What is Three-fourths divided by one-sixth?

Question

A fraction bar labeled 1. Under the 1 are 4 boxes containing one-fourth. Under the 4 boxes are 6 boxes containing one-sixth. Under the 6 boxes are 12 boxes containing StartFraction 1 Over 12 EndFraction.
3
4
4 and StartFraction 1 Over 12 EndFraction
4 and one-half

Answer 1

To solve the problem of dividing three-fourths by one-sixth, we follow the rule for dividing fractions, which involves multiplying by the reciprocal of the second fraction.

Here are the steps:

1. Start with the fractions: \[ \frac{3}{4} \div \frac{1}{6} \]

2. Take the reciprocal of the second fraction (one-sixth): \[ \frac{1}{6} \text{ becomes } \frac{6}{1} \]

3. Multiply the first fraction by the reciprocal: \[ \frac{3}{4} \times \frac{6}{1} \]

4. Multiply the numerators and the denominators: \[ = \frac{3 \times 6}{4 \times 1} = \frac{18}{4} \]

5. Simplify \(\frac{18}{4}\): \[ = \frac{9}{2} \]

6. Convert \(\frac{9}{2}\) into a mixed number: \[ 4 \frac{1}{2} \]

Therefore, the answer to three-fourths divided by one-sixth is \(4\) and \(\frac{1}{2}\).