The green part is the answer.
Multiplying by a fraction smaller than 1 makes a number smaller: half of something is less than the thing itself.
23 of 34: cut a rectangle into 4 columns and into 3 rows. There are now 3 × 4 = 12 equal pieces (the denominator). The part with both colours is 2 × 3 = 6 pieces (the numerator).
A fraction times a whole number
35 × 20 = 20 ÷ 5 × 3 = 12
Divide by the denominator, multiply by the numerator (or the other way round).
Dividing by a fraction
3 ÷ 14 asks: how many quarters fit into 3? Answer: 12. The shortcut is keep, change, flip: keep the first number, change ÷ to ×, and flip the second fraction.
How many fit?
Change the wholes and the fraction.
23 ÷ 45 = 23 × 54 = 1012 = 56
6 ÷ 12 asks: how many halves fit into 6? 2 halves fit into every whole, so 6 × 2 = 12. Dividing by 12 is the same as multiplying by 21: the fraction flipped over.
Mixed numbers
Turn mixed numbers into improper fractions before you multiply or divide: 112 × 23 = 32 × 23 = 66 = 1.
Do not multiply the wholes and fractions separately: 212 × 2 is not 414, but 52 × 2 = 5.
Check yourself
- Fraction × fraction: numerator × numerator, denominator × denominator.
- Divide by a fraction: keep, change ÷ to ×, flip the second fraction.
- Mixed numbers become improper fractions first.
- Multiplying by a fraction smaller than 1 makes the answer smaller.
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 4 steps! Now you are ready for the quiz.- Practice sheet for this classQuestions + memo · 2 A4 pagesPractice sheet
- Numbers9 pages · PDFPaperMemo
Ready for more? The Grade 7 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.
- Halve or double a recipe with fractions together: “34 cup of sugar for half the cake?” (38 cup)
- 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 7 Maths. Always check your teacher’s notes and textbook too.