Competition · AMC preparation · step 4 of 4
AMC 8 · 2023 · #1
Grade 5 arithmeticPick an answer.
AMC 8 2023 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
Doing the whole expression in one shot invites mistakes. The expression already splits into two parenthesized parts, so we evaluate each small piece independently and finish with one subtraction. Since the problem is multiple choice, we can also match the computed value to the answer choices as a final check.
Evaluate the first part
First part: multiply before adding, so (8 × 4 + 2) gives 34.
Inside parentheses we still follow the rule: multiply before add.
5.OA.A.1Identify SubproblemsEvaluate the second part
Second part: compute 4 × 2 first, then add 8, giving 16.
Order of operations applies inside parentheses too, even when the multiplication isn't written first.
Inside the second parentheses, 8 + 4 × 2 comes out to 16 because you form 4 × 2 first and only then add it to 8.
▸ Why?
The multiplication sign ties 4 and 2 into a single quantity, and addition can only combine finished quantities, so that product has to be built before the 8 is joined to it.
▸ Why?
Writing 4 × 2 names one amount — four groups of two, which is 8 — not a loose pair of digits to be read left to right with the neighboring 8.
Subtract the two results
Combine the two subresults with the final subtraction: 34 - 16 = 18.
Subtracting two-digit numbers is basic Grade 3 fluency.
3.NBT.A.2Identify SubproblemsMatch the answer choice
The computed value lands exactly on choice (D); the others don't match, so eliminate them.
On a multiple-choice problem, always verify the computed value lands on one of the listed options.
5.OA.A.1Eliminate PossibilitiesThis AMC 8 problem only needs Grade 5 parentheses and order of operations you already know!
- Evaluate the first part
- Evaluate the second part
- Subtract the two results
- Match the answer choice
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