Division of Fractions - Examples, Exercises and Solutions

To solve the division of fractions problem $\frac{1}{6} \div \frac{1}{3}$, we'll apply the concept of multiplying by the reciprocal.

• Step 1: Identify the reciprocal of the second fraction. The reciprocal of $\frac{1}{3}$ is $\frac{3}{1}$.
• Step 2: Multiply the first fraction by this reciprocal. Therefore, calculate $\frac{1}{6} \times \frac{3}{1}$.
• Step 3: Perform the multiplication. Multiply the numerators: $1 \times 3 = 3$. Multiply the denominators: $6 \times 1 = 6$.
• Step 4: Simplify the resulting fraction. The fraction $\frac{3}{6}$ simplifies to $\frac{1}{2}$ because both the numerator and denominator can be divided by 3.

Therefore, the solution to the problem is $\frac{1}{2}$.

To solve the division of fractions $\frac{2}{4} : \frac{2}{2}$, follow these steps:

• Step 1: Identify the fractions — the first fraction is $\frac{2}{4}$, and the second fraction is $\frac{2}{2}$.
• Step 2: Find the reciprocal of the second fraction. The reciprocal of $\frac{2}{2}$ is $\frac{2}{2}$, as it simplifies to 1.
• Step 3: Multiply the first fraction by the reciprocal of the second fraction:

$\frac{2}{4} \times \frac{2}{2} = \frac{2 \times 2}{4 \times 2} = \frac{4}{8}$

Step 4: Simplify the resulting fraction $\frac{4}{8}$. Since the greatest common divisor of 4 and 8 is 4, divide both numerator and denominator by 4:

$\frac{4}{8} = \frac{4 \div 4}{8 \div 4} = \frac{1}{2}$

Therefore, the solution to the problem is $\frac{1}{2}$.

To solve the division of the fractions $\frac{1}{9}$ and $\frac{1}{3}$, we'll employ the method of "invert and multiply":

• Step 1: Identify the reciprocal of the divisor. The divisor is $\frac{1}{3}$, and its reciprocal is $\frac{3}{1}$.
• Step 2: Convert the division into a multiplication. Therefore, $\frac{1}{9} \div \frac{1}{3}$ becomes $\frac{1}{9} \times \frac{3}{1}$.
• Step 3: Carry out the multiplication of the two fractions.
  $\frac{1}{9} \times \frac{3}{1} = \frac{1 \times 3}{9 \times 1} = \frac{3}{9}$.
• Step 4: Simplify the resulting fraction.
  $\frac{3}{9}$ simplifies to $\frac{1}{3}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 3.

Therefore, the solution to the problem $\frac{1}{9} \div \frac{1}{3}$ is $\frac{1}{3}$.

To solve the division of two fractions $\frac{1}{2} \div \frac{1}{2}$, we follow these steps:

• Step 1: Recognize that dividing by a fraction is equivalent to multiplying by its reciprocal. In this case, we replace division with multiplication by flipping the second fraction.
• Step 2: Thus, $\frac{1}{2} \div \frac{1}{2}$ becomes $\frac{1}{2} \times \frac{2}{1}$.
• Step 3: Perform the multiplication: Multiply the numerators and the denominators.
  Numerator: $1 \times 2 = 2$
  Denominator: $2 \times 1 = 2$
• Step 4: Simplify the result: The fraction $\frac{2}{2}$ simplifies to 1.

Thus, the result of the division $\frac{1}{2} \div \frac{1}{2}$ is $1$.

To solve the division problem $\frac{4}{12}:\frac{2}{4}$, we will follow these steps:

• Step 1: Identify the fractions involved: $\frac{4}{12}$ and $\frac{2}{4}$.
• Step 2: Convert the division into multiplication by the reciprocal of the divisor. The reciprocal of $\frac{2}{4}$ is $\frac{4}{2}$.
• Step 3: Multiply the first fraction by this reciprocal:

$\frac{4}{12} \times \frac{4}{2} = \frac{4 \times 4}{12 \times 2}$

$= \frac{16}{24}$

• Step 4: Simplify the resulting fraction. The greatest common divisor of 16 and 24 is 8.

$\frac{16 \div 8}{24 \div 8} = \frac{2}{3}$

Thus, the solution to the problem is $\frac{2}{3}$.