Ratio and Proportion - SSAT Elementary Level Quantitative
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What is 10% of 100?
What is 10% of 100?
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10% of 100 is calculated by multiplying .10 by 100.
10% of 100 is calculated by multiplying .10 by 100.
What is 13% of 100?
What is 13% of 100?
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13% of 100 is calculated by multiplying .13 by 100.
13% of 100 is calculated by multiplying .13 by 100.
Solve for the variable:
Solve for the variable:
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There are two ways to solve. First, you may see that the top numbers are related by multiplying by 2.
This means that the bottom numbers must also be related by multiplying by 2.
The missing number is therefore 8.
The other way to solve is to cross multiply:
Solve for 
by dividing 24 by 3:
The answer is again 8.
There are two ways to solve. First, you may see that the top numbers are related by multiplying by 2.
This means that the bottom numbers must also be related by multiplying by 2.
The missing number is therefore 8.
The other way to solve is to cross multiply:
Solve for
The answer is again 8.
Solve for the variable:
Solve for the variable:
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Cross multiply:
Solve for 
by dividing 135 by 9:
Cross multiply:
Solve for
Solve for the variable:
Solve for the variable:
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Cross multiply:
Solve for x by dividing 60 by 12:
Cross multiply:
Solve for x by dividing 60 by 12:
What is 
of 
?
What is
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of 
is calculated by multiplying .
by 
.
What is 
of 
?
What is
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of 
is calculated by multiplying 
by 
.
Sofia goes to the movies with 
. She spends 
on her ticket and 
on food and drink.
What fraction of Sofia's original 
was not spent?
Sofia goes to the movies with
What fraction of Sofia's original
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Adding Sofia's expenses shows that she spent a total of 
dollars. Subtracting this from the original amount of money she had gives the unspent portion: 
.
The ratio of the unspent portion to the original amount gives the fraction of the money that was not spent: 
.
Adding Sofia's expenses shows that she spent a total of
The ratio of the unspent portion to the original amount gives the fraction of the money that was not spent:
Brad is paid 
per hour at his current job. If a promotion would increase Brad's pay by 
, what would Brad make per hour after a promotion?
Brad is paid
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To find 
of Brad's pay, multiply it by 
(since 
is the original number and 
is twice that). 
, which is the amount of the increase to Brad's pay. Add this increase to the original pay to get the new pay: 
per hour.
To find
Solve for x:
Solve for x:
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Multiply both sides by 3 to yield:
Multiply both sides by 3 to yield:
Solve for y:
Solve for y:
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Multiply both sides by 8 to yield:
Therefore:
Therefore:
Multiply both sides by 8 to yield:
Therefore:
Therefore:
A 
sweater is on sale for 
. What percentage of the original price has been discounted for the sale?
A
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Set up a proportion of the new price to the old price to see how they relate.
of the original price
Subtract 
from 
to find the amount that was discounted.
Convert 
to a decimal by multiplying both the top and bottom of the fraction by 
, then convert to a percentage.
, which is equivalent to 
or 
Set up a proportion of the new price to the old price to see how they relate.
Subtract
Convert
Mary wants to enlarge a picture that she has in her office. The original picture is 
cm (width) by 
cm (length). What would be the length of the enlarged picture if the width is 
cm?
Mary wants to enlarge a picture that she has in her office. The original picture is
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To find the length of the enlarged picture, we must set up a proportion:
cross multiply:
Divide both sides by 5:
To find the length of the enlarged picture, we must set up a proportion:
cross multiply:
Divide both sides by 5:
Megan's teacher says that if Megan wants to join the girl's basketball team, she has to have at least 
of this quarter's homework turned in. If there have been 
assignments so far this quarter, how many of these does Megan have to have turned in so that she can join the team?
Megan's teacher says that if Megan wants to join the girl's basketball team, she has to have at least
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In order to solve this problem, we need to make a ratio. Megan's teacher says she needs to have turned in 90% of her homework. First we need to change 90% into a fraction:
Using this information, we need to fill in the following ratio to find out how many assignments Megan needs to have turned in to be at 90% completion:
To solve this ratio, we need to cross multiply.
Now we have an equation to solve.
If we divide both sides by 100, we are left with our final answer.
Megan must have at least 45 assignments turned in if she wants to join the basketball team.
In order to solve this problem, we need to make a ratio. Megan's teacher says she needs to have turned in 90% of her homework. First we need to change 90% into a fraction:
Using this information, we need to fill in the following ratio to find out how many assignments Megan needs to have turned in to be at 90% completion:
To solve this ratio, we need to cross multiply.
Now we have an equation to solve.
If we divide both sides by 100, we are left with our final answer.
Megan must have at least 45 assignments turned in if she wants to join the basketball team.
Find the unknown value: 
Find the unknown value:
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To solve the proportion, cross multiply and find the value of the missing variable.
Divide by 
on both sides.
To solve the proportion, cross multiply and find the value of the missing variable.
Divide by
Solve: 
Solve:
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Solve by cross multipling the two fractions.
Divide by 
on both sides.
Solve by cross multipling the two fractions.
Divide by
If I have 6 red marbles and 5 blue marbles, what proportion of the marbles are red.
If I have 6 red marbles and 5 blue marbles, what proportion of the marbles are red.
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To find a proportion, simply divide what you desire by the total.
In this problem the desired is the number of red marbles and the total is all of the marbels.
Thus,
To find a proportion, simply divide what you desire by the total.
In this problem the desired is the number of red marbles and the total is all of the marbels.
Thus,
I have 7 green marbles and 4 blue marbles. Find the proportion of green marbles.
I have 7 green marbles and 4 blue marbles. Find the proportion of green marbles.
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To find a proportion, simply divide the desired amount by the total amount. We know our total by simply adding the marble amounts that compose it. Thus,
To find a proportion, simply divide the desired amount by the total amount. We know our total by simply adding the marble amounts that compose it. Thus,
Solve the following proportion:
Solve the following proportion:
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When solving a proportion, it is easiest to re-write it using fraction. So,
can be re-written as
Now, to solve this, we will cross multiply and divide.
To cross multiply, we will take the numerator of the first fraction and multiply it by the denominator of the second fraction. Then, we multiply the denominator of the first fraction by the numerator in the second, and set them equal to each other.
It might be easier to see an example.
Now, we divide to solve for x.
When solving a proportion, it is easiest to re-write it using fraction. So,
can be re-written as
Now, to solve this, we will cross multiply and divide.
To cross multiply, we will take the numerator of the first fraction and multiply it by the denominator of the second fraction. Then, we multiply the denominator of the first fraction by the numerator in the second, and set them equal to each other.
It might be easier to see an example.
Now, we divide to solve for x.