Question

7 1/4 divided 5/6

Answer 1

To divide \( 7 \frac{1}{4} \) by \( \frac{5}{6} \), we first need to convert the mixed number \( 7 \frac{1}{4} \) into an improper fraction.

1. Convert \( 7 \frac{1}{4} \) to an improper fraction:
\[
7 \frac{1}{4} = 7 \times 4 + 1 = 28 + 1 = 29
\]
So, \( 7 \frac{1}{4} \) becomes \( \frac{29}{4} \).

2. Now, we need to divide \( \frac{29}{4} \) by \( \frac{5}{6} \). To divide by a fraction, we multiply by its reciprocal:
\[
\frac{29}{4} \div \frac{5}{6} = \frac{29}{4} \times \frac{6}{5}
\]

3. Multiply the fractions:
\[
\frac{29 \times 6}{4 \times 5} = \frac{174}{20}
\]

4. Simplify \( \frac{174}{20} \):
- Find the greatest common divisor (GCD) of 174 and 20, which is 2.
- Divide both the numerator and denominator by 2:
\[
\frac{174 \div 2}{20 \div 2} = \frac{87}{10}
\]

5. Convert \( \frac{87}{10} \) back to a mixed number:
\[
87 \div 10 = 8 \text{ R } 7 \quad \text{(which gives us 8 with a remainder of 7)}
\]
So, \( \frac{87}{10} = 8 \frac{7}{10} \).

Thus, \( 7 \frac{1}{4} \div \frac{5}{6} = 8 \frac{7}{10} \).