Number Concepts and Operations - SSAT Upper Level Quantitative
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What is the ratio of 6 inches to 12 feet
What is the ratio of 6 inches to 12 feet
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First, we need to convert 6 inches into feet.
There are 12 inches in a foot. $\frac{6 inches}{12 inches}$=\frac{1}{2}$.
So 6 inches is equal to $\frac{1}{2}$ feet. Now our ratio is $\frac{1}{2}$ to 12. To find this ratio we divide 12 by $\frac{1}{2}$.
12div $\frac{1}{2}$=12times $\frac{2}{1}$=12times 2=24.
So the ratio is 1:24.
First, we need to convert 6 inches into feet.
There are 12 inches in a foot. $\frac{6 inches}{12 inches}$=\frac{1}{2}$.
So 6 inches is equal to $\frac{1}{2}$ feet. Now our ratio is $\frac{1}{2}$ to 12. To find this ratio we divide 12 by $\frac{1}{2}$.
12div $\frac{1}{2}$=12times $\frac{2}{1}$=12times 2=24.
So the ratio is 1:24.
What is the ratio of 3 gallons to 5 quarts?
What is the ratio of 3 gallons to 5 quarts?
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First convert gallons to quarts. There are 4 quarts in a gallon. So 3 gallons is equivalent to 4times 3=12 quarts.
Now we have 12 quarts to 5 quarts. This ratio cannot reduce, so our answer is 12:5.
First convert gallons to quarts. There are 4 quarts in a gallon. So 3 gallons is equivalent to 4times 3=12 quarts.
Now we have 12 quarts to 5 quarts. This ratio cannot reduce, so our answer is 12:5.
Bob gets paid 
an hour for the regular hours he works and 
an hour for any overtime hours he works. All hours over 40 in a week are considered overtime. If Bob works 44 hours this week, how much did he make?
Bob gets paid
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You first calculate how much he makes for normal hours, which is the number of hours works multiplied by the wage. So for normal hours, 
. For overtime, it is 
. Add the amount made in overtime and the normal hours and you get 
.
You first calculate how much he makes for normal hours, which is the number of hours works multiplied by the wage. So for normal hours,
There are 500 students at the high school. There are only two menu options: chicken or fish. If 15% of students ordered fish, how many students ordered chicken?
There are 500 students at the high school. There are only two menu options: chicken or fish. If 15% of students ordered fish, how many students ordered chicken?
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If 15% of students ordered fish, then 85% of the students must have ordered chicken. Then multiply 85% or 
.
If 15% of students ordered fish, then 85% of the students must have ordered chicken. Then multiply 85% or
1 mile = 5280 feet
If Greg's house is 5.3 miles away, how far is it in feet?
1 mile = 5280 feet
If Greg's house is 5.3 miles away, how far is it in feet?
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Using the conversion formula, you would multiply 5.3 miles by 5280 feet and you will get 27,984 feet.
Using the conversion formula, you would multiply 5.3 miles by 5280 feet and you will get 27,984 feet.
Joe drove an average of 45 miles per hour along a 60-mile stretch of highway, then an average of 60 miles per hour along a 30-mile stretch of highway. What was his average speed, to the nearest mile per hour?
Joe drove an average of 45 miles per hour along a 60-mile stretch of highway, then an average of 60 miles per hour along a 30-mile stretch of highway. What was his average speed, to the nearest mile per hour?
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At 45 mph, Joe drove 60 miles in 
hours.
At 60 mph, he drove 30 miles in 
hours.
He made the 90-mile trip in 
hours, so divide 90 by 
to get the average speed in mph:
At 45 mph, Joe drove 60 miles in
At 60 mph, he drove 30 miles in
He made the 90-mile trip in
Convert 15.68 to a percent.
Convert 15.68 to a percent.
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To convert a number to a percent, you just multiply it by 
. So 
%.
To convert a number to a percent, you just multiply it by
What number can 1536 be divided by that would give no remainder?
What number can 1536 be divided by that would give no remainder?
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The menu of a local coffeehouse reads as follows:
Sandy orders some drinks for herself and some friends. She orders three cappuccinos, two iced teas, two cafe lattes, and an espresso. The sales tax is five percent. How much change does she receive back for a twenty-dollar bill?
The menu of a local coffeehouse reads as follows:
Sandy orders some drinks for herself and some friends. She orders three cappuccinos, two iced teas, two cafe lattes, and an espresso. The sales tax is five percent. How much change does she receive back for a twenty-dollar bill?
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The three cappuccinos cost: 
The two iced teas cost 
The two cafe lattes cost 
The espresso costs 
.
Add these amounts to get the cost before tax:
The tax is five percent of 
or:
Add both values in order to obtain the total cost after tax.
As a result, the change from a twenty-dollar bill is as follows:
The three cappuccinos cost:
The two iced teas cost
The two cafe lattes cost
The espresso costs
Add these amounts to get the cost before tax:
The tax is five percent of
Add both values in order to obtain the total cost after tax.
