Ratio and Proportion for Class 6 Mathematics
Ratio and Proportion for Class 6 Mathematics is taught as a complete chapter lesson, not as a loose revision list. Ratio and Proportion helps students compare quantities fairly. The source NCERT solutions cover ratios of students, games, shapes, speeds, units, money, ages, sharing in a ratio, equivalent ratios, proportions, middle terms, and extreme terms. In this lesson, we will move through the chapter topic by topic: Meaning and Order of Ratio, Simplifying Ratios and Equivalent Ratios, Ratios With Units, Sharing in a Given Ratio, Proportion, Middle Terms, and Extreme Terms. The goal is to understand the concept, connect it to examples, practise questions, and write answers clearly in tests.
How This Lesson Helps You Learn
Understand
Definitions, formulas, proofs, explanations, and diagrams come first.
Clarify
Common confusion points are handled through direct rules, examples, and mistakes.
Practise
Worked examples, try-it-yourself tasks, quizzes, and questions help you test yourself.
1. Introduction
Ratio and Proportion for Class 6 Mathematics is taught as a complete chapter lesson, not as a loose revision list. Ratio and Proportion helps students compare quantities fairly. The source NCERT solutions cover ratios of students, games, shapes, speeds, units, money, ages, sharing in a ratio, equivalent ratios, proportions, middle terms, and extreme terms.
In this lesson, we will move through the chapter topic by topic: Meaning and Order of Ratio, Simplifying Ratios and Equivalent Ratios, Ratios With Units, Sharing in a Given Ratio, Proportion, Middle Terms, and Extreme Terms. The goal is to understand the concept, connect it to examples, practise questions, and write answers clearly in tests.
2. Learning Objectives
- Understand the main idea of Ratio and Proportion: how quantities are compared by ratio and how equal ratios form a proportion.
- Explain meaning and order of ratio with examples.
- Explain simplifying ratios and equivalent ratios with examples.
- Explain ratios with units with examples.
- Explain sharing in a given ratio with examples.
- Explain proportion, middle terms, and extreme terms with examples.
- Use diagrams, tables, or flowcharts wherever they make the explanation clearer.
- Practise short-answer, application, and worked-example questions.
3. Prerequisites
- You should know the basic vocabulary used in Mathematics.
- You should be ready to read Ratio and Proportion slowly and connect each idea to one example.
- You should keep a notebook for definitions, diagrams, solved examples, and mistakes.
4. What Is Ratio and Proportion?
Ratio and Proportion centres on how quantities are compared by ratio and how equal ratios form a proportion. The ratio of a to b is written as a:b.
5. Key Definitions
- Ratio and Proportion: the main chapter idea explained in Mathematics using meaning, reason, example, and practice.
- A ratio compares two quantities of the same kind.
- The order of a ratio matters.
- Ratios should be simplified to lowest terms.
- Quantities must be converted to the same unit before forming a ratio.
- A proportion is equality of two ratios.
6. Concept Explanation
- A ratio compares two quantities of the same kind.
- The order of a ratio matters.
- Ratios should be simplified to lowest terms.
- Quantities must be converted to the same unit before forming a ratio.
- A proportion is equality of two ratios.
- In a:b :: c:d, a and d are extreme terms; b and c are middle terms.
- Sharing in a ratio uses total parts.
Topic-by-Topic Explanation
These explanations break the chapter into important topics, sub-topics, examples, and visual prompts so the lesson is easier to revise.
Meaning and Order of Ratio
The ratio of a to b is written as a:b.
If there are 20 girls and 15 boys, the ratio of girls to boys is 20:15 = 4:3.
Girls to boys is different from boys to girls.
A ratio should usually be written in simplest form.
Draw 20 marks for girls and 15 for boys, then group both by 5 to show 4:3.
Simplifying Ratios and Equivalent Ratios
To simplify a ratio, divide both terms by their highest common factor.
81:108 becomes 3:4 because both numbers can be divided by 27.
Equivalent ratios are formed by multiplying or dividing both terms by the same non-zero number.
For example, 4:6 and 8:12 are equivalent because both simplify to 2:3.
Show 81:108 divided by 27 on both sides to become 3:4.
Ratios With Units
Ratios can be compared only after the quantities are in the same unit.
30 minutes to 1.5 hours becomes 30 minutes to 90 minutes, so the ratio is 1:3.
40 cm to 1.5 m becomes 40 cm to 150 cm, so the ratio is 4:15.
500 ml to 2 litres becomes 500 ml to 2000 ml, so the ratio is 1:4.
Make a conversion table for time, length, money, and capacity before simplifying ratios.
Sharing in a Given Ratio
To divide 20 pens in the ratio 3:2, add the parts: 3 + 2 = 5.
The first share is 3/5 of 20 = 12.
The second share is 2/5 of 20 = 8.
The source also uses age ratios, such as dividing money according to ages 15 years and 12 years.
