Operations with Fractions Practice Problems & Solutions

To solve $\frac{5}{9} \div \frac{7}{18}$, we will proceed with the following steps:

• Step 1: Identify the dividend and divisor: $\frac{5}{9}$ and $\frac{7}{18}$.
• Step 2: Find the reciprocal of the divisor. The reciprocal of $\frac{7}{18}$ is $\frac{18}{7}$.
• Step 3: Multiply the dividend by the reciprocal of the divisor: $\frac{5}{9} \times \frac{18}{7}.$
• Step 4: Multiply the numerators: $5 \times 18 = 90$.
• Step 5: Multiply the denominators: $9 \times 7 = 63$.
• Step 6: The resulting fraction from the multiplication is $\frac{90}{63}.$
• Step 7: Simplify $\frac{90}{63}$. The greatest common divisor (GCD) of 90 and 63 is 9. Divide both the numerator and the denominator by 9: $\frac{90 \div 9}{63 \div 9} = \frac{10}{7}.$
• Step 8: Convert $\frac{10}{7}$ into a mixed number. Since $10$ divided by $7$ is $1$ with a remainder of $3$, this is $1\frac{3}{7}.$

So, the solution to the problem is $1\frac{3}{7}$.

To solve the problem of multiplying the fractions $\frac{1}{4}$ and $\frac{3}{2}$, we will follow these steps:

• Step 1: Multiply the numerators of the fractions.
• Step 2: Multiply the denominators of the fractions.
• Step 3: Write the result as a fraction and simplify if needed.

Now, let's work through each step:

Step 1: Multiply the numerators:
The numerators are $1$ and $3$. Thus, $1 \times 3 = 3$.

Step 2: Multiply the denominators:
The denominators are $4$ and $2$. Thus, $4 \times 2 = 8$.

Step 3: Write the result as a fraction and simplify:
The resulting fraction is $\frac{3}{8}$. This fraction is already in simplest form.

Therefore, the solution to the problem is $\frac{3}{8}$.

Among the choices provided, the correct answer is choice 3: $\frac{3}{8}$.

Let us solve the problem of multiplying the two fractions $\frac{2}{3}$ and $\frac{5}{7}$.

• Step 1: Identify the numerators and denominators. Here, the numerators are $2$ and $5$, and the denominators are $3$ and $7$.
• Step 2: Multiply the numerators: $2 \times 5 = 10$.
• Step 3: Multiply the denominators: $3 \times 7 = 21$.
• Step 4: Put the results together in a new fraction: $\frac{10}{21}$.
• Step 5: Simplify the fraction if needed. In this case, $\frac{10}{21}$ is already in its simplest form as $10$ and $21$ have no common factors besides $1$.

Therefore, the solution to the problem $\frac{2}{3} \times \frac{5}{7}$ is $\frac{10}{21}$.

To solve this problem, we need to multiply the fractions $\frac{3}{5}$ and $\frac{1}{2}$.

• Step 1: Multiply the numerators of the fractions. The numerators are $3$ and $1$, so $3 \times 1 = 3$.
• Step 2: Multiply the denominators of the fractions. The denominators are $5$ and $2$, so $5 \times 2 = 10$.
• Step 3: Combine the results from steps 1 and 2 to form the new fraction. The fraction becomes $\frac{3}{10}$.
• Step 4: Simplify the fraction, if possible. In this case, $\frac{3}{10}$ is already in its simplest form.

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

To multiply fractions, we multiply numerator by numerator and denominator by denominator

1*4 = 4

4*5 = 20

4/20

Note that we can simplify this fraction by 4

4/20 = 1/5