All Operations in Fractions: Solving the problem

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 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

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: $\frac{3}{8}$.

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 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 this problem, we'll 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 needed.

Now, let's work through each step:

Step 1: The fractions are given as $\frac{3}{4}$ and $\frac{1}{2}$. Multiplying the numerators, we get:

Step 2: Next, multiply the denominators:

Step 3: Combine these results to write the product of the fractions:

The resulting fraction $\frac{3}{8}$ is already in its simplest form, so no further simplification is necessary.

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

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 $\frac{3}{10}$.

The multiplication of fractions $\frac{7}{8}$ and $\frac{4}{6}$ requires the direct operation of multiplying numerators with numerators and denominators with denominators.

• Multiply the numerators: $7 \times 4 = 28$
• Multiply the denominators: $8 \times 6 = 48$
• Form the resulting fraction: $\frac{28}{48}$

Now, we need to simplify $\frac{28}{48}$. Find the greatest common divisor (GCD) of 28 and 48, which is 4.

• Divide both numerator and denominator by their GCD: $\frac{28 \div 4}{48 \div 4} = \frac{7}{12}$

Therefore, the solution to the problem is $\frac{7}{12}$.

Thus, the correct answer is $\frac{7}{12}$, which corresponds to choice 3.

To solve this problem, we'll follow these steps:

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

Now, let's work through each step:
Step 1: Multiply the numerators: $2 \times 3 = 6$.
Step 2: Multiply the denominators: $7 \times 5 = 35$.
Thus, the product of the fractions is $\frac{6}{35}$.

Therefore, the solution to the problem is $\frac{6}{35}$.

To solve this problem, we need to multiply two fractions, $\frac{1}{3}$ and $\frac{4}{7}$, by following these steps:

• Step 1: Multiply the numerators:
  $1 \times 4 = 4$.
• Step 2: Multiply the denominators:
  $3 \times 7 = 21$.
• Step 3: Combine the results to form a new fraction:
  Thus, $\frac{1}{3} \times \frac{4}{7} = \frac{4}{21}$.

This fraction, $\frac{4}{21}$, is in its simplest form since there are no common factors between 4 and 21 other than 1.

Therefore, the solution to the problem is $\frac{4}{21}$.