Solve the Fraction Division: 6/10 ÷ 2/5 Step-by-Step

To solve the division $\frac{6}{10} \div \frac{2}{5}$, we use the method of multiplying by the reciprocal of the divisor.

First, identify the reciprocal of the divisor $\frac{2}{5}$. The reciprocal is obtained by swapping the numerator and denominator, resulting in $\frac{5}{2}$.

Next, replace the division operation with multiplication by the reciprocal:

$\frac{6}{10} \times \frac{5}{2}$.

Now, perform the multiplication of the fractions by multiplying numerator by numerator and denominator by denominator:

$\frac{6 \times 5}{10 \times 2} = \frac{30}{20}$.

Simplify the fraction $\frac{30}{20}$ by finding the greatest common divisor. Both 30 and 20 can be divided by 10:

$\frac{30 \div 10}{20 \div 10} = \frac{3}{2}$.

The simplified fraction $\frac{3}{2}$ can also be expressed as a mixed number:

$1\frac{1}{2}$.

Therefore, the solution to the problem $\frac{6}{10} \div \frac{2}{5}$ is $1\frac{1}{2}$, aligning with choice 1.