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

## Example Questions

### Example Question #1 : Rational Numbers

In a high school of  students, the ratio of freshmen to sophomores to juniors to seniors is . How many juniors does this high school have?

Explanation:

Let  be the number of freshmen,  be the number of sophomores,  be the number of juniors, and  be the number of seniors.

Because the high school has  students,

Since we want to find out how many juniors there are, we need the value of .

### Example Question #1 : Proportion / Ratio / Rate

In a high school, the ratio of freshmen to seniors is . If there are  seniors, how many freshmen are there?

Explanation:

Set up the following proportion, with  being the number of freshmen.

Now, cross-multiply and solve for .

### Example Question #1 : Rational Numbers

On a beach, the ratio of crabs to seagulls is . If there are  crabs and seagulls on the beach, how many crabs are there?

Explanation:

Let  be the number of crabs and  be the number of seagulls.

Since there are  crabs and seagulls on the beach,

Because the question asks for the number of crabs, we need to find the value of .

### Example Question #2 : Decide If Two Quantiies Are In A Proportional Relationship: Ccss.Math.Content.7.Rp.A.2a

There are  boys and  girls at a playground. What is the ratio of boys to girls?

Explanation:

Write the numbers of boys and girls as a fraction, then simplify.

can also be written as

### Example Question #2 : Rational Numbers

At a high school, there are  freshmen,  sophomores,  juniors, and  seniors. What is the ratio of seniors to freshmen?

to

to

to

to

to

Explanation:

Write the number of seniors and numbers of freshmen as a fraction:

That fraction is equivalent to .

### Example Question #3 : Rational Numbers

The angles in a triangle are in the ratio . What is the angle measurement of the largest angle?

Explanation:

Let  be the values of the angles.

Since all the angles in a triangle need to add up to ,

Because we want the value of the largest angle, we need to find the value of .

### Example Question #11 : How To Find A Ratio

John and Michela are business partners who agreed to split profits at a ratio of , with Michela taking the larger share. If their business made  in the first year, how much money did Michela make?

Explanation:

Let  be the amount John takes home and  be the amount Michela takes home.

We want to know how much Michela made so we need to find the value of .

### Example Question #11 : Rational Numbers

The angles in a triangle have a ratio of . What is the measurement of the smallest angle?

Explanation:

Let  be the values of the angles.

Since there are  degrees in a triangle,

Since we want the value of the smallest angle, find the value of .

### Example Question #12 : How To Find A Ratio

In a factory, there are  glass bottles. If the ratio of red bottles to blue bottles is , how many more blue bottles than red bottles are there?

Explanation:

First, find the number of red bottles and blue bottles.

Let  be the number of red bottles and  be the number of blue bottles. Since there is a total of  bottles at the factory,

There are  red bottles. Find the value of  to find the number of blue bottles.

Now, because the question wants to find how many more blue bottles than red bottles there are, subtract the number of red bottles from the number of blue bottles.

### Example Question #12 : Rational Numbers

The ratio of offensive players to defensive players on a football team is . If there are  players on the team, how many offensive players are there?