Discussion
Evaluate: \( \dfrac{325 + 325 + 325 + 325}{4 \times 325} \)
Answer: A
Correct answer: 1
Simplify the numerator first. Four copies of 325 added together is \[ 325 + 325 + 325 + 325 = 4 \times 325 = 1300. \] The denominator is also \( 4 \times 325 = 1300 \), so the fraction is \[ \frac{1300}{1300} = 1. \] The point of the question is to be recognised rather than computed: repeated addition of the same quantity is multiplication, so the numerator and denominator are the same expression written two different ways, and the value must be 1 without any arithmetic at all. The distractor 4 is what comes of cancelling only the 325 and forgetting the 4, and 325 of cancelling only the 4. Reading the extent of the division bar carefully is what such questions test - \( \frac{325 \times 4}{4} \times \frac{4}{325} \) is a different expression with the value 4, and the placement of the brackets is all that separates them.
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