Proportional Reasoning-2
CBSE · Class 8 · Mathematics
Summary of Proportional Reasoning-2 for CBSE Class 8 Mathematics. Key concepts, important points, and chapter overview.
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Overview
Proportional reasoning compares quantities that change together in a fixed pattern. Some quantities change in the same direction, like the quantities in direct proportion. Some change in opposite directions, like speed and time for a fixed distance, which form inverse proportion. Ratios can involve
Key Concepts
Two ratios
Two ratios a : b and c : d are proportional if a × d = b × c, or if a/c = b/d. The idli batter ratios 6:3 and 4:2 are proportional because both cross
A Representative Fraction is an expression
A Representative Fraction is an expression that shows the ratio between a distance on the map and the corresponding actual distance on the ground. For
Ratios can have many terms when
Ratios can have many terms when each quantity changes by the same factor. Viswanath’s spice mix ratio is 8:4:2:1, and Puneet’s scaled version is 4:2:1
A whole quantity is divided by
A whole quantity is divided by first adding all parts of the ratio, then sharing the total in that proportion. For 12 in the ratio 2:1, the result is
The total angle in a circle
The total angle in a circle is 360°. Slice angles must be proportional to the data values. For grades A-E in the ratio 12:10:8:6:4, the simplified rat
Learning Objectives
- Understand proportional relationships using ratio notation
- Check whether two ratios are proportional by cross-multiplication
- Use representative fraction to read map scales
- Work with ratios having more than two terms
- Divide a whole in a given ratio
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Sources & Official References
- NCERT Official — ncert.nic.in
- CBSE Academic — cbseacademic.nic.in
- CBSE Official — cbse.gov.in
- National Education Policy 2020 — education.gov.in
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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