To divide \( 3 \frac{2}{5} \) by \( \frac{3}{10} \), we first need to convert the mixed number into an improper fraction. 1. Convert \( 3 \frac{2}{5} \) to an improper fraction: \[ 3 \frac{2}{5} = \frac{(3 \times 5) + 2}{5} = \frac{15 + 2}{5} = \frac{17}{5} \] 2. Now, divide \( \frac{17}{5} \) by \( \frac{3}{10} \): \[ \frac{17}{5} \div \frac{3}{10} = \frac{17}{5} \times \frac{10}{3} \] 3. Multiply the fractions: \[ = \frac{17 \times 10}{5 \times 3} = \frac{170}{15} \] 4. Simplify \( \frac{170}{15} \) by finding the greatest common divisor (GCD) of 170 and 15, which is 5: \[ \frac{170 \div 5}{15 \div 5} = \frac{34}{3} \] 5. Convert \( \frac{34}{3} \) back to a mixed number: \[ 34 \div 3 = 11 \quad \text{with a remainder of } 1 \] So, \( \frac{34}{3} = 11 \frac{1}{3} \). Thus, \( 3 \frac{2}{5} \div \frac{3}{10} = \frac{34}{3} \) or \( 11 \frac{1}{3} \).

3 2/5 divided 3/10

1 answer

To divide \( 3 \frac{2}{5} \) by \( \frac{3}{10} \), we first need to convert the mixed number into an improper fraction.

Convert \( 3 \frac{2}{5} \) to an improper fraction: \[ 3 \frac{2}{5} = \frac{(3 \times 5) + 2}{5} = \frac{15 + 2}{5} = \frac{17}{5} \]
Now, divide \( \frac{17}{5} \) by \( \frac{3}{10} \): \[ \frac{17}{5} \div \frac{3}{10} = \frac{17}{5} \times \frac{10}{3} \]
Multiply the fractions: \[ = \frac{17 \times 10}{5 \times 3} = \frac{170}{15} \]
Simplify \( \frac{170}{15} \) by finding the greatest common divisor (GCD) of 170 and 15, which is 5: \[ \frac{170 \div 5}{15 \div 5} = \frac{34}{3} \]
Convert \( \frac{34}{3} \) back to a mixed number: \[ 34 \div 3 = 11 \quad \text{with a remainder of } 1 \] So, \( \frac{34}{3} = 11 \frac{1}{3} \).

Thus, \( 3 \frac{2}{5} \div \frac{3}{10} = \frac{34}{3} \) or \( 11 \frac{1}{3} \).