# ISEE Lower Level Quantitative : Ratio and Proportion

## Example Questions

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### Example Question #1 : How To Find A Ratio

Stacy has started collecting coins.  She has twice as many wheat pennies as she does 1946 dimes, and three times as many 1983 quarters as she does 1946 dimes.  If Stacy has  1946 dimes, what is the ratio of wheat pennies to 1983 quarters?

Explanation:

We know that Stacy has 1946 dimes.

We also know that she has twice as many wheat pennies, so we must multiply by to find the total number of wheat pennies.

We also know that Stacy has three times as many 1986 quarters, so we multiply by to find the total number of 1986 quarters.

Now our ratio of wheat pennies to 1986 quarters is , but this can be simplified because both numbers are divisible by .

So our ratio becomes

### Example Question #2 : How To Find A Ratio

Cassie works a four hour shift at the coffee shop.  During her shift,  customers order coffee,  order orange juice, and  order hot choclate.  What is the ratio of customers who order orange juice to those who order coffee?

Explanation:

Since there are customers who order orange juice, is the first number of our ratio.

The second number of our ratio is , because people order coffee.

Therefore, our ratio is :

### Example Question #3 : How To Find A Ratio

Steve is having a birthday party. So far, he has invited thirty-nine of his friends from school, fifteen of whom are girls. He wants to make the ratio of girls to boys at the party two to one. How many more girls does he need to invite, assuming no more boys are invited?

Explanation:

Counting Steve, there are forty attendees so far, fifteen of whom are girls and twenty-five of whom (including Steve) are boys. To obtain a two-to-one girl to boy ratio, he needs to invite a total of fifty girls, so he needs to invite thirty-five more.

### Example Question #4 : How To Find A Ratio

Scott's mother bakes 12 cookies and he eats half of them. Scott's mom then puts red frosting on 4 cookies and blue frosting on the rest of the cookies. What is the ratio of cookies with red frosting to cookies with blue frosting?

Explanation:

If Scott's mother bakes 12 cookies and he eats half of them, that means he will eat 6 cookies, leaving 6 uneaten cookies.

If Scott's mom then puts red frosting on 4 cookies and blue frosting on the rest of the cookies, 2 cookies will get blue frosting. ().

Therefore, the ratio of cookies with red frosting to cookies with blue frosting is , which is equal to .

### Example Question #5 : How To Find A Ratio

For every 3 peanuts in a bag of trail mix, there are 1 chocolate chip and 2 raisins. What is the proportion of raisins in the mix?

Explanation:

Given that there are 3 peanuts for every 1 chocolate chip and 2 raisins, the proportion of raisins can be found by dividing the number of raisins by the sum of all the items in the mix. This results in:

### Example Question #6 : How To Find A Ratio

Jose is  times taller than his baby brother Michael. If Jose is  inches tall, how tall is Michael?

inches

inches

inches

inches

inches

Explanation:

The ratio of Jose to Michael's height is .

Thus, if Jose is  inches taller than Michael must be  times shorter.

We can write this as the expression, .

Also, an equivalent ratio for  = .

### Example Question #1 : How To Find A Ratio

Find an equivalent ratio.

Explanation:

An equivalent ratio of  is .

This is the furthest simplification of the ratio.
The greatest common divisor is needed to simplify the expression.

Both  and  are divisible by ,   and  .

### Example Question #8 : How To Find A Ratio

Solve for

Explanation:

To solve this problem the relationship between the two numbers in the first ratio needs to be established.

Since,  is  times larger than , an equivalent ratio must have the same relationship.

Thus,  must be  times larger than , and

Thus,

### Example Question #9 : How To Find A Ratio

There are  students in a fifth grade class. If there are  girls in the class, what is the ratio of the number of boys in the class to the total number of students in the class?

Explanation:

First, find the number of boys in the class by subtracting the number of girls in the class from the total number of students.

Now, we know that the ratio of the number of boys in the class to the total number of students in the class is .

We can express that ratio as the following fraction:

### Example Question #10 : How To Find A Ratio

There are  students in a computer science class. If there are  boys in the class, what is the ratio of the number of girls in the class to the total number of students in the class?