Question

Divide: -5 5/6 ÷ (-2 1/6). Enter your answer as a mixed number, in simplified form, in the box.

a) 2 2/3
b) -2 2/3
c) 2 1/2
d) -2 1/2

Answer 1

To divide -5 5/6 by (-2 1/6), convert both to improper fractions, multiply by the reciprocal, simplify, and convert back to a mixed number, yielding the answer of 2 2/3, which is positive due to division rules.

Step-by-step explanation:

To divide -5 5/6 by (-2 1/6), we need to convert these mixed numbers into improper fractions and then multiply the first fraction by the reciprocal of the second.

First, let's convert -5 5/6 into an improper fraction:

-5 5/6 = -35/6 (since -5 * 6 + 5 = -30 + 5 = -35)

Next, let's convert -2 1/6 into an improper fraction:

-2 1/6 = -13/6 (since -2 * 6 + 1 = -12 + 1 = -13)

Now we multiply -35/6 by the reciprocal of -13/6, which is -6/13:

-35/6 × -6/13 = 210/78

Since both 210 and 78 have a common factor of 6, we can simplify the fraction:

210/78 = 35/13

Finally, we convert this improper fraction back into a mixed number:

35/13 = 2 9/13, which simplifies further to 2 2/3 since 9/13 has no common factors.

Because we divided two negative numbers, the result is positive following the rules of division, so the answer is 2 2/3. Therefore, the correct option is (a) 2 2/3.