Simplify `4 (4)/(5) div 6 (2)/(5) = ?`

Options

A. `3//4`
B. `5//7`
C. `7//11`
D. `5//8`

Answer

To simplify the expression \( 4 \frac{4}{5} \div 6 \frac{2}{5} \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers into improper fractions.

For \( 4 \frac{4}{5} \):
- Multiply the whole number (4) by the denominator (5): \( 4 \times 5 = 20 \)
- Add the numerator (4): \( 20 + 4 = 24 \)
- So, \( 4 \frac{4}{5} = \frac{24}{5} \)

For \( 6 \frac{2}{5} \):
- Multiply the whole number (6) by the denominator (5): \( 6 \times 5 = 30 \)
- Add the numerator (2): \( 30 + 2 = 32 \)
- So, \( 6 \frac{2}{5} = \frac{32}{5} \)

Now we can rewrite the expression:
\[ 4 \frac{4}{5} \div 6 \frac{2}{5} = \frac{24}{5} \div \frac{32}{5} \]

### Step 2: Change Division to Multiplication
To divide by a fraction, we multiply by its reciprocal. Thus, we change the division to multiplication:
\[ \frac{24}{5} \div \frac{32}{5} = \frac{24}{5} \times \frac{5}{32} \]

### Step 3: Simplify the Expression
Now we can simplify the expression:
- The \( 5 \) in the numerator and denominator cancels out:
\[ \frac{24}{5} \times \frac{5}{32} = \frac{24}{32} \]

### Step 4: Reduce the Fraction
Now, we simplify \( \frac{24}{32} \):
- Both 24 and 32 can be divided by 8:
\[ \frac{24 \div 8}{32 \div 8} = \frac{3}{4} \]

### Final Answer
Thus, the simplified form of \( 4 \frac{4}{5} \div 6 \frac{2}{5} \) is:
\[ \frac{3}{4} \]

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