# ACT Math : Negative Numbers

## Example Questions

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### Example Question #1 : Negative Numbers

What is 1 + (–1) – (–3) + 4 ?

7

1

6

9

3

7

Explanation:

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

### Example Question #2 : Negative Numbers

Solve the following equation for :

Explanation:

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.

### Example Question #1 : Negative Numbers

Compute the following:

Explanation:

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.

### Example Question #1 : How To Multiply Negative Numbers

If a = –2 and b = –3, then evaluate a3 + b2

17

8

5

9

1

1

Explanation:

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

### Example Question #1 : How To Multiply Negative Numbers

Evaluate:

–3 * –7

–10

–21

21

10

4

21

Explanation:

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

### Example Question #3 : How To Multiply Negative Numbers

Evaluate.

Explanation:

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

### Example Question #4 : How To Multiply Negative Numbers

Solve.

Explanation:

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

### Example Question #11 : Negative Numbers

Evaluate 3x3 + x2 if x = 2

20

28

22

14

20

Explanation:

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

### Example Question #6 : How To Multiply Negative Numbers

Simplify the following expression: (–4)(2)(–1)(–3)

12

24

–16

–24

–24

Explanation:

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.

### Example Question #7 : How To Multiply Negative Numbers

Evaluate the following: