Operations on Fractions

Lessons

Primary 6 · Mathematics

Operations on Fractions

6 lessons

Lesson 6 of 6

Solving problems with fractions

35 min

Let's begin

Fractions are everywhere in family life in Rwanda: sharing land, planning a salary, filling bottles from a jerrycan. In this lesson you will decide which operation each problem needs, and solve problems with more than one step.

Which operation?

“a fraction of” an amount → multiply.
“how many … fit / can be filled” → divide.
“shared equally among” → divide.
“what is left” → subtract from the whole (the whole is 1).

Worked example 1

(salary): Gatete earns 240 000 Frw a month. He spends 13 on rent and 14 on food. How much is left?

Fraction spent: 13 + 14 = 412 + 312 = 712.
Fraction left: 1 − 712 = 512.
Money left: 512 of 240 000 = 240 000 ÷ 12 × 5 = 20 000 × 5 = 100 000 Frw.
Check: rent 80 000, food 60 000, left 100 000. ✔

Worked example 2

(a fraction of the remainder): A farmer harvested 60 bags of maize. He sold 25 of them. He gave 13 of the remaining bags to his relatives. How many bags does he have left?

Sold: 25 of 60 = 60 ÷ 5 × 2 = 24 bags.
Remaining: 60 − 24 = 36 bags.
Given away: 13 of 36 = 12 bags.
Left: 36 − 12 = 24 bags.

Careful: “13 of the remainder” is 13 of 36, not 13 of 60.

Worked example 3

(how many fit): A jerrycan holds 22 12 litres of water. How many 34-litre bottles can be filled from it?

22 12 ÷ 34 = 452 ÷ 34.
Keep, change, flip: 452 × 43 = 1806 = 30 bottles.

Worked example 4

(finding the whole): 35 of the pupils in a class are girls. There are 18 girls. How many pupils are in the class?

35 of the class = 18, so 15 of the class = 18 ÷ 3 = 6.
The whole class (55) = 6 × 5 = 30 pupils.
This is the same as 18 ÷ 35 = 18 × 53 = 30.

Worked example 5

(sharing land): A plot of 4 12 hectares is shared equally among 3 children. Each child plants coffee on 23 of his or her share. How much land does each child use for coffee?

Each share: 4 12 ÷ 3 = 92 × 13 = 32 = 1 12 hectares.
Coffee: 23 of 1 12 = 23 × 32 = 1 hectare.

Tip

Read, draw, decide. Read the problem twice, draw a quick bar for the whole, and decide the operation before you calculate. Always ask: “a fraction of WHAT?”

✦

Try it yourself

Work each one in your exercise book first, then tap Show answer to check.

1

Uwase has 12 000 Frw. She spends 14 on a book and 13 on a school bag. How much is left?

Show answerHide answer

Answer: Spent 3 000 + 4 000 = 7 000, so 5 000 Frw is left.

2

How many 1 12-litre bottles can be filled from 12 litres of juice?

Show answerHide answer

Answer: 12 ÷ 32 = 12 × 23 = 8 bottles.

3

23 of a number is 40. What is the number?

Show answerHide answer

Answer: 40 ÷ 2 × 3 = 60.

4

A shop had 48 kg of rice. It sold 58 of it on Monday and 12 of the rest on Tuesday. How much rice is left?

Show answerHide answer

Answer: Monday: 30 kg; rest 18 kg; Tuesday: 9 kg; left 9 kg.

Quick check

Match each kind of question to what you do.

Tap one on the left, then its partner on the right.

What you learned today

“Of” → multiply; “how many fit” and “shared equally” → divide; “left” → subtract from 1 whole.
In two-step problems, notice whether a fraction is of the WHOLE or of the REMAINDER.
To find the whole from a part, divide the part by its fraction.

Sources and credits

4.3 Multiply and Divide Fractions, from Prealgebra 2e by Lynn Marecek, MaryAnne Anthony-Smith and Andrea Honeycutt Mathis, OpenStax (read on LibreTexts), licensed under CC BY 4.0. Adapted by Ganzaa.
Grade 6, Unit 4: Dividing Fractions (lessons 1–11), IM 6–8 Math, authored by Illustrative Mathematics and originally developed by Open Up Resources, licensed under CC BY 4.0. Adapted by Ganzaa.

The stories, Rwandan worked examples and practice questions were written by Ganzaa.

1Which operation?

Try it yourself

Which operation?