Multiplication of Fractions: Reducing the fraction

To solve the problem, we will calculate the product of the fractions $\frac{1}{6}$ and $\frac{2}{3}$ using the standard method for multiplying fractions.

Step 1: Multiply the numerators.
The numerators are 1 and 2. Thus, the product of the numerators is $1 \times 2 = 2$.

Step 2: Multiply the denominators.
The denominators are 6 and 3. Thus, the product of the denominators is $6 \times 3 = 18$.

Step 3: Form the resulting fraction from the products obtained in the previous steps.
This gives us the fraction $\frac{2}{18}$.

Step 4: Simplify the fraction.
To simplify $\frac{2}{18}$, find the greatest common divisor (GCD) of 2 and 18, which is 2. Divide both the numerator and the denominator by their GCD:
$\frac{2 \div 2}{18 \div 2} = \frac{1}{9}$

Therefore, the simplified result of $\frac{1}{6} \times \frac{2}{3}$ is $\frac{1}{9}$.

We compare this result with the multiple-choice options and confirm that the correct answer is:

$\frac{1}{9}$

To solve this problem, let's multiply the fractions $\frac{2}{5}$ and $\frac{1}{2}$.

Step 1: Multiply the numerators:
$2 \times 1 = 2$

Step 2: Multiply the denominators:
$5 \times 2 = 10$

Step 3: Construct the fraction using the products from steps 1 and 2:
$\frac{2}{10}$

Step 4: Simplify the fraction. We can divide both the numerator and the denominator by their greatest common divisor, which is 2:
$\frac{2 \div 2}{10 \div 2} = \frac{1}{5}$

Thus, the product of $\frac{2}{5}$ and $\frac{1}{2}$ is $\frac{1}{5}$.

Therefore, the solution to the problem is $\frac{1}{5}$.

To solve the problem of multiplying the fractions $\frac{2}{4}$ and $\frac{4}{5}$, follow these steps:

• Step 1: Multiply the numerators. We have the numerators $2$ and $4$, so we calculate $2 \times 4 = 8$.
• Step 2: Multiply the denominators. We have the denominators $4$ and $5$, so we calculate $4 \times 5 = 20$.
• Step 3: Form the new fraction using the results from Steps 1 and 2. This gives us $\frac{8}{20}$.
• Step 4: Simplify the fraction $\frac{8}{20}$. The greatest common divisor (GCD) of $8$ and $20$ is $4$.
• Step 5: Divide both the numerator and the denominator by their GCD, $4$: $\frac{8 \div 4}{20 \div 4} = \frac{2}{5}$.

Therefore, the simplified product of $\frac{2}{4}$ and $\frac{4}{5}$ is $\frac{2}{5}$.

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

• Step 1: Multiply the numerators of the fractions.
• Step 2: Multiply the denominators of the fractions.
• Step 3: Simplify the resulting fraction if necessary.

Let's begin solving the problem:

Step 1: Multiply the numerators:
$2 \times 1 = 2$.

Step 2: Multiply the denominators:
$3 \times 4 = 12$.

Putting these together, the product of the fractions is:
$\frac{2}{12}$.

Step 3: Simplify the fraction $\frac{2}{12}$. Both the numerator and the denominator are divisible by 2:
Divide the numerator and denominator by 2:
$\frac{2 \div 2}{12 \div 2} = \frac{1}{6}$.

Therefore, the product of $\frac{2}{3}$ and $\frac{1}{4}$ simplifies to $\frac{1}{6}$.

From the given choices, the correct answer is choice 3: $\frac{1}{6}$.

To solve this multiplication of fractions problem, we will follow these steps:

• Step 1: Multiply the numerators of the fractions.
• Step 2: Multiply the denominators of the fractions.
• Step 3: Simplify the resulting fraction, if possible.

Now, let's carry out these steps:
Step 1: Multiply the numerators: $2 \times 1 = 2$.
Step 2: Multiply the denominators: $4 \times 2 = 8$.
Step 3: The resulting fraction is $\frac{2}{8}$. We simplify by dividing the numerator and the denominator by their greatest common divisor, which is 2. So, $\frac{2}{8} = \frac{2 \div 2}{8 \div 2} = \frac{1}{4}$.

Therefore, the solution to the problem is $\frac{1}{4}$.

To solve this problem, follow these steps:

• Step 1: Multiply the numerators of the fractions. The numerators are $2$ and $3$.
• Step 2: Multiply the denominators of the fractions. The denominators are $3$ and $4$.
• Step 3: Simplify the resulting fraction if necessary.

Now, let us perform the multiplication:

Step 1: Multiply the numerators:

$2 \times 3 = 6$

Step 2: Multiply the denominators:

$3 \times 4 = 12$

So, the product of the fractions is:

$\frac{6}{12}$

Step 3: Simplify the fraction. To simplify, find the greatest common divisor (GCD) of 6 and 12, which is 6. Divide both numerator and denominator by 6:

$\frac{6 \div 6}{12 \div 6} = \frac{1}{2}$

Therefore, the simplified product of the fractions $\frac{2}{3} \times \frac{3}{4}$ is $\frac{1}{2}$.

This matches choice 4, which is $\frac{1}{2}$.

To solve this problem, we'll multiply the fractions and simplify the result:

• Step 1: Multiply the numerators together: $6 \times 5 = 30$.
• Step 2: Multiply the denominators together: $8 \times 6 = 48$.
• Step 3: Write the result as a single fraction: $\frac{30}{48}$.
• Step 4: Simplify the fraction by finding the GCD of 30 and 48, which is 6.
• Step 5: Divide both the numerator and the denominator by their GCD:

$\frac{30 \div 6}{48 \div 6} = \frac{5}{8}$

Therefore, the solution to the problem is $\frac{5}{8}$.