Ratio: complete guide with one liner questions

Ratio: A Complete Guide

1. Definition and Examples

A ratio is a comparison of two numbers, often written as a fraction or using a colon (:).

• Examples: 1:2, 3:4, 2/3

Questions:

Q1. What is the ratio of 3 to 4?

A1. The ratio is 3:4 or 3/4.

Q2. Express the ratio 2:3 as a fraction.

A2. The ratio 2:3 can be written as 2/3.

Q3. If a:b = 2:3, what is the value of a/b?

A3. a/b = 2/3.

Q4. What is the ratio of boys to girls in a class of 20 boys and 15 girls?

A4. The ratio is 20:15 or 4:3.

Q5. If x:y = 1:2, what is the value of x+y:y?

A5. x+y:y = (1+2):2 = 3:2.

Q6. Express the ratio 5:10 in simplest form.

A6. The simplest form is 1:2.

Q7. What is the ratio of 10 cm to 20 cm?

A7. The ratio is 1:2.

Q8. If a:b = 3:4, what is the value of b/a?

A8. b/a = 4/3.

Q9. What is the ratio of 2 hours to 3 hours?

A9. The ratio is 2:3.

Q10. Express the ratio 12:16 in simplest form.

A10. The simplest form is 3:4.

Q11. If x:y = 2:3, what is the value of x:x+y?

A11. x:x+y = 2:(2+3) = 2:5.

Q12. What is the ratio of 5 kg to 10 kg?

A12. The ratio is 1:2.

Q13. If a:b = 1:2, what is the value of a-b:b?

A13. a-b:b = (1-2):2 = -1:2.

Q14. Express the ratio 7:14 in simplest form.

A14. The simplest form is 1:2.

Q15. What is the ratio of 3:6 in simplest form?

A15. The simplest form is 1:2.

2. Types of Ratios

Ratios can be classified into different types:

• Simple Ratio: A ratio of two numbers, e.g., 2:3
• Compound Ratio: A ratio of ratios, e.g., (2:3):(4:5)
• Duplicate Ratio: A ratio of squares, e.g., (2:3)^2 = 4:9
• Triplicate Ratio: A ratio of cubes, e.g., (2:3)^3 = 8:27

Questions:

Q1. What is the compound ratio of (2:3):(4:5)?

A1. The compound ratio is (2*4):(3*5) = 8:15.

Q2. What is the duplicate ratio of 2:3?

A2. The duplicate ratio is (2:3)^2 = 4:9.