# 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.

**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,

**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.

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.

**Step 2: **Use the proportion to find the percent of students present in the class.

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.

**Step 2: **Use the proportion to find the percent of blocked shots in a game.

Multiply by 100 on both sides of the equation.

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.

**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.

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.

**Step 2: **Use the percent proportion to find marks scored.

Multiply by 80 on both sides of the equation.

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.

**Step 2: **Use the percent proportion to find the total quantity of alloy.

450 / x – 45 / 100

Multiply both sides by the variable.

Multiply both sides by the reciprocal.

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.

**Step 2: **Use the percent proportion to find the total population of rabbits last year.

Multiply both sides by the variable.

Multiply both sides by the reciprocal.

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

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