# Worksheet on Comparison on Ratios

Practice the questions given in the worksheet on comparison on ratios. We know to compare two ratios we need to convert them into equivalent like fractions.

1. Which ratio is the greater 17 : 21 or 23 : 28?

2. Which of the following ratios is greater?

(i) 3 : 5 and 2 : 11

(ii) 2$$\frac{1}{2}$$ : 3$$\frac{3}{4}$$ and 1$$\frac{1}{2}$$ : 1$$\frac{5}{6}$$

3. Write the following ratios in ascending order.

(i) 2 : 3, 7 : 12 and 13 : 19

(ii) 4 : 13, 12 : 19 and 14 : 25

4. Arrange the following ratios in descending order of magnitude

2 : 3, 8 : 15, 11 : 12 and 7 : 16

5. If a > x > 0, prove that (a$$^{2}$$ - x$$^{2}$$) : (a$$^{2}$$ + x$$^{2}$$) > (a - x) : (a + x)

6. If a and b are unequal quantities of the same sign, which of the two ratios (a$$^{2}$$ + b$$^{2}$$) : (a$$^{3}$$ + b$$^{3}$$) and (a + b) : (a$$^{2}$$ + b$$^{2}$$) is greater?

Answers for the worksheet on comparison on ratios are given below.

1. 23 : 28 is greater than 17 : 21.

2. (i) 3 : 5

(ii) 1$$\frac{2}{3}$$ : 1$$\frac{5}{6}$$

3. (i) 7 : 12, 2 : 3, 13 : 19

(ii) 4 : 13, 14 : 25, 12 : 19

4. 11 : 12, 2 : 3, 8 : 15 and 7 : 16

6. (a + b) : (a$$^{2}$$ + b$$^{2}$$)

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