Dividing Mixed Numbers and Fractions Practice Problems

We need to evaluate the expression $1 \div \frac{2}{3}$.

To do this, we use the principle that dividing by a fraction is equivalent to multiplying by its reciprocal. Therefore, the expression becomes:

$1 \times \frac{3}{2}$.

Next, we multiply the whole number by the reciprocal:

$1 \times \frac{3}{2} = \frac{3}{2}$.

To express $\frac{3}{2}$ as a mixed number, we write it as:

$1\frac{1}{2}$.

Thus, the solution to the problem is $1\frac{1}{2}$, which matches choice 3 from the options provided.

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 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 $6$.

To solve this problem of dividing a fraction by a whole number, we'll follow these steps:

• Step 1: Change the whole number to a reciprocal fraction.
• Step 2: Multiply the original fraction by the reciprocal.
• Step 3: Simplify the resulting fraction, if necessary.

Now, let's apply these steps:
Step 1: The whole number $3$ is converted to the reciprocal fraction $\frac{1}{3}$.
Step 2: Multiply the fraction $\frac{1}{2}$ by $\frac{1}{3}$:

$\frac{1}{2} \times \frac{1}{3} = \frac{1 \times 1}{2 \times 3} = \frac{1}{6}$

Step 3: The resulting fraction $\frac{1}{6}$ is already in its simplest form.

Therefore, when $\frac{1}{2}$ is divided by $3$, the resulting answer is $\frac{1}{6}$.

To solve this problem, we need to compute $\frac{1}{2} \div 4$. Here are the steps:

• Step 1: Recognize that dividing by 4 is equivalent to multiplying by its reciprocal, $\frac{1}{4}$.
• Step 2: Rewrite the division as a multiplication: $\frac{1}{2} \times \frac{1}{4}$.
• Step 3: Perform the multiplication of fractions by multiplying their numerators and denominators. Thus, $\frac{1 \cdot 1}{2 \cdot 4} = \frac{1}{8}$.

Therefore, the solution to the problem is $\frac{1}{8}$.