How to find a ratio - SSAT Middle Level Quantitative
Card 1 of 492
A soccer team played 20 games, winning 5 of them. The ratio of wins to losses is
A soccer team played 20 games, winning 5 of them. The ratio of wins to losses is
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The ratio of wins to losses requires knowing the number of wins and losses. The question says that there are 5 wins. That means there must have been
losses.
The ratio of wins to losses is thus 5 to 15 or 1 to 3.
The ratio of wins to losses requires knowing the number of wins and losses. The question says that there are 5 wins. That means there must have been
The ratio of wins to losses is thus 5 to 15 or 1 to 3.
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Which ratio is equivalent to 
?
Which ratio is equivalent to
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A ratio can be rewritten as a quotient; do this, and simplify it.
Rewrite as
or 
A ratio can be rewritten as a quotient; do this, and simplify it.
Rewrite as
or
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Rewrite this ratio in the simplest form: 
Rewrite this ratio in the simplest form:
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Rewrite in fraction form for the sake of simplicity, then divide each number by 
:
In simplest form, the ratio is 
Rewrite in fraction form for the sake of simplicity, then divide each number by
In simplest form, the ratio is
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Rewrite this ratio in the simplest form: 
Rewrite this ratio in the simplest form:
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Rewrite in fraction form for the sake of simplicity, then divide each number by 
:
The ratio, in simplest form, is 
Rewrite in fraction form for the sake of simplicity, then divide each number by
The ratio, in simplest form, is
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Rewrite this ratio in the simplest form:
Rewrite this ratio in the simplest form:
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A ratio involving fractions can be simplified by rewriting it as a complex fraction, and simplifying it by division:
Write as a product by taking the reciprocal of the divisor, cross-cancel, then multiply it out:
The ratio simplifies to 
A ratio involving fractions can be simplified by rewriting it as a complex fraction, and simplifying it by division:
Write as a product by taking the reciprocal of the divisor, cross-cancel, then multiply it out:
The ratio simplifies to
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Rewrite this ratio in the simplest form:
Rewrite this ratio in the simplest form:
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A ratio involving fractions can be simplified by rewriting it as a complex fraction, and simplifying it by division:
Write as a product by taking the reciprocal of the divisor, cross-cancel, then multiply it out:
The ratio simplifies to 
A ratio involving fractions can be simplified by rewriting it as a complex fraction, and simplifying it by division:
Write as a product by taking the reciprocal of the divisor, cross-cancel, then multiply it out:
The ratio simplifies to
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Note: Figure NOT drawn to scale.
Refer to the above diagram. If one side of the smaller square is three-fifths the length of one side of the larger square, what is the ratio of the area of the gray region to that of the white region?
Note: Figure NOT drawn to scale.
Refer to the above diagram. If one side of the smaller square is three-fifths the length of one side of the larger square, what is the ratio of the area of the gray region to that of the white region?
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Since the answer to this question does not depend on the actual lengths of the sides, we will assume for simplicity that the larger square has sidelength 5; if this is the case, the smaller square has sidelength 3. The areas of the large and small squares are, respectively, 
and 
.
The white region is the small square and has area 9. The grey region is the small square cut out of the large square and has area 
. Therefore, the ratio of the area of the gray region to that of the white region is 16 to 9.
Since the answer to this question does not depend on the actual lengths of the sides, we will assume for simplicity that the larger square has sidelength 5; if this is the case, the smaller square has sidelength 3. The areas of the large and small squares are, respectively,
The white region is the small square and has area 9. The grey region is the small square cut out of the large square and has area
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Note: Figure NOT drawn to scale.
Refer to the above diagram. If one side of the smaller square is three-fourths the length of one side of the larger square, what is the ratio of the area of the gray region to that of the white region?
Note: Figure NOT drawn to scale.
Refer to the above diagram. If one side of the smaller square is three-fourths the length of one side of the larger square, what is the ratio of the area of the gray region to that of the white region?
