Rational Numbers
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SSAT Upper Level Quantitative › Rational Numbers
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.
Convert  to an improper fraction.
Explanation
To convert into an improper fraction, take the whole number  and multiply that with the denominator 
.
Then, we add that to the numerator which is .
Then we take that sum and put it over th denominator  which gives us an answer of:
.
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.
Simplify:
Explanation
Simplify into a complex fraction for the numerator and denominator.
For the numerator, we need to multiply  then the top should read 
.
For the bottom, we need to multiply  in order to add the components. Thus the bottom should read 
.
Dividing fractions is the same as multiplying the numerator by the reciprocal of the denominator.
Therefore, multiply top and bottom by  and then you should see that if you factor a 
 on the bottom, the 
 cancels along with the 
.
The answer then should be .
What is the least common denominator for the fractions  and 
?
Explanation
To find the least common denominator, list out the multiples for each denominator then choose the lowest one that is in both sets.
Convert  to a percent.
Explanation
Percent also means out of one hundred. Set up the following ratio to find the percent value.
Now, solve for , which will be the percent value because in the ratio we set up, 
 is the numerator of a fraction with a denominator of 
.
Multiply these fractions:
Explanation
To multiply the fractions, simply multiply the numerators together and the denominators together.
Then simplify the fraction accordingly:
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.
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.
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.