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

Answer

To solve the question "By what number should `6 2/9` be divided to obtain `4 2/3`?", we will follow these steps:

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

1. **Convert `6 2/9` to an improper fraction**:
- Multiply the whole number (6) by the denominator (9):
\( 6 \times 9 = 54 \)
- Add the numerator (2):
\( 54 + 2 = 56 \)
- So, \( 6 2/9 = \frac{56}{9} \).

2. **Convert `4 2/3` to an improper fraction**:
- Multiply the whole number (4) by the denominator (3):
\( 4 \times 3 = 12 \)
- Add the numerator (2):
\( 12 + 2 = 14 \)
- So, \( 4 2/3 = \frac{14}{3} \).

### Step 2: Set up the equation.

We need to find the number \( x \) such that:
\[ \frac{56}{9} \div x = \frac{14}{3} \]

### Step 3: Rewrite the division as multiplication.

Dividing by \( x \) is the same as multiplying by its reciprocal:
\[ \frac{56}{9} \times \frac{1}{x} = \frac{14}{3} \]

### Step 4: Cross-multiply to solve for \( x \).

Cross-multiplying gives us:
\[ 56 \times 3 = 14 \times 9x \]
This simplifies to:
\[ 168 = 126x \]

### Step 5: Solve for \( x \).

To find \( x \), divide both sides by 126:
\[ x = \frac{168}{126} \]

### Step 6: Simplify the fraction.

To simplify \( \frac{168}{126} \):
- Both 168 and 126 can be divided by 42:
\[ x = \frac{168 \div 42}{126 \div 42} = \frac{4}{3} \]

### Final Answer:

Thus, the number by which `6 2/9` should be divided to obtain `4 2/3` is \( \frac{4}{3} \).

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