Revision Notes: Class 8 Maths Chapter 7 Proportional Reasoning-1

Class 8 Maths Chapter 7: Proportional Reasoning-1 — Quick Revision Notes

• Ratio: a comparison of two quantities of the same kind, written a:b or a/b; both terms must be in the same unit before comparing.
• Proportion: a statement that two ratios are equal, a:b::c:d; true if and only if the cross products are equal, a×d = b×c.
• Simplest form: divide both terms of a ratio by their HCF.
• Similar figures: figures whose corresponding measurements are all in the same ratio — recognisable even when rotated, since the ratio itself (not orientation) is what matters.
• Rule of Three / Unitary method: find the value for a single unit first, then scale up (or down) to the quantity needed — the standard tool for solving proportional word problems.
• Direct proportion: as one quantity increases, the other increases at the same rate, so their ratio stays constant (e.g. bricks needed for a wall length).
• Inverse proportion: as one quantity increases, the other decreases so their product stays constant (e.g. speed × time = a fixed distance).
• Sharing in a given ratio: split the total into (sum of the ratio’s parts) equal shares, then give each person their number of parts.
• Comparing crowding/density: convert both groups to a common basis (e.g. people per sq km) before comparing, rather than comparing raw totals.
• Alternendo property: if a:b = c:d, then a:c = b:d also holds true.

Frequently Asked Questions

What is the difference between direct and inverse proportion?
In direct proportion, as one quantity increases, the other quantity increases in the same ratio, while in inverse proportion, as one quantity increases, the other decreases in such a way that their product remains constant.

Last Updated: September 23, 2026

How can you identify whether two quantities are in direct proportion from a table of values?
Two quantities are in direct proportion if the ratio between corresponding values remains the same throughout the table, meaning dividing each value of one quantity by its corresponding value of the other always gives the same constant.

Written by Satish

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