Draw 20 pens split into 5 equal groups; shade 3 groups for one person and 2 groups for the other.
Proportion, Middle Terms, and Extreme Terms
If a:b = c:d, then a, b, c, and d are in proportion.
It is written as a:b :: c:d.
In a:b :: c:d, a and d are extreme terms. b and c are middle terms.
For example, 15:45 and 40:120 both simplify to 1:3, so they are in proportion.
Write a:b :: c:d and circle a,d as extremes and b,c as middle terms.
7. Rules / Properties
- Always start Ratio and Proportion answers with the correct meaning before writing examples.
- Use the exact Mathematics term when the question asks for a definition, rule, law, property, process, or comparison.
- Write steps in order when the concept involves a method, proof, process, timeline, map, or grammar transformation.
- Write the ratio in the exact order asked.
- Convert units before simplifying.
- Use HCF to reduce ratios quickly.
- For sharing problems, add ratio parts first.
8. Formulae
Important Formulae and Statements
- Ratio of a to b = a:b = a/b.
- Equivalent ratios are made by multiplying or dividing both terms by the same non-zero number.
- If a:b = c:d, then a, b, c, d are in proportion.
- In a:b :: c:d, extremes are a and d; middle terms are b and c.
- Share = required ratio part / total ratio parts x total quantity.
9. Visual Explanation
Draw 20 marks for girls and 15 for boys, then group both by 5 to show 4:3.
Example to connect: Girls to boys = 20:15 = 4:3.
Example to connect: 30 minutes to 1.5 hours = 1:3.
Example to connect: Dividing 20 pens in the ratio 3:2.
Visual Explanation
Draw 20 marks for girls and 15 for boys, then group both by 5 to show 4:3.
10. Worked Examples
Divide 20 pens between Sheela and Sangeeta in the ratio 3:2.
- 1The ratio is 3:2.
- 2Add the ratio parts: 3 + 2 = 5.
- 3Sheela gets 3 parts out of 5.
- 4Sheela gets 3/5 x 20 = 12 pens.
- 5Sangeeta gets 2 parts out of 5.
- 6Sangeeta gets 2/5 x 20 = 8 pens.
Sheela gets 12 pens and Sangeeta gets 8 pens.
11. Applications
Make ratio comparisons from your classroom.
- Count two groups, such as boys and girls or notebooks and textbooks.
- Write the ratio in the correct order.
- Simplify the ratio.
- Create an equivalent ratio by multiplying both terms by 2.
- Write one proportion using your ratio.
12. Common Mistakes
- Comparing quantities without converting them to the same unit.
- Changing the order of the ratio.
- Dividing only one term while simplifying.
- Forgetting to add ratio parts when sharing a quantity.
- Calling two ratios proportional without simplifying or checking equality.
- Confusing middle terms with extreme terms.
13. Practice Questions
- Find the ratio of 81 to 108.
- Find the ratio of 30 minutes to 1.5 hours.
- There are 20 girls and 15 boys. Find the ratio of girls to boys.
- Divide Rs 36 between two children in the ratio of ages 15:12.
- Check whether 4, 6, 8, and 12 are in proportion.
- In 25 cm:1 m :: Rs 40:Rs 160, name the middle and extreme terms.
- Exam check: Write the ratio in the exact order asked.
- Exam check: Convert units before simplifying.
- Exam check: Use HCF to reduce ratios quickly.
- Exam check: For sharing problems, add ratio parts first.
- Exam check: For proportion, simplify both ratios and then compare.
14. Frequently Asked Questions
These questions help you revise Ratio and Proportion in Mathematics with clear, test-ready understanding.
What is a ratio?
A ratio is a comparison of two quantities of the same kind by division.
What is a proportion?
A proportion is a statement that two ratios are equal.
Why should units be the same in a ratio?
A ratio compares like quantities, so both quantities must be measured in the same unit.
15. Summary
- A ratio compares two quantities in a fixed order.
- Ratios must use the same units before comparison.
- Equivalent ratios show the same comparison.
- A proportion means two ratios are equal.
- Sharing in a ratio becomes easy when total parts are found first.
Quick Quiz
Try these before you move ahead. The goal is to catch small doubts early, while the explanation is still fresh.
Quick Self-Test
Revise in Two Minutes
What is the first thing to understand in Ratio and Proportion?
The central relationship: what is involved, what changes, and why it matters in Mathematics.
What is a clear answer structure?
Idea, reason, example. Use it to make answers clear without sounding memorised.
How do I know I really understand Ratio and Proportion?
You can explain it simply, draw a useful visual, solve a basic question, and spot one common mistake.
Before You Say Done
- I can explain Ratio and Proportion in simple words.
- I can draw or describe the main visual model.
- I can solve one basic question step by step.
- I can identify one common mistake and avoid it.
- I can answer a why question, not only a what question.
Continue Learning
Use the visual prompt from this lesson first. Then move into practice and adaptive learning while the method is still fresh.