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.

Written by Satish

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