Question

Emanuel used the calculations below to find the product of the given fractions.

(Three-fifths) (StartFraction 4 over 9 EndFraction) (Negative one-half)

Step 1 StartFraction (3) (4) (negative 1) over (5) (9) (negative 2) EndFraction

Step 2 StartFraction negative 12 over negative 90 EndFraction

Step 3 StartFraction 12 over 90 EndFraction

Step 4 StartFraction 2 over 15 EndFraction

In which step did his first error occur?
step 1
step 2
step 3
step 4

Answer 1

step 1

Explanation:

The product of fractions is the quotient of the product of the numerators and the product of the denominators. When negative fractions are involved, the sign of the result will be negative if the number of minus signs among the factors is odd.

__

setup

The product Emanuel wanted to compute was ...

`(3)/(5)\cdot(4)/(9)\cdot\left(-(1)/(2)\right)`

step 1

The first calculation step used was ...

`=(3\cdot4\cdot(-1))/(5\cdot9\cdot(-2))\qquad\textbf{Error}\text{ -- a minus sign added}`

The error was in the first step where a minus sign was added. This brings the total to an even number of minus signs, changing the sign of the result.

__

A more appropriate first step might have been ...

`=-(3\cdot4\cdot1)/(5\cdot9\cdot2)\qquad\text{correct first step}`