Evaluate 8 + 2 × 5.
Incorrect answer: 50
Multiplication does not always come before division. They share a priority and are evaluated left to right. Also, 3 × (6 + 4) differs from 3 × 6 + 4.
Doing every operation from left to right
Reading order and calculation order are different. Group the operations before computing them.
The correction
18
Multiply 2 × 5 = 10 before adding 8.
- Identify the action described by each phrase: sum, difference, product, or quotient.
- Use parentheses when a whole sum or difference is an input to another operation.
- Evaluate grouping first, then powers, multiplication/division left to right, and addition/subtraction left to right.
Try the reasoning in another example
Write and evaluate “three times the sum of six and four.”
- The sum is (6 + 4). The whole sum is multiplied by 3.
- Write 3 × (6 + 4), then calculate 3 × 10.
Answer: 30
Explain why each step preserves the quantity or relationship. If you can compute the answer but cannot explain the step, revisit the model before adding more questions.
The short check below reuses the first example as a retrieval question and adds a second question. It checks this method; it does not establish a grade level.
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