Proportion Formula - What is Proportion Formula? , Examples (2024)

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 tworatiosare equivalent, they are in proportion. The proportion formulaisused to depict iftwo ratios or fractions are equal. The proportion formula can be given as,

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

Proportion Formula - What is Proportion Formula? , Examples (1)

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 andwhen two quantities x and y are in indirect proportion, then y = k/x, where k is the constant of proportionality.

Proportion Formula - What is Proportion Formula? , Examples (2)

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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 6miles 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. Atthis 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 isa : 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 tworatiosare equivalent, they are in proportion. The proportion formulaisused to depict iftwo 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.

Proportion Formula - What is Proportion Formula? , Examples (2024)

FAQs

Proportion Formula - What is Proportion Formula? , Examples? ›

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.

What is an example of a proportion formula? ›

a/b = c/d or a:b::c:d. For example, let us consider another example of the number of students in 2 classrooms where the ratio of the number of girls to boys is equal. Our first ratio of the number of girls to boys is 2:5 and that of the other is 4:8, then the proportion can be written as: 2:5::4:8 or 2/5 = 4/8.

What are solved examples of proportion? ›

Proportion is an equation that defines that the two given ratios are equivalent to each other. For example, the time taken by train to cover 100km per hour is equal to the time taken by it to cover the distance of 500km for 5 hours. Such as 100km/hr = 500km/5hrs.

What is the formula for proportion method? ›

What is Formula of Ratio and Proportion? The Ratio of two quantities a and b is given by a:b = a/b and the formula for Proportion for two ratios a:b and c:d is a/b = c/d.

How do you solve proportion formulas? ›

The 3 ways to solve a proportion are: vertically, horizontally and diagonally (cross-multiplication). The vertical method is used if one of the ratios has a common multiple between the two quantities. The horizontal method is used if there is a common multiple between both numerators or denominators.

What is the proportional formula? ›

The formula for a proportional equation is y = kx. The letters y and x are the variables in the equation. The letter k represents the constant of proportionality, which remains the same.

What are 5 examples of direct proportion? ›

Direct Proportion Example
  • Marks scored is directly proportional to the performance in the test.
  • Temperature is directly proportional to heat.
  • Energy is directly proportional to work.
  • Speed is directly proportional to distance.
  • Earning is directly proportional to the amount of work done.
6 days ago

What is an example of a proportion for kids? ›

A proportion is a comparison of two numbers that each represent the parts of a whole. Essentially, a proportion says that two fractions are the same, even if the amount is different. For example, 1/2 of 10 marbles is the same proportion as 1/2 of 50 marbles.

Which is the best example of proportion? ›

It is the relationship between the parts of a composition and the whole. In this case, the example of drawing a small building next to a tall building best represents the principle of proportion. This is because the size of the small building is in proportion to the tall building.

What is a proportion in math? ›

A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls. 0.25 are boys (by dividing 1 by 4)

How to find mean proportion? ›

There are various uses of the square root, one of which is to find a mean proportional between any two numbers, which is performed thus: Multiply the two given numbers together, then extract the square root out of their product, and it will be the mean proportional sought.

What is the formula to check proportion? ›

The proportion formula can be written in the form of a/b = c/d or a : b : : c : d.

How do you write a proportion to solve a problem? ›

To write a proportion, set two equivalent fractions equal to each other, using the information in the problem. For example, if you know the ratio of girls to boys in a class is 2 : 3, and you know there are 24 boys in the class, you can write a proportion in order to find the number of girls in the class.

How do you write a direct proportion formula? ›

If y is directly proportional to x, then the direct proportion formula or the direct proportion equation is given by y=kx, where k is a constant of proportionality.

What are the formulas for sample proportions? ›

The sample proportion P is given by P=X/N, where X denotes the number of successes and N denotes the size of the sample in question. This sample proportion reflects that particular sample, and other samples of the population may result in different sample proportions.

What are the formulas of 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.

What is an example of in proportion to? ›

idiom. Your share of the profits will be in proportion to the amount of work that you do. The garage is not in proportion to the house. His head is large in proportion to his body.

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