# SSAT Upper Level Math : Rational Numbers

## Example Questions

### Example Question #1 : Grade 7

If it takes Dennis  minutes to paint  walls, how many minutes does it take him to paint  wall?

Explanation:

Divide the time it take Dennis to paint  walls by the number of walls he painted to find how long it will take him to paint one wall.

It will take Dennis  minutes to paint one wall.

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

An arcade charges players  to play on the machine for  minutes. How much money would it cost a player if she wanted to play for an hour?

Explanation:

First, find out how much money it costs to play for one minute.

Now, multiply this amount by the number of minutes in an hour to find how much it will cost for the player to play for one hour.

It will cost her  to play for one hour.

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

If a doctor charges  per hour for her services, how much would it cost to hire this doctor for  minutes?

Explanation:

First, convert the minutes to hours.

Since  minutes is  hours, multiply this by the doctor's hourly rate to find how much it will cost to hire this doctor for  minutes.

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

A dentist charges  per hour for the first three hours of an appointment. Any amount of time greater than three hours is charged at  per hour. If a patient had a  hour long appointment, how much would this appointment cost?

Explanation:

Use the dentist's rate to find how much the first three hours of the appointment will cost.

Next, use the dentist's second rate to find out how much the last five hours of the appointment will cost.

Now, add these values together to get the cost of the entire appointment.

### 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 #1151 : Ssat Upper Level Quantitative (Math)

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 #1 : How To Find The Ratio Of A Fraction

A pie is made up of   crust,  apples, and  sugar, and the rest is jelly. What is the ratio of crust to jelly?

Explanation:

A pie is made up of   crust,  apples,  sugar, and the rest is jelly. What is the ratio of crust to jelly?

To compute this ratio, you must first ascertain how much of the pie is jelly. This is:

Begin by using the common denominator :

So, the ratio of crust to jelly is:

This can be written as the fraction:

, or

### Example Question #4 : How To Find The Ratio Of A Fraction

In a solution,  of the fluid is water,  is wine, and  is lemon juice. What is the ratio of lemon juice to water?

Explanation:

This problem is really an easy fraction division. You should first divide the lemon juice amount by the water amount:

Remember, to divide fractions, you multiply by the reciprocal:

This is the same as saying:

### Example Question #1 : How To Find The Ratio Of A Fraction

If  and , what is the ratio of  to ?