Negative numbers - HSPT Math
Card 1 of 476
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?
Tap to reveal answer
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.
← Didn't Know|Knew It →
–7 – 7= x
–7 – (–7) = y
what are x and y, respectively
–7 – 7= x
–7 – (–7) = y
what are x and y, respectively
Tap to reveal answer
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
← Didn't Know|Knew It →
If 
is a positive number, and 
is also a positive number, what is a possible value for 
?
If
Tap to reveal answer
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
← Didn't Know|Knew It →
Which of the following operations always gives a negative result?
Which of the following operations always gives a negative result?
Tap to reveal answer
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:
← Didn't Know|Knew It →
Solve for 
:
Solve for
Tap to reveal answer
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:
← Didn't Know|Knew It →
Solve the following equation:
Solve the following equation:
Tap to reveal answer
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:
← Didn't Know|Knew It →
Choose the answer which best solves the following equation:
Choose the answer which best solves the following equation:
Tap to reveal answer
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:
← Didn't Know|Knew It →
Evaluate: 
Evaluate:
Tap to reveal answer
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.
← Didn't Know|Knew It →
Subtract: 
Subtract:
Tap to reveal answer
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
← Didn't Know|Knew It →
Solve: 
Solve:
Tap to reveal answer
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.
← Didn't Know|Knew It →
Evaluate: 
Evaluate:
Tap to reveal answer
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:
← Didn't Know|Knew It →
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?
Tap to reveal answer
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
← Didn't Know|Knew It →
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?
Tap to reveal answer
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.
← Didn't Know|Knew It →
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?
Tap to reveal answer
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.
← Didn't Know|Knew It →
Evaluate 3x3 + x2 if x = _–_2
Evaluate 3x3 + x2 if x = _–_2
Tap to reveal answer
When multiplying a negative number an odd number of times, the answer is negative. When multiplying a negative number an even number of times, the answer is positive. Order of operations also applies: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction, from left to right. A mnemonic to remember the order of operations is “Please excuse my dear Aunt Sally.”
3(_–2)3 + (–_2)2
= 3(_–_8) + (4)
= _–_24 + 4
= _–_20
When multiplying a negative number an odd number of times, the answer is negative. When multiplying a negative number an even number of times, the answer is positive. Order of operations also applies: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction, from left to right. A mnemonic to remember the order of operations is “Please excuse my dear Aunt Sally.”
3(_–2)3 + (–_2)2
= 3(_–_8) + (4)
= _–_24 + 4
= _–_20
← Didn't Know|Knew It →
Simplify the following expression: (–4)(2)(–1)(–3)
Simplify the following expression: (–4)(2)(–1)(–3)
Tap to reveal answer
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.
← Didn't Know|Knew It →
If a = –2 and b = –3, then evaluate a3 + b2
If a = –2 and b = –3, then evaluate a3 + b2
Tap to reveal answer
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
← Didn't Know|Knew It →
What is 1 + (–1) – (–3) + 4 ?
What is 1 + (–1) – (–3) + 4 ?
Tap to reveal answer
You simplify the expression to be 1 – 1 + 3 + 4 = 7
You simplify the expression to be 1 – 1 + 3 + 4 = 7
← Didn't Know|Knew It →
Evaluate:
–3 * –7
Evaluate:
–3 * –7
Tap to reveal answer
Multiplying a negative number and another negative number makes the product positive.
Multiplying a negative number and another negative number makes the product positive.
← Didn't Know|Knew It →
Evaluate.
Evaluate.
Tap to reveal answer
Multiplying a negative and a positive number creates a negative product:
Multiplying a negative and a positive number creates a negative product:
← Didn't Know|Knew It →