Negative Numbers - ACT Math

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.

Starting at and adding is the same as subtracting . .

Starting at and adding is the same as subtracting . .

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.

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

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:

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:

Multiplying a negative number and another negative number makes the product positive.

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.

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 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

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

A negative number multiplied by a positive number will always be negative.

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

You simplify the expression to be 1 – 1 + 3 + 4 = 7

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.

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.