# Common Core: 7th Grade Math : Ratios & Proportional Relationships

## Example Questions

### Example Question #1 : How To Find Rate

On a map, . If two cities are  apart on the map, how many miles apart are they in reality?

Explanation:

Set up the following proportion:

,

where  is the number of miles the cities are apart.

Now, solve for .

The two cities are  miles apart.

### Example Question #11 : Ratios & Proportional Relationships

Chuck is building a driveway that measures  feet by  feet. He needs to use  pounds of cement for every square foot of driveway. How many pounds of cement does he need to complete the driveway?

Explanation:

First, find the area of the driveway.

Since it takes  pounds of cement per square feet,

pounds will be needed to complete the driveway.

### Example Question #11 : Grade 7

Joanna can finish  math problems in  minutes. How many minutes would it take her to finish  math problems?

Explanation:

First, find out how long it will take her to finish  math problem.

Since it takes Joanna  minutes to finish one problem, multiply this number by the amount of questions she needs to do.

It will take her  minutes to finish  questions.

### Example Question #11 : Compute Unit Rates Associated With Ratios Of Fractions: Ccss.Math.Content.7.Rp.A.1

A car travels  miles in  hours. At what rate does the car travel?

Explanation:

Divide the number of miles by the number of hours to get the number of miles per hour.

### Example Question #12 : Ratios & Proportional Relationships

Joe used  of a bag of oranges to squeeze  of a gallon of juice. At this rate, how many bags of oranges does he use per gallon of juice?

Explanation:

The phrase "bags of oranges does he use per gallon" gives us a clue that we are going to divide. In this problem, we can replace the word "per" with a division sign; therefore, we will have bags of oranges, , divided by gallons, :

Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.

Therefore:

Joe will use  bags of oranges to fill a gallon of juice.

### Example Question #13 : Compute Unit Rates Associated With Ratios Of Fractions: Ccss.Math.Content.7.Rp.A.1

A landscaper can mow  of a yard in  of an hour. If he continues at this rate, how many yards can the landscaper mow per hour?

Explanation:

The phrase "per hour" gives us a clue that we are going to divide. In this problem, we can replace the word "per" with a division sign; therefore, we will have yards, , divided by hours, :

Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.

Therefore:

The landscaper can mow  yards per hour.

### Example Question #12 : Grade 7

Hannah loves to shop. She can shop in  of the mall in  of an hour. If she continues at this rate, how much of the mall can she shop per hour?

Explanation:

The phrase "per hour" gives us a clue that we are going to divide. In this problem, we can replace the word "per" with a division sign; therefore, we will have the portion of the mall, , divided by hours, :

Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.

Therefore:

Hannah can shop in  of the mall per hour.

### Example Question #12 : Compute Unit Rates Associated With Ratios Of Fractions: Ccss.Math.Content.7.Rp.A.1

Charlie walks  of a mile  in  of an hour. If he continues this rate, what is Charlie's speed in miles per hour

Explanation:

The phrase "miles per hour" gives us a clue that we are going to divide. In this problem, we can replace the word "per" with a division sign; therefore, we will have miles, , divided by hours, :

Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.

Therefore:

Charlie can walk at a speed of:

### Example Question #14 : Compute Unit Rates Associated With Ratios Of Fractions: Ccss.Math.Content.7.Rp.A.1

Alan walks  of a mile  in  of an hour. If he continues this rate, what is Alan's speed in miles per hour

Explanation:

The phrase "miles per hour" gives us a clue that we are going to divide. In this problem, we can replace the word "per" with a division sign; therefore, we will have miles, , divided by hours, :

Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.

Therefore:

Alan can walk at a speed of:

### Example Question #15 : Compute Unit Rates Associated With Ratios Of Fractions: Ccss.Math.Content.7.Rp.A.1

Jake walks  of a mile  in  of an hour. If he continues this rate, what is Jake's speed in miles per hour

Explanation:

The phrase "miles per hour" gives us a clue that we are going to divide. In this problem, we can replace the word "per" with a division sign; therefore, we will have miles, , divided by hours, :

Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.

Therefore:

Jake can walk at a speed of: