Ratio and Proportion - ISEE Lower Level (grades 5-6) Mathematics Achievement
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A cookie recipe that bakes 12 cookies calls for 3 eggs. How many eggs would be needed to make 36 cookies?
A cookie recipe that bakes 12 cookies calls for 3 eggs. How many eggs would be needed to make 36 cookies?
36 cookies is 3 times more than 12. Multiply the number of eggs by 3 to get 9.
36 cookies is 3 times more than 12. Multiply the number of eggs by 3 to get 9.
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A group of 6th grade students at Manor Intermediate are going on a field trip to the local theme park.
There are 2 chaperones required for every 9 students on the field trip. How many chaperones will need to attend the field trip if there are 27 students going?
A group of 6th grade students at Manor Intermediate are going on a field trip to the local theme park.
There are 2 chaperones required for every 9 students on the field trip. How many chaperones will need to attend the field trip if there are 27 students going?
The best way to solve this problem is to set it up as two ratios that are equivalent to each other. This forms a proportion. Make sure to set up the ratios so that the relationships go together across the equal sign.
Use cross products to then solve for the missing value.
Therefore, mental math or division can be used to find
.
Since 
,
there would need to be 6 chaperones attending the field trip.
The best way to solve this problem is to set it up as two ratios that are equivalent to each other. This forms a proportion. Make sure to set up the ratios so that the relationships go together across the equal sign.
Use cross products to then solve for the missing value.
Therefore, mental math or division can be used to find
Since
there would need to be 6 chaperones attending the field trip.
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Give the value of 
that makes this proportion statement correct:
Give the value of
Cross-multiply, then solve for 
:
Cross-multiply, then solve for
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Give the value of 
that makes this proportion statement correct:
Give the value of
Solve for 
by multiplying both sides by 60:
Solve for
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If Eric can read a page from his text book in 
minutes, how many pages can he read in 15 minutes?
If Eric can read a page from his text book in
The problem can be represented by the proportion 
.
Solve: 
Eric can read 
pages in 15 minutes.
The problem can be represented by the proportion
Solve:
Eric can read
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If Kristin makes $300 in a week when she works 15 hours, how much would she make if she worked 24 hours next week at the same rate?
If Kristin makes $300 in a week when she works 15 hours, how much would she make if she worked 24 hours next week at the same rate?
To find the rate at which she is currently paid, divide $300 by the hours she works, 15, to see that she earns $20 per hour. To find her earnings for next week, multiply 24 hours by $20 per hour to see that she will make $480 next week.
Or set up the proportion 
and solve for 
.
To find the rate at which she is currently paid, divide $300 by the hours she works, 15, to see that she earns $20 per hour. To find her earnings for next week, multiply 24 hours by $20 per hour to see that she will make $480 next week.
Or set up the proportion
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If 1 inch on a map represents 5 miles, how far apart, in miles, are two cities that are 6.6 inches apart on the map?
If 1 inch on a map represents 5 miles, how far apart, in miles, are two cities that are 6.6 inches apart on the map?
Set up a proportion with the inches on the map and physical miles:
Solve for x:
Set up a proportion with the inches on the map and physical miles:
Solve for x:
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A bag of marbles contains 4 green marbles, 7 black marbles, and 5 red marbles. What is the proportion of green marbles?
A bag of marbles contains 4 green marbles, 7 black marbles, and 5 red marbles. What is the proportion of green marbles?
First, sum the total number of marbles:
Next, divide the total number of green marbles by the total number of marbles and simplify:
First, sum the total number of marbles:
Next, divide the total number of green marbles by the total number of marbles and simplify:
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A bag has 11 green chips, 7 blue chips, and 6 red chips. What is the proportion of green chips?
A bag has 11 green chips, 7 blue chips, and 6 red chips. What is the proportion of green chips?
The proportion is determined by dividing the number of selected items by the total number of items.
The proportion is determined by dividing the number of selected items by the total number of items.
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A drawer contains 5 pairs of blue socks, 2 pairs of white socks, 4 pairs of brown socks, and 7 pairs of black socks. What is the proportion of brown socks?
A drawer contains 5 pairs of blue socks, 2 pairs of white socks, 4 pairs of brown socks, and 7 pairs of black socks. What is the proportion of brown socks?
A proportion is determined by dividing the number of a specific event by the total number of events:
A proportion is determined by dividing the number of a specific event by the total number of events:
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There are 24 students in Mrs. Brown's classroom. 6 of them have red backpacks. What percentage of the students have red backpacks?
There are 24 students in Mrs. Brown's classroom. 6 of them have red backpacks. What percentage of the students have red backpacks?
Let's first determine the fraction of students in the class that have red backpacks. We can then convert the fraction to a percentage.
The question tells us that 6 out of 24 students have red backpacks. This is equal to six over twenty-four:
We can reduce the fraction by removing a common factor.
The percentage that is equivalent to 
is 25 percent, or 
.
Therefore, 
is the correct answer.
Let's first determine the fraction of students in the class that have red backpacks. We can then convert the fraction to a percentage.
The question tells us that 6 out of 24 students have red backpacks. This is equal to six over twenty-four:
We can reduce the fraction by removing a common factor.
The percentage that is equivalent to
Therefore,
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Megan buys cookie packs that come in either small or large sizes. The small size has 3 vanilla cookies and 2 chocolate cookies. The large size has the same proportion of vanilla and chocolate cookies. The large comes with 6 chocolate cookies. How many vanilla cookies are in the large box?
