Proportion / Ratio / Rate - SSAT Upper Level Quantitative
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In a zoo with 
animals, the ratio of mammals to reptiles to birds is 
. How many birds does the zoo have?
In a zoo with
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Let 
be the number of mammals,
be the number of reptiles, and 
be the number of birds.
Since the zoo has 
animals,
Because we want the number of birds, we need to find the value of 
.
Let
Since the zoo has
Because we want the number of birds, we need to find the value of
John and Michela are business partners who agreed to split profits at a ratio of 2:3, with Michela taking the larger share. If their business made 
in the first year, how much money did Michela make?
John and Michela are business partners who agreed to split profits at a ratio of 2:3, with Michela taking the larger share. If their business made
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Let 
be the amount John takes home and 
be the amount Michela takes home.
Since their business made 
,
We want to know how much Michela made so we need to find the value of 
.
Let
Since their business made
We want to know how much Michela made so we need to find the value of
When television remotes are shipped from a certain factory, 1 out of every 200 is defective. What is the ratio of defective to nondefective remotes?
When television remotes are shipped from a certain factory, 1 out of every 200 is defective. What is the ratio of defective to nondefective remotes?
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One remote is defective for every 199 non-defective remotes.
One remote is defective for every 199 non-defective remotes.
On a desk, there are 
papers for every 
paper clips and 
papers for every 
greeting card. What is the ratio of paper clips to total items on the desk?
On a desk, there are
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Begin by making your life easier: presume that there are 
papers on the desk. Immediately, we know that there are 
paper clips. Now, if there are 
papers, you know that there also must be 
greeting cards. Technically you figure this out by using the ratio:
By cross-multiplying you get:
Solving for 
, you clearly get 
.
(Many students will likely see this fact without doing the algebra, however. The numbers are rather simple.)
Now, this means that our desk has on it:
papers
paper clips
greeting cards
Therefore, you have 
total items. Based on this, your ratio of paper clips to total items is:
, which is the same as 
.
Begin by making your life easier: presume that there are
By cross-multiplying you get:
Solving for
(Many students will likely see this fact without doing the algebra, however. The numbers are rather simple.)
Now, this means that our desk has on it:
Therefore, you have
In a garden, there are 
pansies, 
lilies, 
roses, and 
petunias. What is the ratio of petunias to the total number of flowers in the garden?
In a garden, there are
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To begin, you need to do a simple addition to find the total number of flowers in the garden:
Now, the ratio of petunias to the total number of flowers in the garden can be represented by a simple division of the number of petunias by 
. This is:
Next, reduce the fraction by dividing out the common 
from the numerator and the denominator:
This is the same as 
.
To begin, you need to do a simple addition to find the total number of flowers in the garden:
Now, the ratio of petunias to the total number of flowers in the garden can be represented by a simple division of the number of petunias by
Next, reduce the fraction by dividing out the common
This is the same as
In a classroom of 
students, each student takes a language class (and only one—nobody studies two languages). 
take Latin, 
take Greek, 
take Anglo-Saxon, and the rest take Old Norse. What is the ratio of students taking Old Norse to students taking Greek?
In a classroom of
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To begin, you need to calculate how many students are taking Old Norse. This is:
Now, the ratio of students taking Old Norse to students taking Greek is the same thing as the fraction of students taking Old Norse to students taking Greek, or:
Next, just reduce this fraction to its lowest terms by dividing the numerator and denominator by their common factor of 
:
This is the same as 
.
To begin, you need to calculate how many students are taking Old Norse. This is:
Now, the ratio of students taking Old Norse to students taking Greek is the same thing as the fraction of students taking Old Norse to students taking Greek, or:
Next, just reduce this fraction to its lowest terms by dividing the numerator and denominator by their common factor of
This is the same as
Express 
as a ratio.
Express
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Ratios take the form of numerator:deminator when in colon form.
Ratios take the form of numerator:deminator when in colon form.
In a biology class, 
students are freshmen, 
students are sophomores, and 
students are juniors. What is the ratio of sophomores to freshmen in the class?
In a biology class,
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The ratio of sophomores to freshmen in the class can be expressed by the fraction 
.
Now, simplify this fraction.
That fraction can also be expressed as 
.
The ratio of sophomores to freshmen in the class can be expressed by the fraction
Now, simplify this fraction.
That fraction can also be expressed as
A video store lent out 
videos during the fall semester. 
of the videos were lost, and the rest were returned. What is the ratio of lost videos to returned videos?
A video store lent out
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First, find the number of videos that were returned.
Now, the ratio of videos lost to videos returned can be expressed as the following fraction:
This fraction can then be expressed as 
.
First, find the number of videos that were returned.
Now, the ratio of videos lost to videos returned can be expressed as the following fraction:
This fraction can then be expressed as
In a music class of 
students, 
students play the clarinet, 
students play the violin, 
students play the oboe, and the rest play the piano. What is the ratio of piano players to oboe players in the class?
In a music class of
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First, find out how many piano players there are in the class.
