What is StartFraction 7 Over 9 EndFraction divided by one-third?

Question

A fraction bar labeled 1. Under the 1 are 9 boxes containing one-ninth. Under the 9 boxes are 3 boxes containing one-third.
2
2 and StartFraction 1 Over 9 EndFraction
2 and one-third
3

Answer 1

To divide a fraction by another fraction, you multiply the first fraction by the reciprocal of the second fraction. Here, we have:

\[ \frac{7}{9} \div \frac{1}{3} \]

To find this, we can write it as:

\[ \frac{7}{9} \times \frac{3}{1} \]

Now, multiply the numerators and the denominators:

\[ \frac{7 \times 3}{9 \times 1} = \frac{21}{9} \]

Next, we can simplify \(\frac{21}{9}\). Both 21 and 9 are divisible by 3:

\[ \frac{21 \div 3}{9 \div 3} = \frac{7}{3} \]

Now, we can express \(\frac{7}{3}\) as a mixed number:

\[ \frac{7}{3} = 2 \frac{1}{3} \]

So, the answer to the division \(\frac{7}{9} \div \frac{1}{3}\) is:

\[ \boxed{2 \frac{1}{3}} \]