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# Proportion Formula

Before we begin with the proportion formula, let us first recall the concept of proportion. If two ratios are equal, they are said to be in proportion. If a, b, c, d are the four elements in proportion then it means that a/b = c/d. The elements a and d are called extremes, while b and c are called mean terms. In the ratio, the product of means equals the product of extremes. Any two ratios are said to be equal if their cross-products are equal. Let us understand the proportion formula using solved examples.

## What is the Proportion Formula?

According to the definition of proportion, when two ratios are equivalent, they are in proportion. The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as,

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

### Proportion Formula

a : b :: c : d = a/b = c/d

where,

- a, d = Extreme terms
- b, c = Mean terms

The other formulas related to proportion are:

- The product of means = the product of extremes. This can be written as ad = bc
- There are two other proportional formulas based on direct or indirect variation. If two quantities x and y are in direct proportion, then y = kx and when two quantities x and y are in indirect proportion, then y = k/x, where k is the constant of proportionality.

## Examples Using Proportion Formula

**Example 1: What is the value of x in 12 : x :: 4 : 5?**

**Solution:**

Using the proportion formula,

a : b :: c : d = a/b = c/d

12/x = 4/5

x = 15

Therefore, the value of x = 15

**Example 2: Sam runs 6 miles in 30 minutes. At this rate, how far could he run in 45 minutes?**

**Solution:**

Let us assume the unknown quantity here to be x.

Using the proportion formula,

6 : 30 :: x : 45 = 6/30 = x/45

x = 9 miles

Therefore, the distance covered by Sam in 45 mins = 9 miles.

**Example 3: Jane walked 4 miles in 30 minutes. At this rate, how far could she walk in 60 minutes?**

**Solution:**

Let us assume the unknown quantity here to be x.

Using the proportion formula,

4 : 30 :: x : 60

4/30 = x/60

x = 8

Therefore, the distance covered by Jane in 60 minutes is 8 miles

## FAQs on Proportion Formula

### What is Meant by Proportion Formula?

Any equation is said to be in proportion when the elements in them are in proportion. That means if the elements in an equation are a, b, c, and d, then the equation would be in proportion when a, b, c, and d are in proportion. The elements a and d are called extremes, while b and c are called mean terms. In the ratio, the product of means equals the product of extremes. Any two ratios are said to be equal if their cross-products are equal. The formula is a : b :: c : d = a/b = c/d.

### What is the Formula to Find the Proportion of a Value?

The formula to find the proportion of a value is:

a : b :: c : d = a/b = c/d

where,

- a, d = Extreme terms
- b, c = Mean terms

### How to Calculate a Value Using the Proportion Formula?

According to the definition of proportion, when two ratios are equivalent, they are in proportion. The proportion formula is used to depict if two ratios or fractions are equal. We can find the missing value by dividing the given values. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

### Using the Proportion Formula, Determine the Value of x in x : 32 :: 78 : 64

Using the proportion formula,

a : b :: c : d = a/b = c/d

x : 32 :: 78 : 64

x/32 = 78/64

x = 39

Therefore, the value of x is 39.

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