Multiplication of Fractions: Using the commutative law

To solve the problem $\frac{1}{2} \times \frac{2}{3} \times \frac{1}{2}$, follow these steps:

• Step 1: Multiply the numerators

We multiply the numerators of the fractions together: $1 \times 2 \times 1 = 2$.

• Step 2: Multiply the denominators

Similarly, multiply the denominators of the fractions: $2 \times 3 \times 2 = 12$.

• Step 3: Form the resulting fraction

After multiplying the numerators and denominators, we form the fraction: $\frac{2}{12}$.

• Step 4: Simplify the fraction

We simplify $\frac{2}{12}$ by finding the greatest common divisor (GCD) of 2 and 12, which is 2. Dividing both the numerator and denominator by 2, we get:

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

Thus, the correct solution is $\frac{1}{6}$.

To solve the exercise $\frac{3}{5} \times \frac{2}{3} \times \frac{2}{5}$, we will follow a step-by-step approach:

Step 1: Multiply the numerators:
$3 \times 2 \times 2 = 12$

Step 2: Multiply the denominators:
$5 \times 3 \times 5 = 75$

Step 3: Form the fraction by placing the product of numerators over the product of denominators:
$\frac{12}{75}$

Step 4: Simplify the fraction. We find the greatest common divisor of 12 and 75, which is 3:
Divide the numerator and the denominator by 3:
$\frac{12 \div 3}{75 \div 3} = \frac{4}{25}$

Therefore, the simplified product of the given fractions is $\frac{4}{25}$.

Let's solve this problem step-by-step:

• Step 1: Multiply the numerators of the fractions. We have $1 \times 1 \times 1 = 1$.
• Step 2: Multiply the denominators of the fractions. We have $2 \times 3 \times 2 = 12$.
• Step 3: Combine the results to form a fraction: $\frac{1}{12}$.
• Step 4: Simplify the fraction if possible. Since the fraction $\frac{1}{12}$ is already in its simplest form, no further simplification is needed.

Thus, the product of $\frac{1}{2} \times \frac{1}{3} \times \frac{1}{2}$ is $\frac{1}{12}$.

The correct answer choice is $\frac{1}{12}$, matching choice 4.

Therefore, the solution to the problem is $\frac{1}{12}$.

To solve this problem, we need to multiply the three given fractions:
$\frac{2}{4} \times \frac{2}{3} \times \frac{2}{4}$

The steps involved in multiplying these fractions are as follows:

• Step 1: Multiply the numerators. The numerators are 2, 2, and 2. Multiplying these together gives:
  $2 \times 2 \times 2 = 8$.
• Step 2: Multiply the denominators. The denominators are 4, 3, and 4. Multiplying these together gives:
  $4 \times 3 \times 4 = 48$.
• Step 3: Combine the results to form a new fraction:
  $\frac{8}{48}$.
• Step 4: Simplify the fraction. To simplify $\frac{8}{48}$, we find the greatest common divisor (GCD) of 8 and 48, which is 8. Divide both the numerator and denominator by 8:
  $\frac{8 \div 8}{48 \div 8} = \frac{1}{6}$.

Therefore, the solution to the given exercise is $\frac{1}{6}$.

To solve this problem, follow these steps:

• Step 1: Identify the fractions to be multiplied: $\frac{1}{3}$, $\frac{3}{4}$, $\frac{1}{3}$.
• Step 2: Multiply the numerators: $1 \times 3 \times 1 = 3$.
• Step 3: Multiply the denominators: $3 \times 4 \times 3 = 36$.
• Step 4: Write the resulting fraction: $\frac{3}{36}$.
• Step 5: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3: $\frac{3 \div 3}{36 \div 3} = \frac{1}{12}$.

The solution to the problem is therefore $\frac{1}{12}$.