What is StartFraction 8 Over 9 EndFraction divided by two-thirds?

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.
1 and one-sixth
1 and StartFraction 2 Over 9 EndFraction
1 and one-third
1 and two-thirds

Answer 1

To find the result of \(\frac{8}{9}\) divided by \(\frac{2}{3}\), we can multiply by the reciprocal of \(\frac{2}{3}\).

The steps are as follows:

1. Write the division as multiplication by the reciprocal: \[ \frac{8}{9} \div \frac{2}{3} = \frac{8}{9} \times \frac{3}{2} \]

2. Multiply the numerators and the denominators: \[ = \frac{8 \times 3}{9 \times 2} = \frac{24}{18} \]

3. Simplify \(\frac{24}{18}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 6: \[ = \frac{24 \div 6}{18 \div 6} = \frac{4}{3} \]

4. Now we can convert \(\frac{4}{3}\) into a mixed number: \[ \frac{4}{3} = 1 \frac{1}{3} \]

So, the final answer is: \[ 1 \text{ and } \frac{1}{3} \]

Therefore, the correct choice from the options is: 1 and one-third.