In worksheet on ratios the questions are related to the basic concept of ratio, ratio in the simplest form, comparison of ratios, conversion of ratios, and also find the equivalent ratios. Recall the topic and then practice the questions on ratio.
1. Express the following ratios in the simplest form.
(a) 30 : 45
(b) 250 : 100
(c) 1.5 : 5.1
(d) 2.1 : 7
(e) 8x : 12x
(f) 2¹/₆ ∶ 1¹/₃
(g) ¹/₈ ∶ ¹/₁₀
(h) ²/₃ ∶ ⁵/₇ : 1
(i) 2¹/₅ ∶ 1¹/₄ : 1¹/₅
(j) ²/₅ ∶ ³/₁₀
(k) ¹/₂ ∶ ¹/₄ ∶ ¹/₆
(l) 4p²q : 10pq²
(m) a dozen to a score
(n) 9 months : 2¹/₂ years
(o) 5 m : 600 cm
2. Compare the following ratios.
(a) 2 : 3 and 4 : 5
(b) 11 : 19 and 19 : 21
(c ) ¹/₂ ∶ ¹/₃ and ¹/₃ ∶ ¹/₄
(d) 1¹/₅ : 1¹/₃ and ²/₅ ∶ ³/₂
3. (a) If a : b = 6 : 5 and b : c = 10 : 9, find a : c.
(b) If x : y = ¹/₆ ∶ ¹/₈ and y : z = ¹/₈ ∶ ¹/₁₀, find x : z
(c) If p : q = 1¹/₂ : 2¹/₃ and q : r = 1¹/₃ : ²/₅ find p : q : r
(d) If a : b = 6 : 7 and b : c = 3 : 5, find a : b : c
4. Are the following ratios equivalent?
(a) 3 : 5 and 15 : 25
(b) 1 : 4 and 2 : 3
(c) 8 : 3 and 24 : 30
(d) 2.5 : 3.5 and 0.5 : 0.7
Worksheet on Word Problems on Ratios:
5. In a school library, the ratio of science books to that of math books is 4 : 5. If there are 384 science books, find the number of math books in the library.
6. The ratio of the number of male and female teachers in a school is 2 : 11. If the number of male teachers is 112, find the number of female teachers.
7. An alloy contains zinc and copper in the ratio 7 : 9. Find the weight of copper if it has 31.5 kg of zinc.
8. Two numbers are in the ratio 7 : 5. If their difference is 96, find the numbers.
9. Two numbers are in the ratio 3 : 2 and their sum is 60. Find the numbers.
10. The three angles of a scalene triangle are in the ratio 2 : 3 : 5. Find the measures of the angles.
11. Divide $90 in the ratio 7 : 8.
12. Divide 36 chocolates in the ratio 2 : 3 : 4.
13. A line segment of length 20 cm is divided into three parts in the ratio 1 : 2 : 3. Find the length of each part.
14. A certain amount is divided into two parts in the ratio 4 : 5. If the first part is 120, find the total.
15. Divide $700 into three parts such that the first part is 2/3 of the second and the ratio between the second and third is 4 : 5.
16. Divide 108 bottles of juice between A and B in the ratio ¹/₅ : ¹/₇.
17. The sides of the quadrilateral are in the ratio 1 : 2 : 3 : 4 and the perimeter is 40 cm. Find the length of each side.
18. Divide one month profit of $ 10,000 between Michael and Robert in a ratio 1 : 4.
19. Divide 1000 in two parts such that the ratio of parts be 7 : 3.
20. The number of cards collected by Mary, Jennifer and Elizabeth are in the ratio 1 : 3 : 5 respectively. If Mary has a collection of 45 cards, find the number of cards with Jennifer and Elizabeth.
Answers for the worksheet on ratios are given below to check the exact answers of the questions.
1. (a) 2 : 3
(b) 5 : 2
(c) 5 : 17
(d) 3 : 10
(e) 2 : 3
(f) 13 : 8
(g) 5 : 4
(h) 14 : 15 : 21
(i) 44 : 25 : 24
(j) 4 : 3
(k) 6 : 3 : 2
(l) 2p : 5q
(m) 3 : 5
(n) 3 : 10
(o) 5 : 6
2. (a) 2/3 < 4/5
(b) 11 : 19 < 19 : 21
(c) 1/2 ∶ 1/3 > 1/3 ∶ 1/4
(d) 1¹/₅ ∶ 1¹/₃ > ²/₅ ∶ ³/₂
3. (a) 4 : 3
(b) 5 : 3
(c) 45 : 70 : 21
(d) 18 : 21 : 35
4. (a) equivalent
(b) not equivalent
(c) not equivalent
(d) equivalent
5. 480
6. 616
7. 40.5 kg
8. 336, 240
9. 36, 24
10. 36°, 54°, 90°
11. $42, $48
12. 8, 12, 16 chocolates
13. 3¹/₃ cm, 6²/₃ cm, 10 cm
14. 270
15. $160, $240, $300
16. 63 bottles, 45 bottles
17. 4 cm, 8 cm, 12 cm, 16 cm
18. Michael = $ 2,000 and Robert = $ 8,000
19. 700 and 300
20. Jennifer = 135 and Elizabeth = 225
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