Problem 3 · AMC 8 Stretch
Core
Arithmetic & Operations
logical-reasoningrecognizing-false-rules
Find the value of \(3+2\times 5\). (A common wrong answer is \(25\), from adding first.)
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Answer: 13
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Hint 1 of 4
There is a rule about which operation goes first. Which one wins: \(\times\) or \(+\)?
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Hint 2 of 4
Picture the \(\times\) sign as a stronger 'glue' than the \(+\) sign. The \(2\times 5\) sticks together as one block before the \(+\) does anything.
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Hint 3 of 4
Work out the glued block \(2\times 5\) first, then add the \(3\).
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Approach: Order of operations — multiplication binds tighter than addition
- Multiplication is done before addition. Adding first (the trap) gives \(3+2=5\) then \(5\times 5=25\) — wrong.
- The \(\times\) is like stronger glue than \(+\), so \(2\times 5\) clumps into one block worth \(10\) first.
- Then add: \(3 + 10 = 13\).
- So \(3+2\times 5=13\).
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