Proportional Reasoning-1 — Chapter Summary
CBSE · Class 8 · Mathematics
Summary of Proportional Reasoning-1 for CBSE Class 8 Mathematics. Part of the CBSE Class 8 Mathematics syllabus.
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Overview
Proportional reasoning compares quantities that change in the same way. Ratios show the relationship between two quantities, and proportional ratios keep the same simplest form. The chapter also shows how to check proportionality by simplification and by cross multiplication. The Rule of Three gives
Key Concepts
A ratio compares two quantities
A ratio compares two quantities. In a ratio a:b, for every a units of the first quantity, there are b units of the second quantity. The numbers 60 and
Two ratios are proportional when their
Two ratios are proportional when their simplest forms are the same. The symbol :: is used to show this, as in a:b::c:d.
A ratio is reduced to simplest
A ratio is reduced to simplest form by dividing both terms by their HCF. For example, 60:40 becomes 3:2 because the HCF of 60 and 40 is 20.
For
For a:b::c:d, the terms satisfy ad = bc. This helps find the unknown fourth term. The unknown term d can be found by d = bc/a.
Āryabhaṭa called proportionality problems Rule
Āryabhaṭa called proportionality problems Rule of Three problems. The given numbers are pramāṇa, phala, and ichchhā, and the unknown is ichchhāphala.
Learning Objectives
- Understand ratios as comparisons of two quantities
- Find the simplest form of a ratio by using the HCF
- Identify proportional ratios using simplest forms
- Use the symbol :: to show proportionality
- Solve unknown terms in proportions by cross multiplication
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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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