By what number should `6 2/9` be divided to obtain `4 2/3`?

Answer

To solve the problem of finding the number by which `6 2/9` should be divided to obtain `4 2/3`, we can follow these steps:

### Step 1: Convert the mixed numbers to improper fractions.

1. **Convert `6 2/9`**:
- Multiply the whole number (6) by the denominator (9):
\( 6 \times 9 = 54 \)
- Add the numerator (2) to this result:
\( 54 + 2 = 56 \)
- Therefore,
\[ 6 \frac{2}{9} = \frac{56}{9} \]

2. **Convert `4 2/3`**:
- Multiply the whole number (4) by the denominator (3):
\( 4 \times 3 = 12 \)
- Add the numerator (2) to this result:
\( 12 + 2 = 14 \)
- Therefore,
\[ 4 \frac{2}{3} = \frac{14}{3} \]

### Step 2: Set up the equation.

We want to find the number \( x \) such that:
\[ \frac{56}{9} \div x = \frac{14}{3} \]
This can be rewritten as:
\[ \frac{56}{9} = x \times \frac{14}{3} \]

### Step 3: Solve for \( x \).

To isolate \( x \), we can rearrange the equation:
\[ x = \frac{56}{9} \div \frac{14}{3} \]
Dividing by a fraction is the same as multiplying by its reciprocal:
\[ x = \frac{56}{9} \times \frac{3}{14} \]

### Step 4: Simplify the expression.

1. Multiply the numerators:
\[ 56 \times 3 = 168 \]
2. Multiply the denominators:
\[ 9 \times 14 = 126 \]
3. Therefore, we have:
\[ x = \frac{168}{126} \]

### Step 5: Simplify the fraction.

To simplify \( \frac{168}{126} \):
- Find the greatest common divisor (GCD) of 168 and 126, which is 42.
- Divide both the numerator and the denominator by 42:
\[ \frac{168 \div 42}{126 \div 42} = \frac{4}{3} \]

### Final Answer:
Thus, the number by which `6 2/9` should be divided to obtain `4 2/3` is:
\[ \frac{4}{3} \text{ or } 1 \frac{1}{3} \]