Arithmetic - HSPT Math
Card 1 of 2932
Simplify the following expression: (–4)(2)(–1)(–3)
Simplify the following expression: (–4)(2)(–1)(–3)
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First, we multiply –4 and 2. A negative and a positive number multiplied together give us a negative number, so (–4)(2) = –8. A negative times a negative is a positive so (–8)(–1) = 8. (8)(–3) = –24.
First, we multiply –4 and 2. A negative and a positive number multiplied together give us a negative number, so (–4)(2) = –8. A negative times a negative is a positive so (–8)(–1) = 8. (8)(–3) = –24.
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If a = –2 and b = –3, then evaluate a3 + b2
If a = –2 and b = –3, then evaluate a3 + b2
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When multiplying negative numbers, we get a negative answer if there are an odd number of negative numbers being multiplied. We get a positive answer if there are an even number of negative numbers being multiplied.
a3 + b2 becomes (–2)3 + (–3)2 which equals –8 + 9 = 1
When multiplying negative numbers, we get a negative answer if there are an odd number of negative numbers being multiplied. We get a positive answer if there are an even number of negative numbers being multiplied.
a3 + b2 becomes (–2)3 + (–3)2 which equals –8 + 9 = 1
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What is 1 + (–1) – (–3) + 4 ?
What is 1 + (–1) – (–3) + 4 ?
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You simplify the expression to be 1 – 1 + 3 + 4 = 7
You simplify the expression to be 1 – 1 + 3 + 4 = 7
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Evaluate:
–3 * –7
Evaluate:
–3 * –7
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Multiplying a negative number and another negative number makes the product positive.
Multiplying a negative number and another negative number makes the product positive.
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A tree 
feet high casts a shadow 20 feet long at the same time a tree 30 feet high casts a shadow how many feet long? Give your answer in terms of 
.
A tree
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The ratio of the height of an object to the length of the shadow it casts at a point in time is the same for all objects, so, if we let the length of the shadow cast by the second tree be 
:
Set the cross-products equal to each other and solve for 
, the correct choice.
The ratio of the height of an object to the length of the shadow it casts at a point in time is the same for all objects, so, if we let the length of the shadow cast by the second tree be
Set the cross-products equal to each other and solve for
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When evaluating the expression
,
which operation will be performed third?
When evaluating the expression
which operation will be performed third?
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In the order of operations, additions and subtractions are performed left to right. Therefore, the four operations are performed in the following order: leftmost addition, leftmost subtraction, rightmost addition, rightmost subtraction. Therefore, the rightmost addition is performed third.
In the order of operations, additions and subtractions are performed left to right. Therefore, the four operations are performed in the following order: leftmost addition, leftmost subtraction, rightmost addition, rightmost subtraction. Therefore, the rightmost addition is performed third.
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When evaluating the expression
,
in which order must the operations be carried out?
When evaluating the expression
in which order must the operations be carried out?
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According to the order of operations, the operation inside the parentheses, which is the subtraction, is performed first. This leaves a multiplication and an exponentiation (the squaring); by the order of operations, the squaring is performed next, then the multiplication.
According to the order of operations, the operation inside the parentheses, which is the subtraction, is performed first. This leaves a multiplication and an exponentiation (the squaring); by the order of operations, the squaring is performed next, then the multiplication.
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When evaluating the expression
,
in which order must the operations be carried out?
When evaluating the expression
in which order must the operations be carried out?
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According to the order of operations, since no grouping symbols are present (the parentheses are setting apart a negative number, not an operation), the exponentiation (the cubing) is worked first, then the multiplication, then the addition.
According to the order of operations, since no grouping symbols are present (the parentheses are setting apart a negative number, not an operation), the exponentiation (the cubing) is worked first, then the multiplication, then the addition.
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When evaluating the expression
,
which operation must be performed last?
When evaluating the expression
which operation must be performed last?
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According to the order of operations, since no grouping symbols are present (the parentheses are setting apart a negative number, not an operation), the exponentiation must be performed first, followed by the multiplication. The remaining subtraction and addition are performed in left-to-right order, so the subtraction is worked next, and the addition is the final operation performed.
According to the order of operations, since no grouping symbols are present (the parentheses are setting apart a negative number, not an operation), the exponentiation must be performed first, followed by the multiplication. The remaining subtraction and addition are performed in left-to-right order, so the subtraction is worked next, and the addition is the final operation performed.
