Operations with Fractions - SSAT Upper Level Quantitative
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Find the arithmetic mean of the following five numbers.
Find the arithmetic mean of the following five numbers.
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Add the numbers, then divide by 
or, equivalently, multiply by 
.
Find the common denominator of the terms we are adding.
Multiply and simplify.
Add the numbers, then divide by
Find the common denominator of the terms we are adding.
Multiply and simplify.
Solve,
Solve,
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Since the denominators for the fractions are the same, keep the denominator and add the numerators.
Since the denominators for the fractions are the same, keep the denominator and add the numerators.
Scott gave 
of the chocolate chip cookies he made to Cindy, and he gave 
of the cookies to Stephanie. What fraction of his chocolate chip cookies did he give away?
Scott gave
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This question wants you to add 
and 
. First, convert both fractions so that they share the same denominator.
This question wants you to add
A poll was conducted in a class to see what fraction of the class plays sports. 
of the class plays basketball, and 
of the class plays soccer. The rest of the class do not play any sports. What fraction of the class plays a sport?
A poll was conducted in a class to see what fraction of the class plays sports.
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To find what fraction of the class plays a sport, add together 
and 
.
First, convert both fractions so that the denominators are the same.
Now, you can add them together.
To find what fraction of the class plays a sport, add together
First, convert both fractions so that the denominators are the same.
Now, you can add them together.
Peter ate 
of a pie for breakfast, then ate 
of the pie as a morning snack. How much of the pie did Peter eat?
Peter ate
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To find how much of the pie Peter ate, you will need to add together 
and 
.
Start by converting both fractions so that the denominators are the same.
Now, you can add the fractions.
To find how much of the pie Peter ate, you will need to add together
Start by converting both fractions so that the denominators are the same.
Now, you can add the fractions.
On a given week, Jeremy spends 
of his time working on homework and 
of his time doing chores. What fraction of his time is spent doing homework and doing chores?
On a given week, Jeremy spends
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To find how much time Jeremy spends doing his homework and his chores, add together 
and 
.
First, convert both fractions so that they have the same denominator.
Now, you can add the fractions together.
To find how much time Jeremy spends doing his homework and his chores, add together
First, convert both fractions so that they have the same denominator.
Now, you can add the fractions together.
Timothy spends 
of his weekly allowance on comic books and 
of his weekly allowance on candy. What fraction of his weekly allowance does he spend on comic books and candy?
Timothy spends
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To find out how much of his weekly allowance Timothy spends on candy and comic books, add 
and 
together.
To do so, you need to first convert both fractions so that they have the same denominator.
Now you can add together the fractions.
To find out how much of his weekly allowance Timothy spends on candy and comic books, add
To do so, you need to first convert both fractions so that they have the same denominator.
Now you can add together the fractions.
In a jar of marbles, 
of the marbles are red and 
of the marbles of blue. What fraction of the jar of marbles are red and blue marbles?
In a jar of marbles,
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To find out what fraction of the jar are red and blue marbles, add 
and 
together.
First, you need to convert the fractions so that they have the same denominator. Since 
is a multiple of 
, you only need to change one fraction.
Now, add the fractions together.
To find out what fraction of the jar are red and blue marbles, add
First, you need to convert the fractions so that they have the same denominator. Since
Now, add the fractions together.
Jim baked two batches of cookies. In the first batch, he used 
cup of sugar. In his second batch, he used 
cups of sugar. In cups, how much sugar did he use in total?
Jim baked two batches of cookies. In the first batch, he used
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To find how much sugar he used in total, add 
and 
together.
First, make sure that both fractions have the same denominator before you add them. Since 
is a multiple of 
, you will need to convert 
into 
by multiplying both numerator and denominators by 
.
Now, add the fractions.
To find how much sugar he used in total, add
First, make sure that both fractions have the same denominator before you add them. Since
Now, add the fractions.
Lucy gave away 
of her hair ribbons to Megan and 
of her hair ribbons to Patrice. What fraction of her hair ribbons did Lucy give away?
Lucy gave away
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You will need to add together 
and 
.
Since 
is a multiple of 
, we can use 
as the common denominator.
Then, 
You will need to add together
Since
Then,
Solve,
Solve,
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In order to add the fractions, you need to first find a common denominator. For 
and 
, the least common denominator is 
.
Then,
In order to add the fractions, you need to first find a common denominator. For
Then,
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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.
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.
Michael ate 
of a cake for breakfast, and then 
of the same cake for dinner. How much of the cake did Michael eat?
Michael ate
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To figure out how much cake Michael ate, you will need to add the two fractions given in the question.
First, find the common denominator of both fractions and convert them so that they have that denominator.
Now, add the fractions.
To figure out how much cake Michael ate, you will need to add the two fractions given in the question.
First, find the common denominator of both fractions and convert them so that they have that denominator.
Now, add the fractions.
On a certain game show, the audience is polled. 
of the audience enjoys playing football, and 
of the audience enjoys playing basketball. What fraction of the audience enjoys playing football and basketball?
On a certain game show, the audience is polled.
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Add the fractions together. In order to do so, you will need to convert 
so that it shares the same denominator as 
.
Now, add the fractions.
Add the fractions together. In order to do so, you will need to convert
Now, add the fractions.
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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.
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.
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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.
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.
Multiply these fractions:
Multiply these fractions:
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To multiply the fractions, simply multiply the numerators together and the denominators together.
Since this fraction is in its simplest form, that is the final answer.
To multiply the fractions, simply multiply the numerators together and the denominators together.
Since this fraction is in its simplest form, that is the final answer.
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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.
In this case, you can reduce the fractions being multiplied by cross-canceling before multiplying them together.
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.
In this case, you can reduce the fractions being multiplied by cross-canceling before multiplying them together.
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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.
In this case, you can reduce the fractions being multiplied by cross-canceling before multiplying them together.
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.
In this case, you can reduce the fractions being multiplied by cross-canceling before multiplying them together.
Tap to see back →
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.
In this case, you can reduce the fractions being multiplied by cross-canceling before multiplying them together.
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.
In this case, you can reduce the fractions being multiplied by cross-canceling before multiplying them together.