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:
9 + 3 x 2 equals 12 x 2 = 24 because we go left to right always.
Corrected: 9 + 3 x 2 equals 9 + 6 = 15 because multiplication comes before addition.
PEMDAS prioritizes multiplication, so 3 x 2 is done before adding 9 to the result.
2. Fix the sentence:
20 / 4 + 1 equals 20 / 5 = 4 since you add 4 + 1 first.
Corrected: 20 / 4 + 1 equals 5 + 1 = 6 since division is performed before addition.
We must divide 20 by 4 first to get 5, then add 1 for a final answer of 6.
3. Fix the sentence:
For 7 - 3 + 2, you do 3 + 2 first to get 7 - 5 = 2.
Corrected: For 7 - 3 + 2, work left to right: 7 - 3 = 4, then 4 + 2 = 6.
Since addition and subtraction share a rank, we apply them in the order they appear.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. Evaluate: 10 + 5 x 4 = 30
5 x 4 equals 20, and 10 + 20 equals 30 by following PEMDAS rules.
2. Evaluate: 18 / 6 + 7 = 10
18 / 6 equals 3, and 3 + 7 equals 10 because division precedes addition.
3. Evaluate: 15 - 2 x 6 = 3
2 x 6 equals 12, and 15 - 12 equals 3 since multiplication ranks higher than subtraction.
4. In PEMDAS, the letter M stands for multiplication
M represents multiplication, which is performed before addition and subtraction in PEMDAS.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Explain why 6 + 4 x 2 is not equal to 20.
Sample answer: Because we must multiply 4 x 2 first to get 8, then add 6 for a total of 14.
The mistake of getting 20 comes from adding before multiplying, which breaks PEMDAS.
2. When two operations have the same rank, how do you decide which to do first?
Sample answer: You work from left to right when operations share the same rank, like addition and subtraction.
Left-to-right rule applies whenever two equal-rank operations appear next to each other.