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Since the answer to this question does not depend on the actual lengths of the sides, we will assume for simplicity that the larger square has sidelength 
; if this is the case, the smaller square has sidelength 
. The areas of the large and small squares are, respectively, 
and 
.
The white region is the small square and has area 
. The grey region is the small square cut out of the large square and has area 
. Therefore, the ratio of the area of the gray region to that of the white region is 
to 
.
Since the answer to this question does not depend on the actual lengths of the sides, we will assume for simplicity that the larger square has sidelength
The white region is the small square and has area
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In Mrs. Jones' class, the ratio of boys to girls is 3:2. If there are 8 girls in the class, how many total students are in the class?
In Mrs. Jones' class, the ratio of boys to girls is 3:2. If there are 8 girls in the class, how many total students are in the class?
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Using the ratio, we find that there are 12 boys in the class 
.
Summing 12 and 8 gives the total number of 20 students.
Using the ratio, we find that there are 12 boys in the class
Summing 12 and 8 gives the total number of 20 students.
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Express the following ratio in simplest form: 
Express the following ratio in simplest form:
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Rewrite this in fraction form for the sake of simplicity, and divide both numbers by 
:
The ratio, simplified, is 
.
Rewrite this in fraction form for the sake of simplicity, and divide both numbers by
The ratio, simplified, is
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Express this ratio in simplest form: 
Express this ratio in simplest form:
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A ratio of fractions can best be solved by dividing the first number by the second. Rewrite the mixed fraction as an improper fraction, rewrite the problem as a multiplication by taking the reciprocal of the second fraction, and corss-cancel:
The ratio, simplified, is 
.
A ratio of fractions can best be solved by dividing the first number by the second. Rewrite the mixed fraction as an improper fraction, rewrite the problem as a multiplication by taking the reciprocal of the second fraction, and corss-cancel:
The ratio, simplified, is
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Express this ratio in simplest form: 
Express this ratio in simplest form:
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A ratio involving decimals can be simplified as follows:
First, move the decimal point over a common number of places in each number so that both numbers become whole. In this case, it would be two places:
(Note the addition of a zero at the end of the first number.)
Now, rewrite as a fraction and divide both numbers by 
:
The ratio, simplified, is 
.
A ratio involving decimals can be simplified as follows:
First, move the decimal point over a common number of places in each number so that both numbers become whole. In this case, it would be two places:
Now, rewrite as a fraction and divide both numbers by
The ratio, simplified, is
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Write as a unit rate: 
revolutions in 
minutes
Write as a unit rate:
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Divide the number of revolutions by the number of minutes to get revolutions per minute:
,
making 
revolutions per minute the correct choice.
Divide the number of revolutions by the number of minutes to get revolutions per minute:
making
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Carlos owns a hamburger and hot-dog stand. When the fridge in the stand is 
full, there are 16 hamburgers and hot dogs total. If the ratio of hamburgers to hot dogs is always 5:3, how many hot dogs are in the cart when it is full?
Carlos owns a hamburger and hot-dog stand. When the fridge in the stand is
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When solving a ratio problem, first add each part of the ratio:
So, one part in this ratio is equal to 8. The number of hamburgers and hot dogs in the fridge is currently only 
the amount it can hold. To figure out how much it can hold total, we can multiply by the denominator of the fraction since the numerator is 1.
64 is the total amount of hamburgers and hot dogs that can be held in the fridge. Divide 8 into 64 in order to figure out how many parts fit into this number.
This number tells us how many times we need to multiply the ratio by in order to figure out how many hamburgers or hot dogs can be in the fridge at once. Since we are trying to figure out how many hot dogs are in the fridge when it is full, we use the second number, 3. We use the number 3 because, since the ratio is hamburgers to hotdogs, the second number represents the number of hot dogs.
This gives you your answer. There are 24 hot dogs in the fridge when it is full.
