Fractions

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SSAT Upper Level Quantitative › Fractions

Questions 1 - 10
1

Convert into a fraction in simplest form.

Explanation

Think of the decimal as the fraction .

Now, multiply the numerator and denominator by for every digit after the decimal. In this case, because there are digits after the decimal, we will be multiplying by twice, or by .

Now, simplify this fraction.

2

Explanation

Keep in mind that the main fraction line just means "divide."

So then,

Now, divide this like any other fraction.

3

Simplify.

Explanation

When multiplying fractions, find a way to reduce any of the fractions before multplying them out.

For example, since is a multiple of , you would cancel out the and that becomes a and the becomes a .

The same goes for and . The becomes and the goes to .

Overall, the fractions to multiply becomes

. Answer should be .

is not correct because it's not reduced.

4

Explanation

Turn the second fraction upside down to find its reciprocal, and then multiply the first fraction by the reciprocal of the second fraction to divide the two fractions. When multiplying fractions, you can multiply across, finding the products of the numbers being multiplied in the numerator and in the denominator.

5

What is the result of this operation?

Explanation

Since the denominators are exactly the same, we can just subtract the tops.

So

By reducing we get

6

After a discount, a car costs . How much did the car cost before the discount?

Explanation

Let be the cost of the car before the discount. Since we know that the car at a discount costs , we can write the following equation:

Now, solve for to find the cost of the car before the discount.

The car originally cost before the discount was applied.

7

Put the fraction in simplest form.

Explanation

To simplify a fraction, divide both the numerator and the denominator by the same numbers until there is no number that can divide them both without resulting in a remainder.

8

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 .

9

Julie can read pages in minutes. How long, in minutes, would it take Julie to read a book that had pages?

Explanation

First, figure out how long it takes Julie to read 1 page.

It takes Julie minutes to read one page. Now, multiply this by the number of pages she needs to read to find out how long it will take her.

It will take Julie minutes to read pages.

10

Express as a ratio.

Explanation

Ratios take the form of numerator:deminator when in colon form.

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