As a result, the change from a twenty-dollar bill is as follows:
Candidate A gets 
of the votes in an election.
Candidate B gets 35% of the votes.
If 2.8 million people votes, how many more votes than Candidate A did Candidate B receive?
Candidate A gets
Candidate B gets 35% of the votes.
If 2.8 million people votes, how many more votes than Candidate A did Candidate B receive?
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First we need to get 
and 35% in the same terms so that we can subtract one from the other. Since 7ths are repeating decimals, it will be easiest to use fractions.
.
Now we multiply this fraction by 2.8 million, which reduces nicely to 
, which equals 180,000.
First we need to get
Now we multiply this fraction by 2.8 million, which reduces nicely to
of a class of 36 students are boys. If 2 girls and 4 boys were to drop the class, what percentage of the class would be girls?
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First determine how many boys and girls are currently in the class.
boys in the class, which means that there are 20 girls.
When the 6 students drop the new class size will be 30, which will be made up of 
girls and 
boys.
First determine how many boys and girls are currently in the class.
When the 6 students drop the new class size will be 30, which will be made up of
Bill decides to donate 15% of his $4000 and Ted decides to donate 25% of his $8000. What percentage of their combined fortunes do Bill and Ted donate?
Bill decides to donate 15% of his $4000 and Ted decides to donate 25% of his $8000. What percentage of their combined fortunes do Bill and Ted donate?
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This is a simple problem, so long as you don't forget that Bill and Ted have different amounts of money, so you can't simply average 15% and 25% to get 20%.
Calculate how much each donates:
4000(.15)= 600
8000(.25)= 2000
Now divide the total donation by their total wealth:
Now multiply this answer by 100, and then round to the nearest tenth to get 21.7%.
This is a simple problem, so long as you don't forget that Bill and Ted have different amounts of money, so you can't simply average 15% and 25% to get 20%.
Calculate how much each donates:
4000(.15)= 600
8000(.25)= 2000
Now divide the total donation by their total wealth:
Now multiply this answer by 100, and then round to the nearest tenth to get 21.7%.
.24+2.5+\frac{1}{4}$=
.24+2.5+\frac{1}{4}$=
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First, convert $\frac{1}{4}$ into a decimal. We are left with
.24+2.5+.25
Now add the three numbers, being careful to line the decimal points up exactly. From right to left we will add:
-
4 and 5 = 9
-
5, 2, and 2 = 9
-
2 is alone = 2
This leaves us with 2.99 for the final answer.
First, convert $\frac{1}{4}$ into a decimal. We are left with
.24+2.5+.25
Now add the three numbers, being careful to line the decimal points up exactly. From right to left we will add:
-
4 and 5 = 9
-
5, 2, and 2 = 9
-
2 is alone = 2
This leaves us with 2.99 for the final answer.
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Use order of operations, so you would first complete the operation in the parentheses, which would give you 
.
Then you do exponenets, so 
.
Then you do division which is 
.
Then you do addition from left to right, so 
.
Last, you add 
to 
, which is 
.
Use order of operations, so you would first complete the operation in the parentheses, which would give you
Then you do exponenets, so
Then you do division which is
Then you do addition from left to right, so
Last, you add
What is the sum of the two percentages in decimal form?
7 percent and 135 percent
What is the sum of the two percentages in decimal form?
7 percent and 135 percent
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You add the percentages and you get 142 percent. To convert a percent to a decimal, you divide by 100, so the answer is 1.42.
You add the percentages and you get 142 percent. To convert a percent to a decimal, you divide by 100, so the answer is 1.42.
Which of the following angles is supplementary to an angle that is 45 degrees?
Which of the following angles is supplementary to an angle that is 45 degrees?
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Supplementary angles add up to 180 degrees. Given that 
, the correct answer is 135.
Supplementary angles add up to 180 degrees. Given that
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Do the expression in the parantheses and you get 
. Then you do 
and you get 
. Then you do 
and you get 
. Then you add 
.
Do the expression in the parantheses and you get
If Susie bought a pair of shoes for 
, a shirt for 
, and a pair of pants for 
. How much did she spend in total?
If Susie bought a pair of shoes for
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You add all three values and you get 
.
You add all three values and you get
and 
are prime integers. 
and 
. What is the greatest possible value of 
?
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To find the greatest possible value of 
, add the greatest possible value of 
to the greatest possible value of 
. This happens when 
is equal to the greatest prime between 35 and 45, which is 43, and when 
is equal to the greatest prime between 85 and 95, which is 89. Add the two numbers:
To find the greatest possible value of
and are prime integers: 
and 
. How many possible values of 
are there?
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can be equal to any of the prime numbers between 45 and 55, of which there are two - 47 or 53.
can be equal to any of the prime numbers between 15 and 25, of which there are three - 17, 19, and 23.
Their sum can be any of the following:
This makes five possible sums.
Their sum can be any of the following:
This makes five possible sums.