Proportion
- CBSE · NCERT Class 8 Part 1, Ch 7 Proportional Reasoning-1
A proportion says that two ratios are equal, such as 2 : 3 = 4 : 6, where both terms of one are the other's times the same number.
Two ratios are in proportion when one is the other scaled up or down. 2 : 3 and 4 : 6 are in proportion, because both terms of the first were doubled. 2 : 3 and 3 : 4 are not, because the terms did not change by the same factor.
A quick check is cross-multiplying. For a : b = c : d, the product a × d must equal b × c. For 2 : 3 = 4 : 6, 2 × 6 = 12 and 3 × 4 = 12, so they match.
A small example
A photo is 48 cm wide and 36 cm tall. You print a copy 64 cm wide. How tall must it be so the picture does not stretch?
Set up the proportion 48 : 36 = 64 : h. Cross-multiply: 48 × h = 36 × 64 = 2304. So h = 48 cm. Check: 64 : 48 and 48 : 36 both cut down to 4 : 3.
Why it matters later
Class 10 Chapter 6, Triangles, is built on proportion. The basic proportionality theorem says a line parallel to one side divides the other two sides in the same ratio. Similar triangles have their matching sides in proportion. Both lead to the same cross-multiplying step shown above.
Sources
Facts last checked against these sources on 30 September 2026.
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