Order of Operations Introduction — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
For 4 + 2 x 3, you add first to get 6 x 3 = 18.
Corrected: For 4 + 2 x 3, multiply first: 2 x 3 = 6, then 4 + 6 = 10.
Without parentheses, multiplication is always done before addition, so 2 x 3 must be computed first.
2. Fix the sentence:
10 - 2 x 4 equals 8 x 4 = 32 because we work left to right.
Corrected: 10 - 2 x 4 equals 10 - 8 = 2 because multiplication comes before subtraction.
PEMDAS tells us multiplication outranks subtraction, so 2 x 4 must be evaluated before subtracting.
3. Fix the sentence:
For 8 + 6 / 2, you add 8 + 6 = 14, then divide by 2 to get 7.
Corrected: For 8 + 6 / 2, divide first: 6 / 2 = 3, then 8 + 3 = 11.
Division is in the same step as multiplication and is performed before any addition or subtraction.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. In 6 + 4 x 2, you should multiply first before adding.
Multiplication outranks addition, so 4 x 2 must be done before 6 is added.
2. Evaluate: 5 + 2 x 3 = 11
2 x 3 equals 6, and 5 + 6 equals 11 following PEMDAS rules.
3. Evaluate: 12 - 8 / 4 = 10
8 / 4 equals 2, and 12 - 2 equals 10 because division precedes subtraction.
4. The letters PEMDAS are a mnemonic to remember the order of operations.
A mnemonic is a memory aid, and PEMDAS helps students recall each step's order.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Why must we follow the order of operations when evaluating expressions?
Sample answer: We follow the order so everyone gets the same correct answer when evaluating an expression.
Without rules, the same expression could give different answers, which would cause confusion in math.
2. What does PEMDAS stand for, and why is it useful?
Sample answer: PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. It helps remember the order.
Knowing PEMDAS gives a clear, memorable order so expressions are evaluated consistently every time.