NCERT Class 8 Mathematics Mathematics: Chapter 7 — Comparing Quantities
This chapter, "Comparing Quantities," from NCERT Class 8 Mathematics, revisits the concepts of ratios and percentages. It explains how to compare quantities using ratios, illustrating with examples like the ratio of fruits in a basket. The chapter details the conversion of ratios to fractions and vice-versa, and how to express comparisons using percentages. It provides a step-by-step solution to a practical problem involving a school picnic, calculating the ratio of girls to boys, the cost per person including transportation and refreshments, and determining percentages of distances covered. This chapter reinforces fundamental mathematical skills essential for understanding more complex quantitative problems in CBSE curriculum.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 8 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Chapter 7 — Comparing Quantities |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 4 minutes |
| Word count | 620 |
Learning outcomes
- Understand and recall the concept of ratios and percentages.
- Compare quantities using ratios and express them as fractions.
- Calculate percentages of given quantities.
- Solve real-world problems involving ratios and percentages.
- Determine the number of boys and girls given the percentage of one gender.
- Calculate total cost and cost per person for an event.
Vocabulary
| Word | Meaning |
|---|---|
| Ratio | A comparison of two quantities by division. |
| Percentage | A number or ratio expressed as a fraction of 100. |
| Fraction | A part of a whole. |
| Unitary Method | A method of finding the value of a required unit by first finding the value of one unit. |
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Practice questions
- If a basket contains 15 apples and 10 oranges, what is the ratio of apples to oranges? Answer: 15:10 or 3:2
- If 40% of students in a class are girls and there are 24 girls, how many students are there in total? Answer: 60 students
- A car travels 100 km. If it has covered 30 km, what percentage of the distance is covered? Answer: 30%
- What is 25% of 200? Answer: 50
Frequently asked questions
What is a ratio?
A ratio is a comparison of two quantities by division, showing how many times one quantity contains the other.
How is a percentage related to a ratio?
A percentage is a way to express a ratio or a fraction out of 100. For example, a ratio of 1:4 is equivalent to 25%.
How do you find the number of boys if you know the percentage of girls and the total number of students?
First, calculate the number of girls using the given percentage. Then, subtract the number of girls from the total number of students to find the number of boys.
What is the unitary method used for?
The unitary method is used to find the value of a required unit by first finding the value of one unit.
How is the cost per head calculated in the picnic example?
It is calculated by dividing the total expenses (refreshments + transportation) by the total number of people attending.
What does it mean if the percentage of apples in a basket is 80%?
It means that out of the total fruits in the basket, 80 out of every 100 fruits are apples.
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NCERT Class 8 Mathematics — Mathematics — Chapter 7 — Comparing Quantities. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.