Evaluate negative five-sixths divided by two-thirds multiplied by two-thirds giving the answer in its simplest form.
We might immediately notice in this question that we’re dividing negative five-sixths by two-thirds and then multiplying the answer by two-thirds. Dividing any value, in this case, negative five-sixths, by a number and then multiplying by the same number will take us back to the original number. This means that we would expect the answer to be negative five-sixths.
We can check this by doing our usual method of dividing and multiplying fractions. We can begin by dividing negative five-sixths by two-thirds. One way of remembering how to divide fractions is using the acronym KCF. We keep the first fraction the same, in this case, negative five-sixths. We change the division sign into a multiplication sign. We then flip or find the reciprocal of the second fraction. The reciprocal of two-thirds is three-halves or three over two.
Before multiplying the two fractions, we notice that three on the top and six on the bottom are divisible by three. The calculation simplifies to negative five over two multiplied by one over two. This is equal to negative five over four or negative five-quarters. We multiply the numerators and denominators separately.
As we have worked out the calculation inside the parentheses or brackets, we now have negative five over four multiplied by two over three. Once again, we can simplify by dividing the two and four by two. Multiplying the numerators gives us negative five and multiplying the denominators gives us six.
This confirms that the correct answer to the calculation in its simplest form is negative five-sixths.