Find the value of x :- 4 4/5 ÷ 6 2/5 =x.

Options

A. a. 3/4
B. b. 5/7
C. c. 7/11
D. d. 5/8

Answer

To find the value of \( x \) in the equation \( 4 \frac{4}{5} \div 6 \frac{2}{5} = x \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers \( 4 \frac{4}{5} \) and \( 6 \frac{2}{5} \) into improper fractions.

- For \( 4 \frac{4}{5} \):
\[ 4 \frac{4}{5} = 4 \times 5 + 4 = 20 + 4 = 24 \quad \text{(numerator)} \]
So, \( 4 \frac{4}{5} = \frac{24}{5} \).

- For \( 6 \frac{2}{5} \):
\[ 6 \frac{2}{5} = 6 \times 5 + 2 = 30 + 2 = 32 \quad \text{(numerator)} \]
So, \( 6 \frac{2}{5} = \frac{32}{5} \).

### Step 2: Set Up the Division of Fractions
Now we can rewrite the division of the two improper fractions:
\[ x = \frac{24}{5} \div \frac{32}{5} \]

### Step 3: Change Division to Multiplication
To divide by a fraction, we multiply by its reciprocal:
\[ x = \frac{24}{5} \times \frac{5}{32} \]

### Step 4: Simplify the Expression
Now we can simplify:
\[ x = \frac{24 \times 5}{5 \times 32} \]
The \( 5 \) in the numerator and denominator cancels out:
\[ x = \frac{24}{32} \]

### Step 5: Simplify the Fraction
Now we simplify \( \frac{24}{32} \):
\[ x = \frac{24 \div 8}{32 \div 8} = \frac{3}{4} \]

### Final Answer
Thus, the value of \( x \) is:
\[ x = \frac{3}{4} \]

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