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What is Proportion – Definition, Formula, Examples


Proportion in Math

In mathematics, a proportion is a statement that two ratios or fractions are equal. It is used to compare one quantity to another quantity, and to determine the relationships between them.

A proportion can be represented by the following formula:

a/b = c/d

where a, b, c, and d are four numbers. The numbers a and b form one ratio, and the numbers c and d form another ratio. The proportion states that these two ratios are equal to each other.

Examples of Proportions

Here are a few examples of proportions:

  1. If two cars travel the same distance at different speeds, the time they take to travel that distance will be proportional to their speeds. For example, if Car A travels 50 miles in 2 hours at a speed of 25 miles per hour, and Car B travels the same distance in 1 hour at a speed of 50 miles per hour, the two speeds are proportional: 25/50 = 1/2.
  2. If you have a recipe that makes 4 servings of a dish, but you need to make 8 servings, you can use a proportion to calculate how much of each ingredient you’ll need. For example, if the recipe calls for 1 cup of flour for 4 servings, you’ll need 2 cups of flour for 8 servings, because 1/4 = 2/8.
  3. If you have a group of students and you want to determine what percentage of the group is male, you can use a proportion. For example, if there are 20 male students out of a total of 40 students, the proportion of males is 20/40 = 1/2, or 50%.

In general, proportions are useful for solving problems that involve comparisons between two or more quantities. By setting up a proportion and solving for an unknown variable, you can find a missing quantity or determine the relationship between two quantities.

Ratios and Proportions

Ratios and proportions are mathematical concepts that are used to compare quantities and express relationships between them.

A ratio is a way of comparing two numbers or quantities by using division.

For example, if we have 1 apple and 3 oranges,

the ratio of apples to oranges is 3:4, or 3/4.

Ratios can also be written in the form of percentages or decimals.

A proportion is a statement that two ratios are equal.

For example, if we have 3 apples for every 4 oranges and 9 apples, how many oranges do you have?

You can set up a proportion to find out:

3/4 = 9/x

where x is the number of oranges. To solve for x, you can cross-multiply:

3x = 36

x = 12

So you have 12 oranges.

Ratio Formula

The formula for the ratio of two quantities or two entities is:


where “a” and “b” are the two quantities.

The ratio “a:b” can also be written as “a to b.”

Ratios in the fractional form:


In this state, the numerator “a” represents the first quantity, and the denominator “b” represents the second quantity.

Ratios can also write in decimal or percentage form.

ratio formula

The ratio formula is a:b or a/b.

 For example, a ratio of 3:5 can be represented

3:5 = 3/5 = 0.6 = 60%

Proportion Formula

The formula for proportion is:

Proportion Formula


  • “a” and “b” are the first ratio,
  • and “c” and “d” are the second ratio

To solve a proportion, you can use cross-multiplication.

For example, consider the proportion:

2/4 = x/12

To solve for “x,” you can cross-multiply:

2 x 12 = 4 x x

24 = 4x

x = 6

3/4 = 6/12

Therefore, the solution for the proportion is:

3/4 = 1/2

Types of Proportions

  1. Direct Proportion
  2. Inverse Proportion

Frequently Asked Questions on Direct and Inverse Proportion

Here are some frequently asked questions about proportions and ratios:
Q: What is the difference between a ratio and a proportion?
A: A ratio is a comparison of two numbers or quantities, while a proportion is a statement that two ratios are equal.

Q: Can ratios be represented in different forms?
A: Yes
Q: How do you solve a proportion?
A: To solve a proportion, you can use cross-multiplication.

Q: What are some applications of ratios and proportions?
A: Ratios and proportions are used in many fields, including cooking and baking, finance, physics, and engineering.

Q: Can you simplify a ratio?
A: Yes.

Q: How many ratios are needed to create a proportion?
A: You need two ratios to create a proportion.

Q: What happens if you cross-multiply and get a negative result?

A: If you cross-multiply and get a negative result, it means that one of the ratios is negative.

Q: Can you use proportions to solve problems with more than two ratios?
A: Yes.