How to find a ratio - ISEE Lower Level Quantitative Reasoning
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In order to make Lilly's Lemonade, for every 16 oz of water, 6 tablespoons of lemon juice is needed. If you want to use 8 oz of water, how much lemon juice would you need?
In order to make Lilly's Lemonade, for every 16 oz of water, 6 tablespoons of lemon juice is needed. If you want to use 8 oz of water, how much lemon juice would you need?
In order to solve this problem, we must set up a ratio.
For every 16 oz of water, we need 6 tablespoons of lemon juice.
The ratio that we get is
16 : 6.
If we want to use only 8 oz of water, we need to find out how much lemon juice is needed.
The amount of lemon juice we need, x, is currently unknown.
Our new ratio is
8 : x.
Looking at the first number in the two ratios, dividing 16 by 8 will get us
16 ÷ 8 = 2.
Let's divide the second number in our first ratio by 2 to solve for x.
So,
6 ÷ 2 = 3.
We need 3 tablespoons of lemon juice for 8 oz of water.
In order to solve this problem, we must set up a ratio.
For every 16 oz of water, we need 6 tablespoons of lemon juice.
The ratio that we get is
16 : 6.
If we want to use only 8 oz of water, we need to find out how much lemon juice is needed.
The amount of lemon juice we need, x, is currently unknown.
Our new ratio is
8 : x.
Looking at the first number in the two ratios, dividing 16 by 8 will get us
16 ÷ 8 = 2.
Let's divide the second number in our first ratio by 2 to solve for x.
So,
6 ÷ 2 = 3.
We need 3 tablespoons of lemon juice for 8 oz of water.
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Michael's math class has 27 students in it.
There are 9 boys and 18 girls.
What is the ratio of boys to girls in Michael's math class?
Michael's math class has 27 students in it.
There are 9 boys and 18 girls.
What is the ratio of boys to girls in Michael's math class?
There are 9 boys and 18 girls.
This is a ratio of 
Reduce to get 
There are 9 boys and 18 girls.
This is a ratio of
Reduce to get
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Find the ratio
If there are 3 frogs at a pond and 12 toads, what is the ratio of frogs to toads at the pond?
Find the ratio
If there are 3 frogs at a pond and 12 toads, what is the ratio of frogs to toads at the pond?
Since there are 3 frogs and 12 toads, reduce 
by 3 to get 
.
Since there are 3 frogs and 12 toads, reduce
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Janie has a bag full of red, blue, orange, white, and green marbles. There are 5 of each color marble in the bag.
Given the above conditions, what is the probability Janie will pull a red marble from the bag?
Janie has a bag full of red, blue, orange, white, and green marbles. There are 5 of each color marble in the bag.
Given the above conditions, what is the probability Janie will pull a red marble from the bag?
Since there are 5 of each color, there are 25 total marbles in the bag. The probability of picking a red is
Since there are 5 of each color, there are 25 total marbles in the bag. The probability of picking a red is
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Ella has 6 cats and 36 dogs. What is the ratio of dogs to cats in Ella's house?
Ella has 6 cats and 36 dogs. What is the ratio of dogs to cats in Ella's house?
There are 36 dogs and 6 cats, leaving a dog to cat ratio of
Reduced, the answer is
.
There are 36 dogs and 6 cats, leaving a dog to cat ratio of
Reduced, the answer is
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There are 24 pencils in a new box. I have sharpened 18. What is the ratio of unsharpened pencils to pencils in the new box?
There are 24 pencils in a new box. I have sharpened 18. What is the ratio of unsharpened pencils to pencils in the new box?
The ratio needed is unsharpened to new box and it says there are 24 pencils in a new box. It does not say how many are unsharpened but it does give the amount that has been sharpened already.
To find the unsharpened amount subtract the number of pencils sharpened from the number of pencils in the new box. Therefore, it would be 
unsharpened pencils.
The ratio of unsharpened to new box would be 
.
The ratio needed is unsharpened to new box and it says there are 24 pencils in a new box. It does not say how many are unsharpened but it does give the amount that has been sharpened already.
To find the unsharpened amount subtract the number of pencils sharpened from the number of pencils in the new box. Therefore, it would be
The ratio of unsharpened to new box would be
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There are 32 computers in the lab and 30 students from the science class might be using them for a project today. When it is lab time, 15 students are NOT ready to go.
What is the ratio of students that are NOT ready for lab to students in the science class?
There are 32 computers in the lab and 30 students from the science class might be using them for a project today. When it is lab time, 15 students are NOT ready to go.