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Solve:
Solve:
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Solve:
Solve:
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Solve:
Solve:
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Solve:
Solve:
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Anita is sewing a quilt made of 120 patches. She has sewn together 84 patches already. What percentage of the quilt has Anita sewn?
Anita is sewing a quilt made of 120 patches. She has sewn together 84 patches already. What percentage of the quilt has Anita sewn?
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Divide 84 by the entire amount of patches 120 to find the percentage completed.
The answer is Anita has completed 70% of the quilt.
Divide 84 by the entire amount of patches 120 to find the percentage completed.
The answer is Anita has completed 70% of the quilt.
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Fifteen percent of the students in the classroom brought their lunch from home. If 9 students brought their lunch from home, how many students are in the classroom total?
Fifteen percent of the students in the classroom brought their lunch from home. If 9 students brought their lunch from home, how many students are in the classroom total?
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You can think of the total number of students in the classroom as an unknown variable, 
.
You can set up an equation that includes 
and the information given. Normally in a percent problem, you would start with the total amount of something and multiply it by the percent to get the part of that total amount. You can set this up the same way, but the total amount is the missing information:
Total Amount x Percent = Part of Total Amount
You use 
to numerically represent 15 percent.
Now you can algebraically solve for 
, which will give you the total number of students in the class. You do this by dividing each side by 
.
Therefore there are 60 total students.
You can think of the total number of students in the classroom as an unknown variable,
You can set up an equation that includes
Total Amount x Percent = Part of Total Amount
You use
Now you can algebraically solve for
Therefore there are 60 total students.
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Solve: 
Solve:
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Evaluate the inner term inside the parenthesis first. The expression can then be simplifed to an integer.
Evaluate the inner term inside the parenthesis first. The expression can then be simplifed to an integer.
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A class has 25 students. If 60% of them are boys, how many students are girls?
A class has 25 students. If 60% of them are boys, how many students are girls?
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We know that 40% of the class are girls because 60% are boys. To express 40% as a fraction of the 25 total students, we set up a proportion to find the number of girls in the class.
When solving for 
, we find that there are 10 girls in the class.
We know that 40% of the class are girls because 60% are boys. To express 40% as a fraction of the 25 total students, we set up a proportion to find the number of girls in the class.
When solving for
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The time is now 11:17 AM. What time will it be in three hours and twenty-four minutes?
The time is now 11:17 AM. What time will it be in three hours and twenty-four minutes?
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The time is 11:17 AM. In 24 minutes, the minutes will read 
, so it wil be 11:41 AM. Let's then add three hours to it.
The time will be 2:41 PM.
The time is 11:17 AM. In 24 minutes, the minutes will read
The time will be 2:41 PM.
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The length and width of a given make of car are 4.5 and 1.8 meters, respectively.
A scale model of this make of car will be 
feet long. In terms of 
, how wide will this scale model be?
The length and width of a given make of car are 4.5 and 1.8 meters, respectively.
A scale model of this make of car will be
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The ratio of the width of the scale model to its length is the same as the comparable ratio for the actual car, so we can set up this equation:
The ratio of the width of the scale model to its length is the same as the comparable ratio for the actual car, so we can set up this equation:
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Jenny is getting ready for school. She bought school supplies on a tax-free day. She bought notebooks for $1.25 each and crayons for $0.90 each. Jenny bought two more notebooks than crayons. She paid with a ten dollar bill and got $1.05 in change. How many notebooks did she buy?
Jenny is getting ready for school. She bought school supplies on a tax-free day. She bought notebooks for $1.25 each and crayons for $0.90 each. Jenny bought two more notebooks than crayons. She paid with a ten dollar bill and got $1.05 in change. How many notebooks did she buy?
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Define variables as x = number of crayons and x + 2 = number of notebooks
To find out how much she spent, we subtract her change from what she paid with: 10.00 – 1.05 = 8.95
Then we need to solve the problem cost of notebooks plus the cost of crayons equals the total cost.
1.25(x + 2) + 0.90x = 8.95 and solving for x gives 3 crayons and 5 notebooks
Define variables as x = number of crayons and x + 2 = number of notebooks
To find out how much she spent, we subtract her change from what she paid with: 10.00 – 1.05 = 8.95
Then we need to solve the problem cost of notebooks plus the cost of crayons equals the total cost.
1.25(x + 2) + 0.90x = 8.95 and solving for x gives 3 crayons and 5 notebooks
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