How many groups of Two-thirds are in Three-fifths?

Question

A fraction bar labeled 1. Under the 1 are 5 boxes labeled one-fifth. Under the 5 boxes are 3 boxes containing one-third. Under the 3 boxes are 15 boxes labeled StartFraction 1 Over 15 EndFraction.
StartFraction 9 Over 15 EndFraction
StartFraction 9 Over 10 EndFraction
1 and one-third

Answer 1

To find out how many groups of \(\frac{2}{3}\) are in \(\frac{3}{5}\), we can set up the problem as follows:

We want to calculate the division:

\[ \frac{3}{5} \div \frac{2}{3} \]

Dividing by a fraction is the same as multiplying by its reciprocal. Therefore, we can rewrite the equation as:

\[ \frac{3}{5} \times \frac{3}{2} \]

Now, we multiply the numerators together and the denominators together:

\[ \frac{3 \times 3}{5 \times 2} = \frac{9}{10} \]

So, the result of finding how many groups of \(\frac{2}{3}\) are in \(\frac{3}{5}\) is \(\frac{9}{10}\).

Thus, the answer is:

\(\frac{9}{10}\)