Bot GPT 4-o mini 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.
-
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 \( \frac{29}{4} \).
-
Now, we need to divide \( \frac{29}{4} \) by \( \frac{5}{6} \). To divide by a fraction, we multiply by its reciprocal: \[ \frac{29}{4} \div \frac{5}{6} = \frac{29}{4} \times \frac{6}{5} \]
-
Multiply the fractions: \[ \frac{29 \times 6}{4 \times 5} = \frac{174}{20} \]
-
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: \[ \frac{174 \div 2}{20 \div 2} = \frac{87}{10} \]
-
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, \( 7 \frac{1}{4} \div \frac{5}{6} = 8 \frac{7}{10} \).
1 answer