Operations on Fractions
Primary 6 · Mathematics
Operations on Fractions
Lesson 3 of 6
30 min
Let's begin
Ishimwe's family plants beans on 34 of their plot. On 23 of the bean part, they plant climbing beans. What fraction of the whole plot has climbing beans? We need 23 of 34.
Draw the plot as a rectangle. Cut it into 4 columns and shade 3 of them for the beans (34). Now cut it into 3 rows and take 2 of the rows (23 of the beans).
| ▓ | ▓ | ▓ | · |
| ▓ | ▓ | ▓ | · |
| ░ | ░ | ░ | · |
▓ = climbing beans (in 3 columns and 2 rows) ░ = other beans · = no beans
The rectangle has 3 × 4 = 12 small parts. Climbing beans cover 2 × 3 = 6 of them. So 23 of 34 = 612 = 12 of the plot.
Look at where the numbers came from: 2 × 3 = 6 on top, 3 × 4 = 12 on the bottom.
To multiply fractions, multiply the numerators together and multiply the denominators together. Then simplify.
Worked example
45 × 27 = (4 × 2)/(5 × 7) = 835.
If a numerator and a denominator share a factor, divide both by it before multiplying. The numbers stay small.
Worked example
23 × 34
Always change mixed numbers to improper fractions first.
Worked example
1 12 × 2 23
Careful: do not multiply the whole numbers and the fractions separately. 1 × 2 and 12 × 23 would give 2 13, which is wrong.
When you multiply by a fraction less than 1, you take only part of something. So 12 × 34 = 38 is smaller than both 12 and 34.
Tip
Top times top, bottom times bottom. No common denominator is needed to multiply. Cancel first to keep the numbers friendly.
Work each one in your exercise book first, then tap Show answer to check.
35 × 23
Answer: 25. Cancel the 3s first.
58 × 415
Answer: 16. Cancel 5 with 15 and 4 with 8.
1 13 × 34
Answer: 43 × 34 = 1.
2 12 × 1 15
Answer: 52 × 65 = 3.
A farmer has 56 of a hectare. He plants maize on 35 of it. What part of a hectare is maize?
Answer: 35 × 56 = 12 of a hectare.
What you learned today
Sources and credits
The stories, Rwandan worked examples and practice questions were written by Ganzaa.
Quick check
2/5 × 3/4 = ?
