Negative numbers - HSPT Math
Card 1 of 476
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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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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Subtract: 
Subtract:
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It is possible to rewrite the expression as:
Take the negative of the difference of 47 and 23.
The answer is 
.
It is possible to rewrite the expression as:
Take the negative of the difference of 47 and 23.
The answer is
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If x is a negative integer, what else must be a negative integer?
If x is a negative integer, what else must be a negative integer?
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By choosing a random negative number, for example: –4, we can input the number into each choice and see if we come out with another negative number. When we put –4 in for x, we would have –4 – (–(–4)) or –4 – 4, which is –8. Plugging in the other options gives a positive answer. You can try other negative numbers, if needed, to confirm this still works.
By choosing a random negative number, for example: –4, we can input the number into each choice and see if we come out with another negative number. When we put –4 in for x, we would have –4 – (–(–4)) or –4 – 4, which is –8. Plugging in the other options gives a positive answer. You can try other negative numbers, if needed, to confirm this still works.
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–7 – 7= x
–7 – (–7) = y
what are x and y, respectively
–7 – 7= x
–7 – (–7) = y
what are x and y, respectively
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x: –7 – 7= –7 + –7 = –14
y: –7 – (–7) = –7 + 7 = 0
when subtracting a negative number, turn it into an addition problem
x: –7 – 7= –7 + –7 = –14
y: –7 – (–7) = –7 + 7 = 0
when subtracting a negative number, turn it into an addition problem
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If 
is a positive number, and 
is also a positive number, what is a possible value for 
?
If
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Because 
is positive, 
must be negative since the product of two negative numbers is positive.
Because 
is also positive, 
must also be negative in order to produce a prositive product.
To check you answer, you can try plugging in any negative number for .
Because
Because
To check you answer, you can try plugging in any negative number for
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Which of the following operations always gives a negative result?
Which of the following operations always gives a negative result?
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The sum of two negative numbers is always negative, hence, this is the right choice.
As for the other choices:
The product or quotient of two negative numbers is always positive.
A negative number taken to the power of a positive integer can be either negative or positive depending on whether the exponent is even or odd. 
, which is positive, and 
, which is negative.
The difference of negative numbers can be either negative, positive, or zero:
, but 
The sum of two negative numbers is always negative, hence, this is the right choice.
As for the other choices:
The product or quotient of two negative numbers is always positive.
A negative number taken to the power of a positive integer can be either negative or positive depending on whether the exponent is even or odd.
The difference of negative numbers can be either negative, positive, or zero:
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Solve for 
:
Solve for
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Begin by isolating your variable.
Subtract 
from both sides:
, or 
Next, subtract 
from both sides:
, or 
Then, divide both sides by 
:
Recall that division of a negative by a negative gives you a positive, therefore:
or 
Begin by isolating your variable.
Subtract
Next, subtract
Then, divide both sides by
Recall that division of a negative by a negative gives you a positive, therefore:
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Solve the following equation:
Solve the following equation:
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The rule for dividing negative numbers is the same as for multiplying negative numbers.
If both numbers are negative, you will get a positive answer.
If either number is positive, and the other is negative, you will get a negative answer.
Therefore:
The rule for dividing negative numbers is the same as for multiplying negative numbers.
If both numbers are negative, you will get a positive answer.
If either number is positive, and the other is negative, you will get a negative answer.
Therefore:
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Choose the answer which best solves the following equation:
Choose the answer which best solves the following equation:
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To solve, first put the equation in terms of 
:
First multiply the x to both sides.
Now divide by 12 to solve for x.
Here, because one of the numbers in the equation is positive, and the other is negative, the answer must be a negative number:
To solve, first put the equation in terms of
First multiply the x to both sides.
Now divide by 12 to solve for x.
Here, because one of the numbers in the equation is positive, and the other is negative, the answer must be a negative number:
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Evaluate: 
Evaluate:
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To evaluate this, rewrite the expression with the correct signs.
Positive multiplied with a negative sign results in a negative, and a double negative results in a positive sign.
To evaluate this, rewrite the expression with the correct signs.
Positive multiplied with a negative sign results in a negative, and a double negative results in a positive sign.
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Evaluate: 
Evaluate:
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In order to combine like terms correctly, it is necessary to simplify every term and eliminate the parentheses. Double negatives equal a positive sign.