Now, we can express the ratio of piano players to oboe players as the following fraction:
The fraction can also be expressed by 
.
First, find out how many piano players there are in the class.
Now, we can express the ratio of piano players to oboe players as the following fraction:
The fraction can also be expressed by
In a garden with 
plants, 
are tulips, 
are daisies, 
are roses, and the rest are bluebonnets. What is the ratio of bluebonnets to tulips in this garden?
In a garden with
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First, find the number of bluebonnets in the garden.
The ratio of bluebonnets to tulips can be expressed as a fraction:
The fraction can also be expressed as the ratio 
.
First, find the number of bluebonnets in the garden.
The ratio of bluebonnets to tulips can be expressed as a fraction:
The fraction can also be expressed as the ratio
Express 
as a ratio.
Express
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In the colon form of a ratio, the fraction becomes numerator:denominator.
In the colon form of a ratio, the fraction becomes numerator:denominator.
A smoothie is made with 
cups of apple juice, 
cup of mango juice, 
cups of orange juice, and 
cups of blueberry juice. What is the ratio of the amount of orange juice to the amount of blueberry juice?
A smoothie is made with
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The ratio of orange juice to blueberry juice can be expressed as a fraction:
That fraction can also be expressed as 
.
The ratio of orange juice to blueberry juice can be expressed as a fraction:
That fraction can also be expressed as
Express 
as a ratio in simplest terms.
Express
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First, reduce the fraction.
Now, the simplified fraction can also be expressed as 
.
First, reduce the fraction.
Now, the simplified fraction can also be expressed as
A pan of cupcakes had 
cupcakes on Monday. After one day, 
cupcakes were eaten. What is the ratio of cupcakes eaten to cupcakes remaining?
A pan of cupcakes had
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First, find the number of cupcakes that remain.
Now, set up the ratio of cupcakes eaten to cupcakes remaining as a fraction:
That fraction is equivalent to 
.
First, find the number of cupcakes that remain.
Now, set up the ratio of cupcakes eaten to cupcakes remaining as a fraction:
That fraction is equivalent to
In a group of dolphins, there are 
male dolphins for every 
female dolphins. What is the ratio of female dolphins to male dolphins in this group?
In a group of dolphins, there are
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The ratio of female to male dolphins can be expressed as the following fraction:
That fraction can be expressed using the colon form of a ratio as 
.
The ratio of female to male dolphins can be expressed as the following fraction:
That fraction can be expressed using the colon form of a ratio as
In an animal shelter, there are 
cats, 
birds, and 
dogs. What is the ratio of dogs to the total number of animals at the shelter?
In an animal shelter, there are
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First, find the total number of animals at the shelter.
The ratio of dogs to the total number of animals can be expressed as the following fraction:
That fraction can also be expressed as 
.
First, find the total number of animals at the shelter.
The ratio of dogs to the total number of animals can be expressed as the following fraction:
That fraction can also be expressed as
There are 
marbles in a bag. In the bag, there are 
red marbles, 
blue marbles, and the rest of the marbles are yellow. What is the ratio of yellow marbles to red marbles?
There are
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First, find the number of yellow marbles in the bag.
The ratio of yellow marbles to red marbles can be expressed as a fraction:
That fraction can then be expressed as 
.
First, find the number of yellow marbles in the bag.
The ratio of yellow marbles to red marbles can be expressed as a fraction:
That fraction can then be expressed as
A barn has 
geese, 
ducks, and 
chickens. What is the ratio of geese to chickens?
A barn has
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First, add up the total number of ducks, geese, and chickens.
Now, write the fraction of these animals that are geese and the fraction of these animals that are chickens.
Now, since we want the ratio of geese to chickens, we write the fractions as thus:
Divide and simplify the resulting fraction to find the ratio.
First, add up the total number of ducks, geese, and chickens.
Now, write the fraction of these animals that are geese and the fraction of these animals that are chickens.
Now, since we want the ratio of geese to chickens, we write the fractions as thus:
Divide and simplify the resulting fraction to find the ratio.
If 
pounds of chicken cost 
, how much does 
pounds of chicken cost?
If
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There is more than one way to solve this problem. You can either figure out how much the chicken costs per pound and multiply that cost by three pounds, or you can set up a proportion and solve for the cost of three pounds of chicken that way.
- Solving the Problem Using Cost per Pound
First, find how much the chicken costs per pound.
Since chicken costs 
per pound, multiply this by the number of pounds we need to get the cost.
pounds of chicken cost 
.
- Solving the Problem Using a Proportion
You can set up a proportion to figure out how much 
pounds of chicken costs:
Cross multiply:
Solve for 
, the cost of 
pounds of chicken:
There is more than one way to solve this problem. You can either figure out how much the chicken costs per pound and multiply that cost by three pounds, or you can set up a proportion and solve for the cost of three pounds of chicken that way.
- Solving the Problem Using Cost per Pound
First, find how much the chicken costs per pound.
Since chicken costs
- Solving the Problem Using a Proportion
You can set up a proportion to figure out how much
Cross multiply:
Solve for