Division of Fractions

When we approach solving such questions, we need to know the rule of dividing fractions,

When we need to divide a fraction by a fraction, we use the method of multiplying by the reciprocal.

This means we flip the numerator and denominator of the second fraction, and then perform fraction multiplication.

Instead of:

1/4 : 1/2 =

We get:

1/4 * 2/1 =

We'll remember that in fraction multiplication we multiply numerator by numerator and denominator by denominator

1*2 / 4*1 =
2/4 =

We'll reduce the fraction and get:

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 fraction division $\frac{8}{9} \div \frac{2}{3}$, follow these steps:

• Step 1: Identify the given fractions $\frac{8}{9}$ and $\frac{2}{3}$.
• Step 2: Find the reciprocal of the second fraction. The reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$.
• Step 3: Multiply the first fraction by the reciprocal of the second fraction: $\frac{8}{9} \times \frac{3}{2}$.
• Step 4: Perform the multiplication: multiply the numerators together and the denominators together.

Let's compute the multiplication:

$\frac{8}{9} \times \frac{3}{2} = \frac{8 \times 3}{9 \times 2} = \frac{24}{18}$

Step 5: Simplify the resulting fraction $\frac{24}{18}$.

To simplify, find the greatest common divisor (GCD) of 24 and 18, which is 6. Divide both the numerator and the denominator by 6:

$\frac{24}{18} = \frac{24 \div 6}{18 \div 6} = \frac{4}{3}$

Step 6: If necessary, convert the improper fraction to a mixed number.

Since $\frac{4}{3}$ is an improper fraction, it can be converted to a mixed number:

$\frac{4}{3} = 1 \frac{1}{3}$

Therefore, the solution to the problem $\frac{8}{9} : \frac{2}{3}$ is $1 \frac{1}{3}$.

To solve this problem, we'll break it into these manageable steps:

• Step 1: Identify the fractions:
  $\frac{3}{4}$ and $\frac{1}{2}$.
• Step 2: Find the reciprocal of the second fraction:
• The reciprocal of $\frac{1}{2}$ is $\frac{2}{1}$.
• Step 3: Change the division into multiplication:
• $\frac{3}{4} \div \frac{1}{2}$ becomes $\frac{3}{4} \times \frac{2}{1}$.
• Step 4: Multiply the numerators and the denominators:
• Numerator: $3 \times 2 = 6$
• Denominator: $4 \times 1 = 4$
• So, $\frac{3}{4} \times \frac{2}{1} = \frac{6}{4}$.
• Step 5: Simplify the fraction:
• $\frac{6}{4} = \frac{3}{2}$, since dividing numerator and denominator by 2 gives $\frac{3}{2}$.
• Step 6: Convert the fraction to a mixed number:
• $\frac{3}{2}$ can be written as the mixed number $1\frac{1}{2}$.

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

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 $\frac{1}{2}$.