A2.5 — because PEMDAS puts multiplication before division, so compute 4 × 2 = 8 first, then 20 ÷ 8
B10 — because division and multiplication have equal priority; evaluate left to right: (20 ÷ 4) × 2 = 5 × 2
C40 — because you multiply all numbers together before dividing
D5 — because division always comes first: 20 ÷ 4 = 5, then discard the × 2
Multiplication and division have equal priority — neither comes before the other. When both appear without parentheses, evaluate left to right: 20 ÷ 4 = 5, then 5 × 2 = 10. The most common mistake is reading PEMDAS as 'M before D always,' which gives the wrong answer of 2.5. The mnemonic lists M before D, but they are equal partners evaluated left to right.
Question 2 Multiple Choice
A student means to compute (3 + 4) × 2 but accidentally writes 3 + 4 × 2. What does the written expression equal, and how does it differ from what the student intended?
ABoth expressions equal 14 — parentheses do not change the answer when addition and multiplication are involved
BThe written expression gives 11 (multiply first: 4 × 2 = 8, then 3 + 8 = 11); the intended expression gives 14 (add first: 3 + 4 = 7, then 7 × 2 = 14)
CThe written expression gives 14 (add first); the parentheses version gives 11
DBoth expressions give 11 — addition and multiplication can be performed in any order
Without parentheses, multiplication wins: 3 + 4 × 2 = 3 + 8 = 11. With parentheses, addition happens first: (3 + 4) × 2 = 7 × 2 = 14. The parentheses changed the answer by 3. This is precisely why parentheses exist — when you want addition done before multiplication, you must write the parentheses explicitly. Leaving them out changes the meaning of the expression.
Question 3 True / False
Parentheses in a mathematical expression indicate that the operations inside them should be performed before following the standard order of operations.
TTrue
FFalse
Answer: True
Parentheses are the tool for overriding default priority. Anything inside parentheses is evaluated first, regardless of what operations appear outside them. (5 + 3) × 4 means 'add first, then multiply' — the parentheses say so explicitly. Without them, multiplication would happen first by default, giving a different answer.
Question 4 True / False
According to the order of operations, multiplication should generally be performed before division when both appear in an expression.
TTrue
FFalse
Answer: False
Multiplication and division have equal priority. When both appear in an expression (without parentheses), they are evaluated left to right — whichever appears first from left to right is done first. In 20 ÷ 4 × 2, division comes first (left to right): 20 ÷ 4 = 5, then 5 × 2 = 10. Treating division as lower priority gives the wrong answer of 2.5. The same equal-priority rule applies to addition and subtraction.
Question 5 Short Answer
Why does mathematics need a shared order of operations? What problem would arise without it?
Think about your answer, then reveal below.
Model answer: Without a shared convention, the same expression could be correctly evaluated to different answers by different people. For example, 3 + 4 × 2 could equal 11 (multiply first) or 14 (add first) depending on which order someone chose. Math only works as a shared language when the same notation produces the same result for everyone.
Order of operations is fundamentally a social agreement — the grammar of mathematical notation. Just as grammatical rules ensure 'the cat ate the fish' and 'the fish ate the cat' mean different things, order of operations ensures 3 + 4 × 2 means exactly one thing. Without it, engineers, scientists, and students would get different answers from identical formulas, making mathematical communication impossible.