Ratio and proportion are used widely in mathematics. Both the terms are related to the fractions. Any fraction like p/q, when written p: q is said to be the ratio of two numbers. While proportion concludes that the two ratios are equal.
Ratio and proportions are also used in various concepts or topics of mathematics. To compare height, distance, or dealing with money, we use ratio and proportion. These terms are also useful in different topics of science.
In this post, we will learn about the definition, types, and examples of ratio and proportion.
Contents
Ratio – Definition
In mathematics, the ratio is a term used to compare two quantities having the same units. In this comparison, the ratio tells how many times one term is equal to the other term. We can also express ratios in which one term can be written as the fraction of the other term. Ratios are written in two ways either by using the semicolon sign “:” or by division sign “/”.
r: s
Or
r/s
Types of ratios
There are two well-known types of ratios
- Part to part ratio
- Part to whole ratio
Part to part Ratio
A ratio in which two different quantities are compared is known as the part-to-part ratio. In other words, a ratio that provides a relationship among two different groups is called part to part ratio. For example, the ratio of class 8 to class 9, a ratio of a solution that contains two parts of hydrogen and one part of oxygen, and many other similar examples are termed as a part-to-part ratio.
Part to whole ratio
A ratio in which two quantities are compared in such a way that one quantity is taken from the other quantity is known as part to whole ratio. In other words, a ratio that provides the relationship among two quantities by taking a part from the whole.
For example, a ratio of female students in a school to the total students of the school, a ratio of one piece of pizza to the whole pizza, and many other such examples are terms as part to whole ratio.
Proportion – Definition
Proportion is used to compare two ratios to conclude that both ratios are equal. In other words, we can say that proportion is a term used to express the equality of two ratios or two fractions. Proportion is written in two ways, either by using double semicolon “::” or by equality sign “=”.
r : s : : u : v
Or s
r : s = u : v
Types of proportion
There are two well-known types of proportion.
- Direct proportion
- Inverse proportion
Direct proportion
A proportion in which by increasing one quantity, the other quantity also increased or by decreasing one quantity causes a decrease in the other quantity is known as direct proportion. For example, if we have two quantities a and b, where a is the number of laborers and b is the money paid to the laborers.
If we hire more laborers for work, we have to pay more salary, and if we hire fewer laborers, we have to pay less money. In this way, both the quantities are increasing or decreasing. So, we can conclude that both quantities a and b are directly proportional to each other.
Inverse proportion
A proportion is said to be inverse proportion if the increase in one quantity causes a decrease in the second quantity, or a decrease in one quantity causes an increase in the other quantity. For example, if we have two quantities u and v, where u is a motorbike and v is the fixed distance.
If we increase the speed of the motorbike the time taken to reach the fixed distance will decrease, or if we decrease the speed of the motorbike the time taken to reach the fixed distance will increase. So, we can conclude that u and v are inversely proportional to each other due to an increase in one quantity causing a decrease in the other quantity and vice versa.
How to find ratio and proportion?
To learn how to calculate ratio and proportion, let us use some examples.
Example 1: To find Ratio
In a bag, there are 18 balls. From these 18 balls, 9 are red, 6 are green, and 3 are blue. Find the ratio of
- Red balls to green balls
- Green balls to total balls
- Blue balls to red balls
Solution
Step 1: identify the given information.
Total balls = 18
Red balls = 9
Green balls = 6
Blue balls = 3
Step 2: Find the ratio of red balls to green balls.
Number of red balls = 9
Number of green balls = 6
The ratio is,
9: 6
Simplify
3: 2
Step 3: find the ratio of green balls to the total balls.
Number of total balls = 18
Number of green balls = 6
Difference among total balls and green balls = 18 – 6 = 12
Now the ratio is,
6: 12
Simplify
1: 2
Step 4: Now find the ratio of blue balls and red balls.
Number of red balls = 9
Number of blue balls = 3
Ratio is,
9 : 3
Simplify
3: 1
Example 2: To find the proportion
12 laborers are required to build a 30-meter-long wall, how many laborers are required to build a 45-meter wall at the same time?
Solution
Step 1: Identify the given values.
Labors = 12
First wall = 30m
Second wall = 45m
Labor required to build second wall = x
Step 2: Make given inputs as proportion.
Labor : wall : : labor : wall
12 : 30 : : x : 45
Step 3: Now make proportion bin the form of fraction and put equality sign among them.
12/30 = x/45
Step 4: Now solve above equation by cross multiplication.
12/30 = x/45
12 * 45 = x * 30
540 = 30x
x = 540/30
x = 18
Hence, 18 laborers are required to build a 45m long wall at the same time.
Summary
Both the term ratio and proportion are used to estimate the values. By using these two terms, you can easily solve the problems in which if one or three terms are given and you have to find the second or fourth term.
