Chapter 7: Proportional Reasoning – 1

1. Ratios

A ratio compares two quantities multiplicatively. In 2:3, the comparison means 2 parts for every 3 parts, not a difference of 1. Ratios should compare quantities in compatible units.

2. Equivalent Ratios

Multiplying or dividing both terms of a ratio by the same non-zero number produces an equivalent ratio. Thus 2:3=4:6=10:15.

3. Proportion

A proportion states that two ratios are equal. For example, 3:5=12:20 because both represent the same multiplicative relationship. Cross multiplication is a consequence of equality of fractions.

4. Rule of Three

When three values in a proportional situation are known, the fourth can be found by maintaining the same ratio. Example: 5 notebooks cost ₹150. One costs ₹30, so 8 cost ₹240.

5. Recognising Proportional Situations

Not every pair of changing quantities is proportional. Check whether the ratio remains constant. A recipe, scale drawing or price-per-item situation may be proportional when the rate stays fixed.

6. Tables and Representations

A proportional table has a constant multiplicative relationship. If x doubles and y also doubles, that is evidence of direct proportionality; the ratio y/x should remain constant.

🧠 MCQs

1. 2:3 is equivalent to: A) 4:5 B) 4:6 C) 6:8 D) 8:9
2. If 6 pens cost ₹90, 10 pens cost: A) ₹120 B) ₹135 C) ₹150 D) ₹180
3. In a proportion, corresponding ratios are: A) unequal B) equal C) always integers D) always percentages
4. If y/x is constant, the relationship is: A) proportional B) random C) additive only D) impossible

Answers: 1-B, 2-C, 3-B, 4-A.

📌 Case Study

A school uses 12 litres of paint for 4 classrooms. Assuming identical room sizes and the same coverage, how much paint is required for 9 classrooms? Explain why proportional reasoning is valid.

🔥 HOTS

1. Create a pair of ratios that are equivalent in three different forms.
2. Give a situation that looks proportional but is not, and explain why.
3. Explain why multiplying only one term of a ratio changes the relationship.

✍️ Practice

1. Define ratio and proportion.
2. Simplify 18:24.
3. Solve 7:9=x:45.
4. Explain how a table can reveal proportionality.

🏆 Mastery Checklist

• ☐ I can simplify and generate equivalent ratios.
• ☐ I can identify a proportion.
• ☐ I can solve missing-value problems.
• ☐ I can test whether a situation is genuinely proportional.

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