Question

Is the quotient of 3/5 ÷ 6/7 greater than or less than 3/5? Explain

Answer 1

3/5 divided by 6/7 is 7/10 is greater than 3/5 or 6/10

Answer 2

The quotient of two fraction is the multiplication between the first and the inverse of the second:

$\dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{a}{b} \cdot \dfrac{d}{c}$

So, in your case, you have

$\dfrac{3}{5} \div \dfrac{6}{7} = \dfrac{3}{5} \cdot \dfrac{7}{6} = \dfrac{7}{10}$

So, the question now is: which is larger, 7/10 or 3/5? To answer this question, transform the second fraction so that it will have denominator 10 as well:

$\dfrac{3}{5} = \dfrac{3\cdot 2}{5 \cdot 2} = \dfrac{6}{10}$

So, now it is clear that

$\dfrac{7}{10} > \dfrac{6}{10}$