# What is Proportion in Math and Its Usage with Example

Hello Students, in this you are going to learn what is proportion in math and what is the usage of proportion in mathematics, how ratio and proportion are differentiate with each other. So if you have not read our previous post on ratio then first first visit and read that post then you will easily understand this proportion topic.

## Definition of Proportion in Math

Proportion is a mathematical expression that states that two ratios are equivalent. In other terms, the proportion declares that the two fractions or ratios are equal. In proportion, two sets of provided numbers are said to be directly proportional to one other if they increase or decrease in the same ratio.

For example, the time it takes a car to travel 100 kilometres per hour is the same as the time it takes to travel 400 kilometres in 4 hours.

For example, 100 km/hr = 400 km/4 hours.

Proportions and ratios are considered to be two sides of the same coin. When the values of two ratios are equal, they are said to be in proportion. Proportions are denoted by the symbol **‘::’** or **‘=’**.

## Classification of Proportion

The proportion can be classified into the following categories:

- Direct Proportion
- Inverse Proportion
- Continued Proportion

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## Direct Proportion

The direct proportion defines the relationship between two quantities in which when one number rises, the other quantity increases as well. In the same way, if one amount diminishes, the other quantity reduces as well. As a result, the direction proportion is expressed as ab if “a” and “b” are two quantities. **a∝b**.

## Inverse Proportion

The inverse proportion indicates a relationship between two quantities in which an increase in one item causes the other to decrease. Similarly, if one quantity decreases, the other quantity increases. As a result, a(1/b) represents the inverse proportion of two quantities, say “a” and “b.” **a∝(1/b)**.

## Continued Proportion

Consider the following two ratios: a: b and c: d. We then convert the means to a single term/number in order to get the continuous proportion for the two specified ratio terms. In general, this would be the LCM of means. The LCM of b and c for the given ratio is bc. We get First ratio- ca : bc by multiplying the first ratio by c and the second ratio by b. The second ratio is bc : bd.

As a result, the continuous percentage can be expressed as **ca: bc: bd**.

## Formula for Ratio and Proportion

Now, let us learn the Math ratio and proportion formulas here.

### Ratio Formula

Assume we have two quantities (or two numbers or two creatures) and we need to calculate the ratio between them. The formula for ratio is a: b a/b, where a and b might be any two quantities.

The first term, “a,” is referred to as the antecedent, and the second term, “b,” is referred to as the consequent.

**Example:** 4/9 represents the ratio 4:9, where 4 is the antecedent and 9 is the consequent.

It has no effect on the ratio if we multiply and divide each term of the ratio by the same number (non-zero). For instance, 4:9 = 8:18 = 12:27.

### Proportion Formula

Let’s pretend the two ratios are a:b and c:d in proportion.

The terms ‘b’ and ‘c’ are referred to as ‘means or mean terms, whereas ‘a’ and ‘d’ are referred to as ‘extremes or extreme terms.

**a/b = c/d or a : b :: c : d**

**Example:** Let’s look at another scenario involving a large group of kids in a classroom. If the first ratio of females to boys is 3:5 and the second is 4:8, the percentage may be written as follows:

3 : 5 :: 4 : 8 or 3/5 = 4/8

Here, 3 & 8 are the extremes, while 5 & 4 are the means.

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