PROPORTIONAL 7 REASONING-1 | Class 8 Mathematics Notes
By ConceptScroll Team · Published on 17 July 2026 · 4 min read
PROPORTIONAL 7 REASONING-1 – this guide gives you a concise, exam-ready overview of PROPORTIONAL 7 REASONING-1 from Class 8 Mathematics, written by ConceptScroll editors and reviewed against the latest NCERT textbook.
Introduction to Proportional Reasoning
Proportional reasoning is a fundamental mathematical concept that deals with the comparison of ratios and the understanding of how quantities relate to each other in a multiplicative way. It forms the basis for solving many real-life problems involving scaling, mixing, and sharing. This chapter introduces the concept of proportion, which is an equation stating that two ratios are equal. Understanding proportional reasoning helps students develop critical thinking skills and apply mathematical concepts to everyday situations such as cooking recipes, map reading, and financial calculations.
The chapter begins by revisiting the idea of ratios, which express the relative size of two quantities. For example, if there are 3 apples and 6 oranges, the ratio of apples to oranges is 3:6, which can be simplified to 1:2. Proportional reasoning extends this idea by comparing two such ratios to see if they are equivalent. When two ratios are equal, they are said to be in proportion.
The chapter emphasizes the importance of recognizing proportional relationships and using them to solve problems. It also introduces the cross-multiplication method as a tool to check if two ratios are in proportion and to find unknown quantities in proportional relationships. The concept is illustrated with various examples, such as comparing speeds, mixing solutions, and scaling quantities in recipes.
By the end of this section, students should be able to understand the meaning of proportion, identify proportional relationships, and apply proportional reasoning to solve problems involving ratios.
📊 Diagram: The section includes a diagram showing two ratios represented as fractions a/b and c/d, with arrows indicating cross multiplication between a and d, and b and c to verify proportion.
🧪 Activity: Activity 7.1: Students are asked to find pairs of quantities in their surroundings that are in proportion, such as the ratio of length to width of a book, or the ratio of ingredients in a recipe, and verify if they form a proportion using cross multiplication.
🔗 Connection: This introduction sets the foundation for the next section, which explores the concept of equivalent ratios and how to generate them, leading to a deeper understanding of proportional relationships.
Frequently asked questions
1. Divide ₹4,500 into two parts in the ratio 2 : 3.
Let the two parts be 2x and 3x. Then, 2x + 3x = 4500 => 5x = 4500 => x = 900. So, the two parts are 2900 = ₹1800 and 3900 = ₹2700.
2. In a science lab, acid and water are mixed in the ratio of 1 : 5 to make a solution. In a bottle that has 240 mL of the solution, how much acid and water does the solution contain?
Total parts = 1 + 5 = 6. Volume of acid = (1/6) × 240 = 40 mL. Volume of water = (5/6) × 240 = 200 mL.
3. Blue and yellow paints are mixed in the ratio of 3 : 5 to produce green paint. To produce 40 mL of green paint, how much of these two colours are needed? To make the paint a lighter shade of green, I added 20 mL of yellow to the mixture. What is the new ratio of blue and yellow in the paint?
Total parts = 3 + 5 = 8. Blue paint = (3/8) × 40 = 15 mL. Yellow paint = (5/8) × 40 = 25 mL. After adding 20 mL yellow, new yellow = 25 + 20 = 45 mL. Blue remains 15 mL. New ratio = 15 : 45 = 1 : 3.
4. To make soft idlis, you need to mix rice and urad dal in the ratio of 2 : 1. If you need 6 cups of this mixture to make idlis tomorrow morning, how many cups of rice and urad dal will you need?
Total parts = 2 + 1 = 3. Rice = (2/3) × 6 = 4 cups. Urad dal = (1/3) × 6 = 2 cups.
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