Operations with Fractions Practice Problems & Solutions

To solve the division $\frac{1}{2} \div \frac{3}{5}$, we will follow the multiplication by the reciprocal method. Here are the steps:

• Step 1: Find the reciprocal of the divisor $\frac{3}{5}$, which is $\frac{5}{3}$.
• Step 2: Multiply the dividend $\frac{1}{2}$ by the reciprocal found in Step 1: $\frac{1}{2} \times \frac{5}{3}$.
• Step 3: Multiply the numerators: $1 \times 5 = 5$.
• Step 4: Multiply the denominators: $2 \times 3 = 6$.
• Step 5: Combine the results to form the fraction $\frac{5}{6}$.

The simplified result of $\frac{1}{2} \div \frac{3}{5}$ is $\frac{5}{6}$.

To solve this problem, we need to divide the fraction $\frac{1}{5}$ by the fraction $\frac{1}{10}$. When dividing fractions, the procedure involves multiplying by the reciprocal of the divisor (the second fraction).

Let's start with the solution:

• First, determine the reciprocal of $\frac{1}{10}$. The reciprocal of a fraction is obtained by swapping its numerator and denominator. Thus, the reciprocal of $\frac{1}{10}$ is $\frac{10}{1}$.
• Now multiply $\frac{1}{5}$ by the reciprocal of $\frac{1}{10}$, which is $\frac{10}{1}$:

$\frac{1}{5} \times \frac{10}{1} = \frac{1 \times 10}{5 \times 1} = \frac{10}{5}$

Simplify the fraction $\frac{10}{5}$:

$\frac{10}{5} = 2$

Therefore, the result of $\frac{1}{5} : \frac{1}{10}$ is $2$.

To solve the division of two fractions $\frac{1}{2} : \frac{1}{4}$, follow these steps:

• Step 1: Identify the operation: The problem involves dividing $\frac{1}{2}$ by $\frac{1}{4}$.
• Step 2: Use the reciprocal: In fraction division, multiply by the reciprocal of the second fraction. Thus, $\frac{1}{2} : \frac{1}{4} = \frac{1}{2} \times \frac{4}{1}$.
• Step 3: Perform the multiplication: Now compute the multiplication by multiplying the numerators and the denominators: $\frac{1 \times 4}{2 \times 1} = \frac{4}{2}$.
• Step 4: Simplify the fraction: The fraction $\frac{4}{2}$ simplifies to $2$.

Thus, the solution to the division $\frac{1}{2} : \frac{1}{4}$ is $2$. Therefore, the correct answer choice is $2$ (Choice 1).

To solve the division of fractions problem $\frac{1}{2} \div \frac{2}{3}$, we follow these steps:

• Step 1: Rewrite the division problem as multiplication by the reciprocal: $\frac{1}{2} \div \frac{2}{3}$ becomes $\frac{1}{2} \times \frac{3}{2}$.
• Step 2: Multiply the numerators together: $1 \times 3 = 3$.
• Step 3: Multiply the denominators together: $2 \times 2 = 4$.
• Step 4: Form the new fraction from the resulting numerator and denominator: $\frac{3}{4}$.

Thus, the result of dividing $\frac{1}{2}$ by $\frac{2}{3}$ is $\frac{3}{4}$.

The correct answer is $\frac{3}{4}$.

To solve the problem of dividing the fractions $\frac{1}{2}$ by $\frac{5}{3}$, we proceed as follows:

We can simplify a division of fractions by multiplying the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by swapping its numerator and denominator.

First, we find the reciprocal of $\frac{5}{3}$, which is $\frac{3}{5}$.

Next, we multiply the fractions $\frac{1}{2}$ and $\frac{3}{5}$:

$\frac{1}{2} \times \frac{3}{5} = \frac{1 \times 3}{2 \times 5}.$

This results in

$\frac{3}{10}.$

Thus, the solution to $\frac{1}{2}:\frac{5}{3}$ is $\frac{3}{10}$.