Question

Devin is having trouble with his assignment. His shown work is as follows: − 3 5 5 3 = − 3 5 × 5 3 = − 15 15 = −1 However, this answer does not match the answer that his teacher gives him. What is Devin’s mistake?

Answer 1

Question:

Devin is having trouble with his assignment. His shown work is as follows:

$\frac{-3}{5} / \frac{5}{3} = \frac{-3}{5} * \frac{5}{3} = \frac{-15}{15} = -1$

However, this answer does not match the answer that his teacher gives him.

What is Devin’s mistake?

Answer:

See Explanation Below

Step-by-step explanation:

Given

$\frac{-3}{5} / \frac{5}{3} = \frac{-3}{5} * \frac{5}{3} = \frac{-15}{15} = -1$

Required

Spot and correct the mistake

Devin's mistake is in between step 1 and step 2.

To divide fractions;

You start by converting the division sign to multiplication sign.

But when doing this, you have to consider that the denominator and numerator of the second fraction will swap positions.

So, Devin's mistake is at

$\frac{-3}{5} / \frac{5}{3} = \frac{-3}{5} * \frac{5}{3}$

Because he didn't swap the position of 5 and 3 in the second fraction when changing the division to multiplication.

His calculation should be as follows

$\frac{-3}{5} / \frac{5}{3} = \frac{-3}{5} * \frac{3}{5}$

$\frac{-3}{5} / \frac{5}{3} = \frac{-9}{25}$

If he wishes to leave his answer in decimal, it'll be

$\frac{-3}{5} / \frac{5}{3} = -0.36$