Key Concepts
- Percent proportion.
- Use a proportion to find the percent.
- Use a proportion to find the part.
- Use a proportion to find the whole
3.2 Connect percent and proportion
What is percent proportion?
When the ratio of part to whole is equal to the ratio of a percent to 100, we call it a percent proportion.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-4391.png)
Example: If 35% of 80 students in a class are girls. Find the number of girls in the class.
Solution: Here, we are finding the number of girls(part) in the class of 80 students (whole).
Let us assume the number of girls in the class as ‘g’.
The percent proportion becomes,
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-4392.png)
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-4404.png)
Percent proportion formula:
Percent proportion helps in solving problems. It is expressed in the form of
Where,
- Percent is the number with a % sign.
- Part is the number with the word IS.
- Whole is the number with the word OF.
Example: 30 is what percent of 90?
Solution: Here, 30 is a part and 90 is whole.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-4405.png)
The percent proportion becomes,
=percent.
Percent = 33.33%
3.2.1 Use a proportion to find the percent
Example 1: There are 50 students in the class. If 7 students are absent on a day, find the present percent on that day.
Solution: We observe that 100% of the class is considered as 50, out of which we are finding present percent if 7 are absent. Let us consider the present percent as ‘p.’
Total number of students = 50
Number of student’s absent = 7
Number of student’s present = 50 – 7 = 43
Step 1: Draw a bar diagram and write a proportion to represent the number of students present and the total number of students in the class.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-4394.png)
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-4393.png)
Step 2: Use the proportion to find the percent of students present in the class.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-4407.png)
Multiply by 100 on both sides of the equation.
43 × 2 = p
p = 86
Therefore, we conclude that 86% of the students were present on that day.
Example 2: A hockey goalie stops 37 out of 40 shots in a game. What percent of the attempted goals did he block?
Solution: We observe that 100% of the shots is considered as 40, out of which 37 are blocked. Let us consider the blocked percent as ‘b’.
Total number of attempted shots = 40.
Number of shots stopped= 37.
Step 1: Draw a bar diagram and write a proportion to represent the number of shots stopped and the total number of shots attempted in a game.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-4408.png)
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-4409.png)
Step 2: Use the proportion to find the percent of blocked shots in a game.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-4395.png)
Multiply by 100 on both sides of the equation.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-4397.png)
37 × 2.5 = b
b = 92.5
Therefore, we conclude that 92.5% of the attempted shots were blocked by the goalie.
3.2.2 Use a proportion to find the part
Example 1: The dimensions of a school ground is 16 feet in length and 10 feet in width. If the proposed plan is to expand the dimensions by 160% of the present dimensions. What is the length of new ground?
Solution: We observe that 100% of current length is considered as 16 feet. We are finding the new length after expanding it by 160%. Let us consider the new length as ‘x’ feet.
Step 1: Draw a bar diagram to represent the problem and then write a percent proportion to find the new length of the ground.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-4413.png)
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-4396.png)
Step 2: Use the percent proportion to find the new length of the ground.
New Length / old length = 160 / 100
Multiply by 16 on both sides of the equation.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-4414.png)
160% of 16 feet is 25.6 feet.
Therefore, we conclude that 25.6 feet will be the new length of the ground.
Example 2: If Emma scores 90% of the 80 marks in English subject. Find the marks scored by Emma.
Solution: We observe that 100% of marks is considered as 80. We are finding marks scored by her, if she gets 90%. Let us consider the marks scored by her as ‘m’.
Step 1: Draw a bar diagram to represent the problem and then write a percent proportion to find marks scored by Emma in English.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-4415.png)
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-4416.png)
Step 2: Use the percent proportion to find marks scored.
Multiply by 80 on both sides of the equation.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-4417.png)
90% of 80 marks is 72 marks.
Therefore, we conclude that 72 marks are scored by Emma in English.
3.2.3 Use a proportion to find the whole
Example 1: An alloy contains 45% of silver. What quantity of alloy is required to get 450 grams of silver?
Solution: We observe that 100% of alloy is not known, out of which 45% is 450 grams of silver. Let us consider the total quantity of the alloy as ‘x’ grams.
Step 1: Draw a bar diagram to represent the problem and then write a percent proportion to find total quantity of alloy.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-4399.png)
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-4398.png)
Step 2: Use the percent proportion to find the total quantity of alloy.
450 / x – 45 / 100
Multiply both sides by the variable.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-4419.png)
Multiply both sides by the reciprocal.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-4420.png)
Therefore, we conclude that quantity of alloy is 1000 grams.
Example 2: The rabbit population in a certain area is 200% of the last year’s population. There are 1,100 rabbits this year. How many were there last year?
Solution: We observe that 100% of last year population is not known, out of which 200% is 1,100 rabbits. Let us consider the last year population of the rabbits as ‘r.’
Step 1: Draw a bar diagram to represent the problem and then write a percent proportion to find the population of rabbits last year.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-4421.png)
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-4398.png)
Step 2: Use the percent proportion to find the total population of rabbits last year.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-4400.png)
Multiply both sides by the variable.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-4422.png)
Multiply both sides by the reciprocal.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-4423.png)
Therefore, we conclude that total population of the rabbits last year is 550.
Exercise:
- Angela makes 2 of her 5 shots in a basketball game. Find the percent of shots she did not make.
- What percent is 18 out of 50?
- In a class of 40 students, 25 students score more than 90 marks out of 100. What percent of students scored less than 90 marks?
- The length of a rectangle is 3 feet initially. If the length is increased to 12 feet, what percent is increased in comparison to initial length?
- Joseph earned $12,000 per month in the year 2021. If he gets $18000 per month in the year 2022. Find the percent hike given by the company.
- The share price of company opened at $1400 per share on Monday. If the share price decreased by $400 on Tuesday. Find the decrease percent in share.
- Mike and Clyde invested in a business. 75% of the profit is taken by Mike and the rest given to Clyde. In a month, Mike gets $6000. Find the total profit of the month.
- Find the daily intake of Iron, if a milk supplies 45% of the iron intake per day which is 8 grams.
- What is a good estimate for 450% of 90? Explain.
- Find 7% of 200 using the proportion given below.
X = 7
What have we learned?
- Understand percent proportion.
- Using a proportion to find the percent.
- Using a proportion to find the part.
- Using a proportion to find the whole
![Percent And Proportion](/_next/image?url=https%3A%2F%2Fwww.turito.com%2Flearn-internal%2Fwp-content%2Fuploads%2F2022%2F09%2FPercent-And-Proportion-1.png&w=1920&q=50)
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