Negative Numbers - ACT Math
Card 0 of 162
Add: 
Add:
Simply the signs before solving. A positive sign multiplied with a negative sign will convert the sign to a negative, and a negative multiplied with a negative will convert the sign to a positive.

Simply the signs before solving. A positive sign multiplied with a negative sign will convert the sign to a negative, and a negative multiplied with a negative will convert the sign to a positive.
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Solve: 
Solve:
Starting at
and adding
is the same as subtracting
.
.
Starting at and adding
is the same as subtracting
.
.
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Add 
Add
Starting at
and adding
is the same as subtracting
.
.
Starting at and adding
is the same as subtracting
.
.
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Solve: 
Solve:
Adding
to
is the same as subtracting
from
.
.
Adding to
is the same as subtracting
from
.
.
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What is
?
What is ?
A negative number divided by a negative number always results in a positive number.
divided by
equals
. Since the answer is positive, the answer cannot be
or any other negative number.
A negative number divided by a negative number always results in a positive number. divided by
equals
. Since the answer is positive, the answer cannot be
or any other negative number.
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Solve for
:

Solve for :
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 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
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Solve the following equation:

Solve the following equation:
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:
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 3x3 + x2 if x = _–_2
Evaluate 3x3 + x2 if x = _–_2
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
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Simplify the following expression: (–4)(2)(–1)(–3)
Simplify the following expression: (–4)(2)(–1)(–3)
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
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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Evaluate:
–3 * –7
Evaluate:
–3 * –7
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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Evaluate.

Evaluate.

Multiplying a negative and a positive number creates a negative product:



Multiplying a negative and a positive number creates a negative product:
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Solve.

Solve.


A negative number multiplied by a positive number will always be negative.
A negative number multiplied by a positive number will always be negative.
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Evaluate the following:

Evaluate the following:
Two odd numbers multiplied always result in an even number. Simply multiple the two as though they were even. Thus

Two odd numbers multiplied always result in an even number. Simply multiple the two as though they were even. Thus
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What is 1 + (–1) – (–3) + 4 ?
What is 1 + (–1) – (–3) + 4 ?
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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Compute the following: 
Compute the following:
Convert all the double signs to a single sign before solving. Remember, two minus (negative) signs combine to form a plus (positive) sign, and a plus (positive) sign and a minus (negative) sign combine to form a minus (negative) sign.


Convert all the double signs to a single sign before solving. Remember, two minus (negative) signs combine to form a plus (positive) sign, and a plus (positive) sign and a minus (negative) sign combine to form a minus (negative) sign.
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Solve the following equation for
:

Solve the following equation for :
To begin, we need to recall how to subtract negative numbers. Remember, when subtracting a negative number, the two negatives cancel out, creating a positive.
So, this:

Becomes this:

We can combine like terms on the left to get:

Then, we can subtract
from both sides in order to get
by itself:

In this case, we are subtracting from a negative number, which is just like adding two negative numbers, or subtracting from a positive number. The result will be more negative, because we will be moving further to the left on the number line.

To begin, we need to recall how to subtract negative numbers. Remember, when subtracting a negative number, the two negatives cancel out, creating a positive.
So, this:
Becomes this:
We can combine like terms on the left to get:
Then, we can subtract from both sides in order to get
by itself:
In this case, we are subtracting from a negative number, which is just like adding two negative numbers, or subtracting from a positive number. The result will be more negative, because we will be moving further to the left on the number line.
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Add: 
Add:
Simply the signs before solving. A positive sign multiplied with a negative sign will convert the sign to a negative, and a negative multiplied with a negative will convert the sign to a positive.

Simply the signs before solving. A positive sign multiplied with a negative sign will convert the sign to a negative, and a negative multiplied with a negative will convert the sign to a positive.
Compare your answer with the correct one above
Solve: 
Solve:
Starting at
and adding
is the same as subtracting
.
.
Starting at and adding
is the same as subtracting
.
.
Compare your answer with the correct one above