What is the ratio of students that are NOT ready for lab to students in the science class?
The question asked for the ratio of the students NOT ready for lab to the students in the science class.
There are 15 students that are not ready for the computer lab.
There are 30 students in the science class.
Therefore, the ratio is 
.
Since 15 and 30 can be reduced by their greatest common factor of 15 the ratio is simplified to 
.
The question asked for the ratio of the students NOT ready for lab to the students in the science class.
There are 15 students that are not ready for the computer lab.
There are 30 students in the science class.
Therefore, the ratio is
Since 15 and 30 can be reduced by their greatest common factor of 15 the ratio is simplified to
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A class of 40 students has 25 boys and 15 girls. Write the ratio of boys to girls in simplest form.
A class of 40 students has 25 boys and 15 girls. Write the ratio of boys to girls in simplest form.
The ratio of boys to girls is 
, but this is not in simplest form. Rewrite this as a fraction for simplicity, then divide both numbers by 
:
In simplest form, the ratio is 
The ratio of boys to girls is
In simplest form, the ratio is
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Sharon has 80 marbles, 60 of which are blue and 20 of which are white. Write the ratio of blue marbles to white marbles in simplest form.
Sharon has 80 marbles, 60 of which are blue and 20 of which are white. Write the ratio of blue marbles to white marbles in simplest form.
The ratio of blue marbles to white marbles is 
, but this is not in simplest form. Rewrite this as a fraction for simplicity, then divide both numbers by 
:
In simplest form, the ratio is 
The ratio of blue marbles to white marbles is
In simplest form, the ratio is
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A total of 35 children took a poll about favorite breakfast foods, choosing between cereal, yogurt, and pancakes. If 14 preferred cereal and 7 preferred yogurt, how many preferred pancakes?
A total of 35 children took a poll about favorite breakfast foods, choosing between cereal, yogurt, and pancakes. If 14 preferred cereal and 7 preferred yogurt, how many preferred pancakes?
To find the children who preferred pancakes, subtract all the other children (cereal + yogurt) from the total:
To find the children who preferred pancakes, subtract all the other children (cereal + yogurt) from the total:
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Susan has a bag of 12 assorted candies that included 3 blue, 2 green, 4 red, and 3 yellow. If Susan picks one piece of candy without looking, which color has a 1 in 6 chance of being picked?
Susan has a bag of 12 assorted candies that included 3 blue, 2 green, 4 red, and 3 yellow. If Susan picks one piece of candy without looking, which color has a 1 in 6 chance of being picked?
There are 2 green candies in the assortment out of a total of 12 candies. The proportion of green candies to total candies is 
, which simplifies to 
. This fraction describes a 1 in 6 chance, which is what we are looking for.
There are 2 green candies in the assortment out of a total of 12 candies. The proportion of green candies to total candies is
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A cake recipe asks for 4 cups of flour and 1 cup of sugar. If Sarah only has 2 cups of flour, how much sugar should she use?
A cake recipe asks for 4 cups of flour and 1 cup of sugar. If Sarah only has 2 cups of flour, how much sugar should she use?
In order to solve this problem, we should set up a ratio.
The ratio of flour to sugar in the recipe is 
If Sarah only has 2 cups of flour, the ratio would be 
where 
is the sugar.
Looking at the first ratio, 2 cups is half of 4, so the sugar would also be half. So the answer is 
cup of sugar.
In order to solve this problem, we should set up a ratio.
The ratio of flour to sugar in the recipe is
If Sarah only has 2 cups of flour, the ratio would be
Looking at the first ratio, 2 cups is half of 4, so the sugar would also be half. So the answer is
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Mrs. Steven's class has a female-to-male student ratio of 3:2. If the class has 18 female students, how many male students are there?
Mrs. Steven's class has a female-to-male student ratio of 3:2. If the class has 18 female students, how many male students are there?
The ratio of female-to-male students is 3:2 or:
Since we have 18 female students, we can set it up like this:
where 
is the unknown number of male students.
Now multiply the fraction by whatever number so that the numerator (the female students) equals 18.
So the amount of male students is 12.
The ratio of female-to-male students is 3:2 or:
Since we have 18 female students, we can set it up like this:
where
Now multiply the fraction by whatever number so that the numerator (the female students) equals 18.
So the amount of male students is 12.
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A baseball team has a 2:1 ratio of seniors to freshmen, respectively. If there are 27 total players, how many are seniors?
