Question

REDUCING RATIOS
1. 12:108
2. 24:28
3. 44:11
4. 250:400

Answer 1

1. 1 : 9

2. 6 : 7

3. 4 : 1

4. 5 : 8

Explanation:

To reduce a given ratio, divide all of the numbers in the ratio by the highest common factor (HCF) of the numbers.

Question 1

Factors of 12: 1, 2, 3, 4, 6 and 12.

Factors of 108: 1, 2, 3 , 4, 6, 9, 12, 18, 27, 36, 54, and 108.

Therefore, the HCF is 12 so divide both parts of the ratio by 12:

`\implies \sf 12:108=(12)/(12):(108)/(12)=1:9`

Question 2

Factors of 24: 1, 2, 3, 4, 6, 8, 12, and 24.

Factors of 28: 1, 2, 4, 7, 14 and 28.

Therefore, the HCF is 4 so divide both parts of the ratio by 4:

`\implies \sf 24:28=(24)/(4):(28)/(4)=6:7`

Question 3

Factors of 44: 1, 2, 4, 11, 22 and 44.

Factors of 11: 1 and 11.

Therefore, the HCF is 11 so divide both parts of the ratio by 11:

`\implies \sf 44:11=(44)/(11):(11)/(11)=4:1`

Question 4

Factors of 250: 1, 2, 5, 10, 25, 50, 125, 250.

Factors of 400: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200 and 400.

Therefore, the HCF is 50 so divide both parts of the ratio by 50:

`\implies \sf 250:400=(250)/(50):(400)/(50)=5:8`