SSAT Upper Level Quantitative › Rational Numbers
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.
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.
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:
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
?
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.
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:
To multiply the fractions, simply multiply the numerators together and the denominators together.
Then simplify the fraction accordingly:
Simplify.
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?
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?
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.