10.8 Summary

Name: CBSE Class 8 Mathematics
Author: Vijayakumar P

Key Points

Two ratios are proportional when their cross-products are equal: a : b :: c : d means a \times d = b \times c, i.e. \dfrac{a}{b} = \dfrac{c}{d}.
A map’s Representative Fraction (RF), like 1 : 75{,}00{,}000, gives the ratio of map distance to ground distance (1 cm on map = 75 km on ground).
A ratio a : b : c : d : \dots means for every a units of the first quantity there are b of the second, c of the third, and so on.
To share x in the ratio p : q : r : \dots, the parts are x \times \dfrac{p}{p+q+r+\dots},\; x \times \dfrac{q}{p+q+r+\dots},\;\dots
A pie chart shares 360° among the data in proportion; simplify the ratio first, then each part = \dfrac{360°}{\text{sum of terms}} times its term.
Quantities are in direct proportion when they change by the same factor and \dfrac{x}{y} = k stays constant.
Quantities are in inverse proportion when one grows as the other shrinks, with the product constant: xy = k, so x_1 y_1 = x_2 y_2. Multiplying x by n multiplies y by \dfrac{1}{n}.