Question

x 2 1/3 = 5 2/3 using inverse operations

Answer 1

To solve the equation \( x \cdot 2 \frac{1}{3} = 5 \frac{2}{3} \) using inverse operations, follow these steps:

1. **Convert the mixed numbers into improper fractions**:
- \( 2 \frac{1}{3} = \frac{7}{3} \) (since \( 2 \times 3 + 1 = 7 \))
- \( 5 \frac{2}{3} = \frac{17}{3} \) (since \( 5 \times 3 + 2 = 17 \))

Now, the equation is:
\[
x \cdot \frac{7}{3} = \frac{17}{3}
\]

2. **Use the inverse operation to isolate \( x \)**:
To isolate \( x \), you can multiply both sides of the equation by the reciprocal of \( \frac{7}{3} \), which is \( \frac{3}{7} \):
\[
x = \frac{17}{3} \cdot \frac{3}{7}
\]

3. **Perform the multiplication**:
\[
x = \frac{17 \cdot 3}{3 \cdot 7}
\]
The \( 3 \) in the numerator and the denominator cancels out:
\[
x = \frac{17}{7}
\]

4. **Convert the improper fraction back to a mixed number (optional)**:
The improper fraction \( \frac{17}{7} \) can be expressed as:
\[
17 \div 7 = 2 \quad \text{(with a remainder of 3)}
\]
So, \( \frac{17}{7} = 2 \frac{3}{7} \).

Thus, the solution to the equation \( x \cdot 2 \frac{1}{3} = 5 \frac{2}{3} \) is:
\[
x = \frac{17}{7} \quad \text{or} \quad x = 2 \frac{3}{7}
\]