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**Ratio Proportion and Variation**

- The ratio of two quantities in the same units is a fraction that one quantity is of the other.
- Thus, a to b is a ratio (a/b), written as a: b
- The first term of a ratio is called antecedent, while the second term is known as consequent. Thus, the ratio 5:8 represents 5/8 with antecedent 5 and consequent 8.
**Note:-**The multiplication or division of each term of a ratio by a same non-zero number does not effect the ratio. E.g:- 3:5 is the same as 6:10 or 9:15 or 12:20.

2. Proportion:-

- The equality of two ratios is called proportion. Thus, 2:3 = 8:12 is written as 2:3::8:12 and we say that 2,3,8 and 12 are in proportion.
- The first and fourth terms are known as extremes, while second and third terms are known as Means
**Note:-**Product of Means = Product of Extremes

3. Fourth Proportional:-

- Duplicate ratio of (a: b) is (a2 : b2)
- Sub duplicate ratio of (a: b) is ${(\sqrt{a}:\sqrt{b})}$
- Triplicate ratio of (a: b) is (a3 : b3)
- Sub â€“ triplicate ratio of (a: b) is ${(a^{1/3}: b^{1/3})}$

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