RWM101 Study Guide

Unit 3: Order of Operations

3a. Calculate problems using negative numbers

  • How do you add negative numbers?
  • How do you subtract negative numbers?
  • When adding positive and negative numbers, how do you know if the answer is positive or negative?

Negative numbers are the opposite of positive numbers – they are less than zero. Negative whole numbers, zero, and positive whole numbers together are called integers.

When adding a positive number and a negative number, the problem can be rewritten as subtraction (see 1a, where we review the commutative property). For example -2 + 5 can be rewritten as 5 - 2. When adding two negative numbers, you can add the numbers as you would with two positive numbers, before making the answer negative. For example, -5 + (-3) = -8.

When subtracting a negative number from a positive number, the double negative makes a positive. So when subtracting a negative number, change the subtraction to addition, and make the number positive. For example, 5 - (-3) = 5 + 3 = 8. When subtracting a negative number from a negative number, the double negative still becomes a positive. However, since the first number is also negative, the problem becomes like our first example. You can now rewrite the problem as subtraction. For example, -5 - (-3)= -5+3 = 3 - 5 = -2

When multiplying or dividing negative numbers, if both numbers are positive or both numbers are negative, the answer will always be positive. If only one of the numbers is negative, the answer will be negative. For example 5 × (-3) = -15 and (-5) × (-3) = 15.

To review, see:


3b. Calculate exponents

  • What does an exponent represent?
  • How do you calculate an exponent?

Exponents represent repeated multiplication. An exponent is written as a superscript, above a number, and tells you how many times to multiply the number by itself. For example, 43 = 4 × 4 × 4.

To review, see:


3c. Apply the order of operations

  • What is the order of operations?

The order of operations is often written as PEMDAS, which stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. It is important to understand the correct order and details of the order of operations.

Parentheses are always first. Simplify within parentheses before moving on.

Exponents are always next. Evaluate any exponents in the problem after the parentheses.

The next step is very important: Although the acronym PEMDAS lists multiplication before division, multiplication is not necessarily done before division. Multiplication and division are done together, starting from left to right. Starting on the left-hand side of the problem, look for multiplication and/or division, and complete in the order that it appears.

Similarly, addition and subtraction are done together, also from left to right.

In the order of operations, think of it as 4 steps: Parentheses, Exponents, Multiplication/Division, and Addition/Subtraction.

To review, see Use the Language of Algebra.


Unit 3 Vocabulary

This vocabulary list includes terms listed above that students need to know to successfully complete the final exam for the course.

  • integers
  • order of operations