# Common Core: 7th Grade Math : Use Proportional Relationships to Solve Multistep Ratio and Percent Problems: CCSS.Math.Content.7.RP.A.3

## Example Questions

### Example Question #11 : Use Proportional Relationships To Solve Multistep Ratio And Percent Problems: Ccss.Math.Content.7.Rp.A.3

6 decreased by what percent is  ?

Explanation:

The difference of 6 and  is

.

Therefore, 6 is being decreased by ; to find out what percent this is of 6, we calculate:

, so

.

The answer that comes closest among the four choices is 20%.

### Example Question #12 : Use Proportional Relationships To Solve Multistep Ratio And Percent Problems: Ccss.Math.Content.7.Rp.A.3

What is the percentage of male students in a class if  are male out of  students?

Explanation:

First you want to make a proportion so  of the class are male.

You can reduce this fraction by  since both the numerator and denominator are divisible by it.

This gives you  which as a decimal is .

To make that into a percentage, you multiple by  and add a "%" symbol.

So that gives you .

### Example Question #13 : Use Proportional Relationships To Solve Multistep Ratio And Percent Problems: Ccss.Math.Content.7.Rp.A.3

is 30% of  is 42% of .

is what percent of  ?

Explanation:

We can choose a specific value for ; the reasoning is independent of this value.

Assume . Then

and

To find out what percent  is of , calculate:

### Example Question #14 : Use Proportional Relationships To Solve Multistep Ratio And Percent Problems: Ccss.Math.Content.7.Rp.A.3

If you get a 25% discount, what percentage of the original price will you have to pay?

Explanation:

The original price will represent 100% of the item price since that represents the whole for the problem.

If you get 25% off, you must take that away from the 100%.

so you will have to pay 75% of the original price.

### Example Question #11 : Use Proportional Relationships To Solve Multistep Ratio And Percent Problems: Ccss.Math.Content.7.Rp.A.3

What is the sale price of a product that costs  if the sale is  off the original price?

Explanation:

First, find  of :

Then, subtract this value from the whole:

### Example Question #11 : Use Proportional Relationships To Solve Multistep Ratio And Percent Problems: Ccss.Math.Content.7.Rp.A.3

What is the sale price of a television if it is % off the original price of

Explanation:

First, multiply:

Then subtract that amount from the original price:

Answer: The sale price is .

### Example Question #17 : Use Proportional Relationships To Solve Multistep Ratio And Percent Problems: Ccss.Math.Content.7.Rp.A.3

A sweater was originally , but the department store is running a  off sale. What is the sale price of the sweater?

Explanation:

In order to solve this problem, we need to calculate  of . The key word "of" is indicative of multiplication; however, we need to start by converting the percentage into a decimal because you cannot multiply a number by a percent.

We can convert a percent into a decimal by moving the decimal two places to the left:

Next, we can multiply:

Remember, we are taking  off the original price, which means we need to subtract.

### Example Question #18 : Use Proportional Relationships To Solve Multistep Ratio And Percent Problems: Ccss.Math.Content.7.Rp.A.3

A sweater was originally , but the department store is running a  off sale. What is the sale price of the sweater?

Explanation:

In order to solve this problem, we need to calculate  of . The key word "of" is indicative of multiplication; however, we need to start by converting the percentage into a decimal because you cannot multiply a number by a percent.

We can convert a percent into a decimal by moving the decimal two places to the left:

Next, we can multiply:

Remember, we are taking  off the original price, which means we need to subtract.

### Example Question #19 : Use Proportional Relationships To Solve Multistep Ratio And Percent Problems: Ccss.Math.Content.7.Rp.A.3

A sweater was originally , but the department store is running a  off sale. What is the sale price of the sweater?

Explanation:

In order to solve this problem, we need to calculate  of . The key word "of" is indicative of multiplication; however, we need to start by converting the percentage into a decimal because you cannot multiply a number by a percent.

We can convert a percent into a decimal by moving the decimal two places to the left:

Next, we can multiply:

Remember, we are taking  off the original price, which means we need to subtract.

### Example Question #11 : Use Proportional Relationships To Solve Multistep Ratio And Percent Problems: Ccss.Math.Content.7.Rp.A.3

A sweater was originally , but the department store is running a  off sale. What is the sale price of the sweater?

Explanation:

In order to solve this problem, we need to calculate  of . The key word "of" is indicative of multiplication; however, we need to start by converting the percentage into a decimal because you cannot multiply a number by a percent.

We can convert a percent into a decimal by moving the decimal two places to the left:

Next, we can multiply:

Remember, we are taking  off the original price, which means we need to subtract.