Mixed Numbers

To solve this problem, let's divide $1$ by $\frac{3}{4}$. The solution involves converting the division into a multiplication:

• Step 1: Recognize $\,1:\frac{3}{4}\,$ as the division $\frac{1}{\frac{3}{4}}$.

• Step 2: Convert division into multiplication: $\frac{1}{\frac{3}{4}} = 1 \times \frac{4}{3}$.

• Step 3: Compute the multiplication: $1 \times \frac{4}{3} = \frac{4}{3}$.

• Step 4: Convert $\frac{4}{3}$ into a mixed number: $1\frac{1}{3}$.

Therefore, the solution to the division $1 : \frac{3}{4}$ is $1\frac{1}{3}$

The correct answer is $(1 \frac{1}{3})$.

To solve this problem, we'll pursue a step-by-step method:

• Step 1: Simplify the fraction $\frac{8}{12}$. The greatest common divisor of 8 and 12 is 4, so dividing both the numerator and denominator by 4 gives $\frac{2}{3}$.
• Step 2: Multiply the integer 3 by the simplified fraction $\frac{2}{3}$.

Let's proceed with these steps:
Step 1: Simplify $\frac{8}{12}$:
$\frac{8}{12} = \frac{8 \div 4}{12 \div 4} = \frac{2}{3}$.

Step 2: Multiply the integer by the fraction:
$3 \times \frac{2}{3} = \frac{3 \times 2}{3} = \frac{6}{3} = 2$.

Thus, the result of the multiplication is $\boxed{2}$.

To solve the division problem $1 : \frac{1}{4}$, we will follow these steps:

• Step 1: Express the division as a fraction operation: $1 \div \frac{1}{4}$.
• Step 2: Use the invert-and-multiply rule. Find the reciprocal of $\frac{1}{4}$, which is $4$.
• Step 3: Multiply the whole number by the reciprocal: $1 \times 4 = 4$.

Thus, after performing these operations, we find that the result of the division $1 : \frac{1}{4}$ is $4$.

To solve this mathematical problem, we need to multiply a whole number, 8, with the fraction, $\frac{1}{2}$.

Here are the steps:

• Step 1: Identify the given values. The integer is 8 and the fraction is $\frac{1}{2}$.
• Step 2: Apply the multiplication formula for an integer and a fraction: $a \times \frac{b}{c} = \frac{a \times b}{c}$.
• Step 3: Multiply the integer by the numerator of the fraction: $8 \times 1 = 8$.
• Step 4: Divide the result by the denominator of the fraction: $\frac{8}{2} = 4$.
• Step 5: Simplify the fraction if necessary. In this case, $\frac{8}{2}$ simplifies directly to 4.

Therefore, the multiplication of 8 by $\frac{1}{2}$ is $4$.

In the context of the multiple-choice options provided, the correct answer is choice (4): $4$.

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

• Step 1: Identify the reciprocal of the divisor.
• Step 2: Multiply the dividend by the reciprocal.

Now, let's work through each step:
Step 1: The divisor is $\frac{1}{2}$. The reciprocal of $\frac{1}{2}$ is 2.

Step 2: Multiply the dividend, which is 3, by the reciprocal of the divisor:
$3 \times 2 = 6$

Therefore, the solution to the problem is $6$.