Operations on Fractions
Primary 6 · Mathematics
Operations on Fractions
Lesson 4 of 6
30 min
Let's begin
Mutesi bakes 3 round cakes for her sister's birthday and cuts each cake into quarters. How many pieces does she have? She is asking: how many quarters are there in 3? That is 3 ÷ 14.
Two numbers are reciprocals if they multiply to give 1. To find the reciprocal of a fraction, flip it: swap the numerator and the denominator.
| Number | Reciprocal | Check |
|---|---|---|
| 25 | 52 | 25 × 52 = 1010 = 1 |
| 7 (= 71) | 17 | 7 × 17 = 1 |
| 1 34 (= 74) | 47 | 74 × 47 = 1 |
0 has no reciprocal, because nothing times 0 gives 1.
Division asks “how many groups?” 3 ÷ 14 asks “how many quarters fit into 3 wholes?”
Each cake gives 4 quarters, so 3 cakes give 3 × 4 = 12 pieces. Notice: dividing by 14 gave the same answer as multiplying by 4, its reciprocal.
Worked example
A trader has 6 litres of juice. She pours it into cups that hold 23 of a litre. How many cups can she fill?
This is sharing a part into equal shares.
Worked example
3 children share 34 of a litre of milk equally. How much does each child get?
To divide by any number, multiply by its reciprocal. Write whole numbers over 1 first: 3 = 31.
Tip
Dividing by a fraction? Flip it and multiply. Only the number you divide BY gets flipped, never the first number.
Work each one in your exercise book first, then tap Show answer to check.
Write the reciprocal of 59 and of 8.
Answer: 95 and 18.
How many halves are there in 7?
Answer: 7 ÷ 12 = 7 × 2 = 14.
4 ÷ 25
Answer: 4 × 52 = 202 = 10.
23 ÷ 4
Answer: 23 × 14 = 212 = 16.
A rope 9 m long is cut into pieces 34 m long. How many pieces are there?
Answer: 9 × 43 = 363 = 12 pieces.
What you learned today
Sources and credits
The stories, Rwandan worked examples and practice questions were written by Ganzaa.
Quick check
Match each number to its reciprocal.
Tap one on the left, then its partner on the right.
