### All ACT Math Resources

## Example Questions

### Example Question #1 : Negative Numbers

What is 1 + (–1) – (–3) + 4 ?

**Possible Answers:**

3

6

9

1

7

**Correct answer:**

7

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

### Example Question #1 : Negative Numbers

Solve the following equation for :

**Possible Answers:**

**Correct answer:**

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 : The Number System

Compute the following:

**Possible Answers:**

**Correct answer:**

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 : Arithmetic

If a = –2 and b = –3, then evaluate a^{3} + b^{2}

**Possible Answers:**

17

5

9

8

1

**Correct answer:**

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.

a^{3} + b^{2} becomes (–2)^{3} + (–3)^{2} which equals –8 + 9 = 1^{}

### Example Question #11 : Concepts

Evaluate:

–3 * –7

**Possible Answers:**

4

21

–10

10

–21

**Correct answer:**

21

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

### Example Question #1 : Negative Numbers

Evaluate.

**Possible Answers:**

**Correct answer:**

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

### Example Question #1 : Negative Numbers

Solve.

**Possible Answers:**

**Correct answer:**

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

### Example Question #1 : Negative Numbers

Evaluate 3x^{3} + x^{2} if x = *–*2

**Possible Answers:**

*–*22

28

14

*–*20

**Correct answer:**

*–*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

### Example Question #1 : Negative Numbers

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

**Possible Answers:**

–16

12

24

–24

**Correct answer:**

–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.

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

Evaluate the following:

**Possible Answers:**

**Correct answer:**

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

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