When solving a ratio problem, first add each part of the ratio:
So, one part in this ratio is equal to 8. The number of hamburgers and hot dogs in the fridge is currently only
64 is the total amount of hamburgers and hot dogs that can be held in the fridge. Divide 8 into 64 in order to figure out how many parts fit into this number.
This number tells us how many times we need to multiply the ratio by in order to figure out how many hamburgers or hot dogs can be in the fridge at once. Since we are trying to figure out how many hot dogs are in the fridge when it is full, we use the second number, 3. We use the number 3 because, since the ratio is hamburgers to hotdogs, the second number represents the number of hot dogs.
This gives you your answer. There are 24 hot dogs in the fridge when it is full.
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A 16-ounce bottle of Charlie's Fizzy Fizz Root Beer costs 89 cents. Give the price per ounce to the nearest tenth of a cent.
A 16-ounce bottle of Charlie's Fizzy Fizz Root Beer costs 89 cents. Give the price per ounce to the nearest tenth of a cent.
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Divide 89 by 16:
The soda costs about 5.6 cents per ounce.
Divide 89 by 16:
The soda costs about 5.6 cents per ounce.
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A batting average is defined as the ratio of hits to turns at bat. It is expressed as a decimal rounded to the nearest thousand.
In 2013, Yadier Molina's batting average was 0.319. If he maintains this same batting average over the 2014 baseball season, how many turns at bat should he expect to need to achieve 50 hits? (Nearest whole number)
A batting average is defined as the ratio of hits to turns at bat. It is expressed as a decimal rounded to the nearest thousand.
In 2013, Yadier Molina's batting average was 0.319. If he maintains this same batting average over the 2014 baseball season, how many turns at bat should he expect to need to achieve 50 hits? (Nearest whole number)
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Since a batting average is a ratio of hits to turns at bat,
Let 
be the number of turns at bat Molina needs to get 50 hits. Then:
Solve for 
:
Molina should need 157 turns at bat,
Since a batting average is a ratio of hits to turns at bat,
Let
Solve for
Molina should need 157 turns at bat,
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There are 
girls and 
boys in Miss Bailey's class. What is the ratio of girls to boys?
There are
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The ratio of girls to boys in Miss Bailey's class is 
, which can be reduced to 
when both the numerator and denominator are divided by 
.
The ratio of girls to boys in Miss Bailey's class is
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In a library, there are 
children's books and 
young adult books. What is the ratio of young adult books to children's books?
In a library, there are
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The ratio of young adult books to children's books is 
to 
, or 
, which can be reduced to 
.
The ratio of young adult books to children's books is
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There are 
male and 
female employees at a company. What is the ratio of females to males?
There are
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The ratio of females to males is 
to 
, or 
, which can be reduced to 
.
The ratio of females to males is
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Sharon is having a birthday party. So far, she has invited twenty of her friends from school, nine of whom are girls. She wants to make the ratio of boys to girls at the party two to one. If she decides to add her two cousins, both girls, to the guest list, and no other girls, how many more boys does she need to invite?
Sharon is having a birthday party. So far, she has invited twenty of her friends from school, nine of whom are girls. She wants to make the ratio of boys to girls at the party two to one. If she decides to add her two cousins, both girls, to the guest list, and no other girls, how many more boys does she need to invite?
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So far, Sharon has invited twenty friends from school - eleven boys and nine girls. Including Sharon's cousins and Sharon herself, there are eleven boys and twelve girls.
For there to be a two-to-one boy-to-girl ratio, Sharon must have twice as many boys as girls. She will need 
boys total, so she will need to invite 
more boys.
So far, Sharon has invited twenty friends from school - eleven boys and nine girls. Including Sharon's cousins and Sharon herself, there are eleven boys and twelve girls.
For there to be a two-to-one boy-to-girl ratio, Sharon must have twice as many boys as girls. She will need
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