Dividing Mixed Numbers and Fractions - Examples, Exercises and Solutions

To solve $\frac{1}{2} : 2$, we need to rewrite the division as multiplication by the reciprocal of 2. The reciprocal of 2 is $\frac{1}{2}$.

Thus, the expression becomes:

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

Calculating the multiplication, we have:

$\frac{1}{4}$

Therefore, the solution to the problem is $\frac{1}{4}$, which corresponds to choice 3.

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 the problem $\frac{1}{3} : 3$, we will follow these clear steps:

• Step 1: Understand that dividing by 3 is equivalent to multiplying by the reciprocal of 3, which is $\frac{1}{3}$.
• Step 2: Convert the division problem $\frac{1}{3} : 3$ into a multiplication problem $\frac{1}{3} \times \frac{1}{3}$.
• Step 3: Perform the multiplication of fractions:

Using the formula $\frac{a}{b} \times \frac{c}{d} = \frac{a \cdot c}{b \cdot d}$, we have:

$\frac{1}{3} \times \frac{1}{3} = \frac{1 \cdot 1}{3 \cdot 3} = \frac{1}{9}$.

Therefore, the solution to the problem is $\frac{1}{9}$.

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'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 $6$.