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# Formulas for Ratio and Proportions

## Formulas for Ratio and Proportion:-

**Definitions:**

#### Ratio:-

The ratio of two quantities in the same units is the fraction that one quantity is of the other. It is a relationship between two numbers by the division of the same kind. Therefore, the ratio of 2 to 3 is 2/3 or can be written as 2 : 3. The first term of a ratio is known as antecedent and the second term is called consequent. Furthermore, it may be noted that 10: 15 equals to 10/15 or 2/3 is equals to 2 : 3. Therefore, multiplication of each term of a ratio by the same number does not affect the ratio.

#### Proportion

The equality of two ratios is known as proportion. It is used to find out the quantity of one class over the total. In other words, the proportion is a part that describes the comparative relation with the overall part.

Subsequently, 2 : 3 equals to 4 : 6, we will write 2 : 3 :: 4 : 6 and we can say that 2, 3, 4, and 6 are in proportion. Consequently, 2, 3, 4, and 6 are called 1^{st}, 2^{nd}, 3^{rd}, and 4^{th} proportional respectively. The first and the fourth proportional are called the extreme terms while the second and the third proportional are called mean terms.

The product of the means equals the product of the extremes.

#### Fourth proportional

If x : y = z: a, then a is called the fourth proportional to x, y, z.

#### Third proportional

If x: y = y: z, then z is called the third proportional to x and y.

#### Mean proportional

Mean proportional between x and y is √xy

#### Comparison of ratios

We say that (x: y) > (z: a), then (x/y) > (z /a).

#### Compounded ratio

The compounded ratio of the ratios (x: y), (z: a), (b : c) is (xzb: yac)

### Ratio and Proportions Formulas & Properties of Ratio

- The ratio of two people a and b is denoted as a : b.
- a : b = ma : mb, where m is a constant.
- x : y : z = X : Y : Z is equivalent to x/X=y/Y=z/Z
- If x/y = z/a then, x+y/x-y = z+a/z-a

### Ratio and Proportions Formulas Property of Proportion

- x/y=z/a , this means x : y ::z:a

**Read Also: How To Solve Ratio and Proportions Questions Quickly**

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