A baseball team has a 2:1 ratio of seniors to freshmen, respectively. If there are 27 total players, how many are seniors?
Since the ratio of seniors-to-freshmen is 2:1, there are twice as many seniors as freshmen. There's a few ways to solve this. One way is to make the algebra equation:
Where 
is the number of freshmen, and 
is the number of seniors, twice as many as the freshmen.
Now solve for 
:
But don't forget! 
is the number of freshmen, and the question asks for seniors, which is:
Since the ratio of seniors-to-freshmen is 2:1, there are twice as many seniors as freshmen. There's a few ways to solve this. One way is to make the algebra equation:
Where
Now solve for
But don't forget!
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Determine the ratio of 86 to 129.
Determine the ratio of 86 to 129.
Ratios represent how one number is related to another. These steps will help you determine the ratio of the numbers shown:
-
Divide both terms of the ratio by the GCF (greatest common factor). In this case, the GCF is 43 because 43 is the greatest number that goes into both numbers evenly.
-
Show the ratio with a colon : and remember to keep the numbers in the same order!
Therefore, the ratio of 86 to 129 is 
.
Ratios represent how one number is related to another. These steps will help you determine the ratio of the numbers shown:
-
Divide both terms of the ratio by the GCF (greatest common factor). In this case, the GCF is 43 because 43 is the greatest number that goes into both numbers evenly.
-
Show the ratio with a colon : and remember to keep the numbers in the same order!
Therefore, the ratio of 86 to 129 is
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There are 7 green chips, 4 black chips, and 8 white chips on a table. What is the ratio of green chips to black chips?
There are 7 green chips, 4 black chips, and 8 white chips on a table. What is the ratio of green chips to black chips?
The ratio is written as:
or 
.
The colon (:) indicates the word "to".
The ratio is written as:
The colon (:) indicates the word "to".
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A car with a tank that holds 15 gallons of gas gets 29 miles to the gallon. If the car's gas gauge reads that the tank is three-fourths full, how many miles can it travel before it needs to be refueled?
A car with a tank that holds 15 gallons of gas gets 29 miles to the gallon. If the car's gas gauge reads that the tank is three-fourths full, how many miles can it travel before it needs to be refueled?
Multiply 15 gallons by 29 miles per gallon to get the distance the car can travel on a full tank:
miles.
Multiply this by three-fourths to get the distance it can travel on three-fourths of a tank.
, so
miles
Multiply 15 gallons by 29 miles per gallon to get the distance the car can travel on a full tank:
Multiply this by three-fourths to get the distance it can travel on three-fourths of a tank.
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A truck with a tank that holds 24 gallons of gas gets 18 miles to the gallon. If the truck's gas gauge reads that the tank is one-half full, how many miles can it travel before it needs to be refueled?
A truck with a tank that holds 24 gallons of gas gets 18 miles to the gallon. If the truck's gas gauge reads that the tank is one-half full, how many miles can it travel before it needs to be refueled?
Multiply 18 miles per gallon by 24 gallons to get the distance the truck can travel on a full tank:
miles
On one-half of a tank, this truck can travel
Multiply 18 miles per gallon by 24 gallons to get the distance the truck can travel on a full tank:
On one-half of a tank, this truck can travel
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A drawer contains 5 pairs of black socks and 7 pairs of red socks. What is the red to black sock ratio?
A drawer contains 5 pairs of black socks and 7 pairs of red socks. What is the red to black sock ratio?
A ratio is determined by comparing the number of one item (red socks) to the number of another item (black socks). Therefore, the red to black ratio is 
.
A ratio is determined by comparing the number of one item (red socks) to the number of another item (black socks). Therefore, the red to black ratio is
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The ratio of boys to girls in a group of 12 students is 1 boy to 2 girls. 
. How many girls are in the group?
The ratio of boys to girls in a group of 12 students is 1 boy to 2 girls.
If there is 1 boy for every 2 girls, and there are 12 students, then that means there must be 4 boys and 8 girls.
The ratio of 
means that there would be 3 students in the smallest group possible (a group with 1 boy and 2 girls).
Thus, if the group has 12 students, we know the group is 4 times bigger than the smallest group possible.
This means that we multiply 4 by the ratio to get the number of boys and girls.
If there is 1 boy for every 2 girls, and there are 12 students, then that means there must be 4 boys and 8 girls.
The ratio of
Thus, if the group has 12 students, we know the group is 4 times bigger than the smallest group possible.
This means that we multiply 4 by the ratio to get the number of boys and girls.
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