Find the quotient.
6start fraction 2 over 7 end fraction ÷ 2three-fourths
A. 2start fraction 2 over 7 end fraction
B. 17Start Fraction 2 over 7 End Fraction
C. 2The term shows 6 over 11.
D. start fraction 7 over 16 end fraction
To divide fractions, we need to flip the second fraction and multiply it by the first fraction.
6start fraction 2 over 7 end fraction ÷ 2three-fourths
= 6start fraction 2 over 7 end fraction × 4 over 2 three-fourths (flip the second fraction and multiply)
= 6 * 2 / 7 * 4 / (2 * 4 / 3) (multiply the numerators and denominators separately)
= 36 / 28 * 8 / 2 (simplify the fractions)
= 9 / 7 * 2 (multiply the numerators and denominators separately)
= 18 / 7 (simplify the fraction)
Therefore, the quotient is 18/7, which is option D.