`1 3/5-:2/3`

Options

A. `2 2/5`
B. `1 9/10`
C. `2 2/5`
D. `7/15`

Answer

To solve the problem \( 1 \frac{3}{5} \div \frac{2}{3} \), we will follow these steps:

### Step 1: Convert the mixed number to an improper fraction.
The mixed number \( 1 \frac{3}{5} \) can be converted to an improper fraction. To do this, multiply the whole number (1) by the denominator (5) and add the numerator (3).

\[ 1 \frac{3}{5} = \frac{(1 \times 5) + 3}{5} = \frac{5 + 3}{5} = \frac{8}{5} \]

### Step 2: Rewrite the division as multiplication.
Next, we need to rewrite the division of fractions as multiplication by the reciprocal. The reciprocal of \( \frac{2}{3} \) is \( \frac{3}{2} \).

\[ \frac{8}{5} \div \frac{2}{3} = \frac{8}{5} \times \frac{3}{2} \]

### Step 3: Multiply the fractions.
Now we will multiply the fractions together. To multiply fractions, multiply the numerators together and the denominators together.

\[ \frac{8 \times 3}{5 \times 2} = \frac{24}{10} \]

### Step 4: Simplify the fraction.
Now, we simplify \( \frac{24}{10} \). Both the numerator and denominator can be divided by 2.

\[ \frac{24 \div 2}{10 \div 2} = \frac{12}{5} \]

### Step 5: Convert back to a mixed number (if necessary).
Since \( \frac{12}{5} \) is an improper fraction, we can convert it back to a mixed number. Divide 12 by 5.

\[ 12 \div 5 = 2 \quad \text{(with a remainder of 2)} \]

So, \( \frac{12}{5} = 2 \frac{2}{5} \).

### Final Answer:
The final answer is \( 2 \frac{2}{5} \).

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