Find the quotient and write it in simplest form. Make sure to show all your work. 2 1/3÷1 2/5 (2 points)

Answer 1

To divide mixed numbers, we need to convert them into improper fractions.

Converting 2 1/3 into an improper fraction:
2 1/3 = (2 * 3 + 1) / 3 = 7/3

Converting 1 2/5 into an improper fraction:
1 2/5 = (1 * 5 + 2) / 5 = 7/5

Now we can divide the two fractions:
(7/3) ÷ (7/5)

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.

(7/3) * (5/7) = (7 * 5) / (3 * 7) = 35/21

To simplify the fraction, we divide the numerator and denominator by their greatest common divisor, which is 7.

35/21 = (35 ÷ 7) / (21 ÷ 7)
35/21 = 5/3

Therefore, the quotient of 2 1/3 ÷ 1 2/5 is 5/3 in its simplest form.