PROPORTIONAL 7 REASONING-1 | Class 8 Mathematics Notes
By ConceptScroll Team · Published on 17 July 2026 · 3 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.
Proportion and Its Properties
This section formally defines proportion as an equation stating that two ratios are equal. If a/b = c/d, then a, b, c, and d are said to be in proportion. The terms a and d are called the extremes, and b and c are called the means.
The section explains the fundamental property of proportions: the product of the extremes equals the product of the means, i.e., a × d = b × c. This property is used extensively to solve problems involving proportions.
Students learn to identify the means and extremes in a proportion and use the property to find unknown terms. For example, if 3/x = 9/12, then by cross multiplication, 3 × 12 = 9 × x, leading to x = 4.
The section also discusses the concept of continued proportion, where three or more quantities are in proportion, such as a:b = b:c = c:d.
Through examples and exercises, students practice verifying proportions and solving for unknowns using the property of proportions. This section builds a strong foundation for solving real-world problems involving proportional relationships.
📊 Diagram: A figure illustrating the proportion a:b = c:d with labels indicating means and extremes, and arrows showing cross multiplication between a and d, and b and c.
🧪 Activity: Activity 7.3: Students verify given ratios to check if they form a proportion by cross multiplying and comparing products. They also find missing terms in given proportions.
🔗 Connection: This section leads to the next one on solving problems using proportions, applying the property of proportions in practical contexts.
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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