Question

Find 2 2/3÷(−1 1/6) . write your answer as a mixed number in simplest form.

Answer 1

To divide 2 2/3 by ─1 1/6 and write the answer as a mixed number in simplest form, convert the mixed numbers to improper fractions, multiply the numerators and denominators, simplify the fraction, and convert it back to a mixed number. The result is -3 1/9.

Step-by-step explanation:

To divide 2 2/3 by ─1 1/6 and write the answer as a mixed number in simplest form, we can follow these steps:

1. Convert both mixed numbers to improper fractions.
2. Multiply the numerator and denominator of the first fraction by the denominator of the second fraction, and the numerator and denominator of the second fraction by the denominator of the first fraction.
3. Divide the multiplied numerators by the multiplied denominators.
4. Convert the resulting fraction back to a mixed number.

Let's go through these steps:

2 2/3 = ((2 * 3) + 2) / 3 = 8/3

−1 1/6 = ((−1 * 6) + 1) / 6 = -7/6

Multiplying the numerators and denominators, we get:

(8/3) * (-7/6) = (8 * -7) / (3 * 6) = -56/18

Simplifying the fraction, we can divide both the numerator and denominator by their greatest common factor, which is 2:

-56/18 = (-28 * 2) / (9 * 2) = -28/9

Converting -28/9 back to a mixed number, we divide the numerator (-28) by the denominator (9) and get a quotient of -3 with a remainder of 1. So the mixed number in simplest form is:

-3 1/9