Question

1. critique reasoning find the error in the work below. then show the correct calculation.

\\(\frac{8}{12} \times 6 = 8 \times \frac{1}{12} \times 6 = 8 \times \frac{1}{72} = \frac{8}{72} = \frac{1}{9}\\)

Explanation:

Step1: Identify the error

In the step \(8\times\frac{1}{12}\times6 = 8\times\frac{1}{72}\), the multiplication of \( \frac{1}{12}\) and \(6\) is done incorrectly. It should be \(\frac{1}{12}\times6=\frac{6}{12}=\frac{1}{2}\), not \(\frac{1}{72}\).

Step2: Correct the calculation

We start with \(\frac{8}{12}\times6\). We can also rewrite \(\frac{8}{12}\times6\) as \(8\times\frac{1}{12}\times6\). Now, multiply \(\frac{1}{12}\) and \(6\) first: \(\frac{1}{12}\times6=\frac{6}{12}=\frac{1}{2}\). Then multiply by \(8\): \(8\times\frac{1}{2} = 4\).

Or, we can simplify \(\frac{8}{12}\) and \(6\) first. \(\frac{8}{12}\) simplifies to \(\frac{2}{3}\) (dividing numerator and denominator by \(4\)), and then \(\frac{2}{3}\times6= 2\times2 = 4\) (since \(6\div3 = 2\)).

Answer:

The error is in the multiplication of \(\frac{1}{12}\) and \(6\) (it was calculated as \(\frac{1}{72}\) instead of \(\frac{1}{2}\)). The correct calculation is \(\frac{8}{12}\times6=\frac{8\times6}{12}=\frac{48}{12} = 4\) (or using the other methods above), so the correct result is \(4\).