Combine like terms. The answer is: 
In order to combine like terms correctly, it is necessary to simplify every term and eliminate the parentheses. Double negatives equal a positive sign.
Combine like terms. The answer is:
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Note: Public domain map from CIA World Factbook.
Refer to the above time zone map. The numbers along the top represent the difference, in hours, between the given time zone and Greenwich Mean Time (the time zone for the United Kingdom).
Which of the following expressions gives the time difference, in hours, between Paris and Dallas?
Note: Public domain map from CIA World Factbook.
Refer to the above time zone map. The numbers along the top represent the difference, in hours, between the given time zone and Greenwich Mean Time (the time zone for the United Kingdom).
Which of the following expressions gives the time difference, in hours, between Paris and Dallas?
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A difference is the result of a subtraction. The time difference between the two cities will be the result of subtracting the numbers along the top of the map for their respective time zones, and taking the absolute value of the difference. The numbers for Paris and Dallas, respectively, are 1 and 
, so the difference in hours between their times is 
.
A difference is the result of a subtraction. The time difference between the two cities will be the result of subtracting the numbers along the top of the map for their respective time zones, and taking the absolute value of the difference. The numbers for Paris and Dallas, respectively, are 1 and
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Note: Public domain map from CIA World Factbook.
Refer to the above time zone map. The numbers along the top represent the difference, in hours, between the given time zone and Greenwich Mean Time (the time zone for the United Kingdom).
A flight took off from Winnipeg, Canada at 5:00 PM and took 7 hours to get to the Azores. What time was it in the Azores when it landed there?
Note: Public domain map from CIA World Factbook.
Refer to the above time zone map. The numbers along the top represent the difference, in hours, between the given time zone and Greenwich Mean Time (the time zone for the United Kingdom).
A flight took off from Winnipeg, Canada at 5:00 PM and took 7 hours to get to the Azores. What time was it in the Azores when it landed there?
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The time difference between Winnipeg and the Azores is the result of subtracting the numbers along the top of their respective timie zones, which are 
and 
:
The Azores is five hours ahead of Winnipeg, so when the flight takes off, since
,
it is 10:00 PM in the Azores.
Add the seven hours flight time, and take the result modulo 12:
The time is 5:00 AM in the Azores when the plane lands there.
The time difference between Winnipeg and the Azores is the result of subtracting the numbers along the top of their respective timie zones, which are
The Azores is five hours ahead of Winnipeg, so when the flight takes off, since
it is 10:00 PM in the Azores.
Add the seven hours flight time, and take the result modulo 12:
The time is 5:00 AM in the Azores when the plane lands there.
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If you have a negative number and multiply it by another, the final answer is positive. What sign did the other number have?
If you have a negative number and multiply it by another, the final answer is positive. What sign did the other number have?
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The only way to get a positive product from multiplication is to multiply two positive numbers together or two negative numbers together.
If the first number was negative, the other number will also have to be negative.
The only way to get a positive product from multiplication is to multiply two positive numbers together or two negative numbers together.
If the first number was negative, the other number will also have to be negative.
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Negative 37 is the square root of what number?
Negative 37 is the square root of what number?
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The square root of a number is the number which, when squared - multiplied by itself - yields that number as its result. Recall that when two negative numbers are multiplied together they result in a positive numbers.
Therefore, negative 37 is the square root of
The square root of a number is the number which, when squared - multiplied by itself - yields that number as its result. Recall that when two negative numbers are multiplied together they result in a positive numbers.
Therefore, negative 37 is the square root of
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Which of the following is a negative number?
(I) 
(II) 
(III) 
Which of the following is a negative number?
(I)
(II)
(III)
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(I) and (II) are both negative, since the product or quotient of a negative number and a positive number is negative.
The sum of a negative number and a positive number assumes the sign of the number with the greater absolute value. Since in (III), the negative number has the higher absolute value (200 versus 180), the sign of the sum is negative.
(I) and (II) are both negative, since the product or quotient of a negative number and a positive number is negative.
The sum of a negative number and a positive number assumes the sign of the number with the greater absolute value. Since in (III), the negative number has the higher absolute value (200 versus 180), the sign of the sum is negative.
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