Megan buys cookie packs that come in either small or large sizes. The small size has 3 vanilla cookies and 2 chocolate cookies. The large size has the same proportion of vanilla and chocolate cookies. The large comes with 6 chocolate cookies. How many vanilla cookies are in the large box?
We know that there are the same proportions of cookies in both the small and large boxes.
Let's start by looking at the small box. We know that there are 3 vanilla and 2 chocolate cookies, or a ratio of 
.
In the large box, we know there are 6 chocolate cookies. If 
is the number of vanilla cookies, then the ratio in the large box is 
.
The ratios must be equal.
Cross-multiply and solve for 
.
We know that there are the same proportions of cookies in both the small and large boxes.
Let's start by looking at the small box. We know that there are 3 vanilla and 2 chocolate cookies, or a ratio of
In the large box, we know there are 6 chocolate cookies. If
The ratios must be equal.
Cross-multiply and solve for
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If the ratio of boys to girls in a class is 
, what fraction of the class is boys?
If the ratio of boys to girls in a class is
If the ratio of boys to girls in a class is 
, that means that for every 3 students, 1 is a boy.
Looking at the ratio, we see that there is one boy for every two girls. In a group of three students, you would have one boy and two girls.
We can write the fraction of boys as the number of boys over the number of students in the group.
If the ratio of boys to girls in a class is
Looking at the ratio, we see that there is one boy for every two girls. In a group of three students, you would have one boy and two girls.
We can write the fraction of boys as the number of boys over the number of students in the group.
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The ratio of men to women in a room is 
. If the room has 21 people, and 2 men then leave the room, what is the proportion of men in the room?
The ratio of men to women in a room is
If there is a room of 21 people in which the ratio of men to women is 
, that means that there are 9 men and 12 women in the room.
If 2 men leave the room, there will be 7 men and 12 women in the room, with a total of 19 people.
Therefore, the proportion of the men in the room is 
.
If there is a room of 21 people in which the ratio of men to women is
If 2 men leave the room, there will be 7 men and 12 women in the room, with a total of 19 people.
Therefore, the proportion of the men in the room is
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The ratio of rabbits to guinea pigs to hamsters in a pet store is 3:2:4. If there are 12 rabbits in the pet store, how many hamsters are there?
The ratio of rabbits to guinea pigs to hamsters in a pet store is 3:2:4. If there are 12 rabbits in the pet store, how many hamsters are there?
Given that the ratio of rabbits to guinea pigs to hamsters in a pet store is 
, each number should be 4 times greater if there are 12 rabbits. This is because 3 times 4 is 12.
Therefore, we can transform the of rabbits to guinea pigs to hamsters into 
.
Therefore, there are 16 hamsters.
Given that the ratio of rabbits to guinea pigs to hamsters in a pet store is
Therefore, we can transform the of rabbits to guinea pigs to hamsters into
Therefore, there are 16 hamsters.
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On a typical day, twenty percent of the pies that a pie store sells are blueberry pies. If the store sells forty pies on just such a typical day, how many blueberry pies were likely sold?
On a typical day, twenty percent of the pies that a pie store sells are blueberry pies. If the store sells forty pies on just such a typical day, how many blueberry pies were likely sold?
If store sells 
pies, and typically 
of the pies that are sold are blueberry, that means that 
of the pies sold were probably blueberry.
Given that 
of 
is 
, it follows that 
of 
is 
.
Therefore, 
is the correct answer.
If store sells
Given that
Therefore,
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If it takes Linda 6 minutes to complete a multiple choice question, then what percentage of a 10 question multiple choice test will she complete in half an hour?
If it takes Linda 6 minutes to complete a multiple choice question, then what percentage of a 10 question multiple choice test will she complete in half an hour?
If it takes Linda 6 minutes to complete a multiple choice question, then she will complete 
questions in 30 minutes.
Therefore, Linda will complete 5 out of 10 questions in half an hour, or 50%.
If it takes Linda 6 minutes to complete a multiple choice question, then she will complete
Therefore, Linda will complete 5 out of 10 questions in half an hour, or 50%.
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Reduce the following proportion to its simplest form:
Reduce the following proportion to its simplest form:
To simplify, you find a common factor for both the numerator and denominator and divide them both by that value.
Both 
and 
have a common factor of 
.
This gives us,
.
To simplify, you find a common factor for both the numerator and denominator and divide them both by that value.
Both
This gives us,
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Rachel and Michael earn the same amount of money per hour. Rachel earns $64.00 for eight hours of work. How long would it take Michael to earn $96.00?
Rachel and Michael earn the same amount of money per hour. Rachel earns $64.00 for eight hours of work. How long would it take Michael to earn $96.00?
In order to solve this problem, you would set up a direct proportion:
To make the process even simpler, you could first reduce the first fraction in this direct proportion. The fraction was reduced to simplest form by dividing both the numerator and the denominator by 8, the greatest common factor or the GCF.
Divide both sides by the coefficient of x, which is 8:
In order to solve this problem, you would set up a direct proportion:
To make the process even simpler, you could first reduce the first fraction in this direct proportion. The fraction was reduced to simplest form by dividing both the numerator and the denominator by 8, the greatest common factor or the GCF.
Divide both sides by the coefficient of x, which is 8:
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On a map, one inch is equal to 
miles. How many inches will be on the map for a a distance of 
miles?
On a map, one inch is equal to
The proportion for the problem will be,
.
You then cross multiple to get
.
To find 
, you divide both sides by 
to get
Therefore
The proportion for the problem will be,
You then cross multiple to get
To find
Therefore
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