3 3/4 divided by 1 1/8

To divide \(3 \frac{3}{4}\) by \(1 \frac{1}{8}\), we first convert the mixed numbers into improper fractions.

1. Convert \(3 \frac{3}{4}\): \[ 3 \frac{3}{4} = 3 \times 4 + 3 = 12 + 3 = 15, \quad \text{so } 3 \frac{3}{4} = \frac{15}{4} \]

2. Convert \(1 \frac{1}{8}\): \[ 1 \frac{1}{8} = 1 \times 8 + 1 = 8 + 1 = 9, \quad \text{so } 1 \frac{1}{8} = \frac{9}{8} \]

Now we have the division: \[ \frac{15}{4} \div \frac{9}{8} \]

To divide by a fraction, we multiply by its reciprocal: \[ \frac{15}{4} \times \frac{8}{9} \]

Now we can multiply the numerators and the denominators: \[ \frac{15 \times 8}{4 \times 9} = \frac{120}{36} \]

Next, we simplify \(\frac{120}{36}\):

1. Find the greatest common divisor (GCD) of 120 and 36, which is 12.
2. Divide both the numerator and the denominator by their GCD: \[ \frac{120 \div 12}{36 \div 12} = \frac{10}{3} \]

The result \(\frac{10}{3}\) can also be converted back into a mixed number: \[ 10 \div 3 = 3 \quad \text{remainder } 1, \quad \text{so } \frac{10}{3} = 3 \frac{1}{3} \]

Thus, \(3 \frac{3}{4} \div 1 \frac{1}{8} = \frac{10}{3}\) or \(3 \frac{1}{3}\).