If the product of two fractions is 16 `1/9` and one of the fractions is 4 `2/7` , then find the other fraction

Answer

To find the other fraction when the product of two fractions is \(16 \frac{1}{9}\) and one of the fractions is \(4 \frac{2}{7}\), we can follow these steps:

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

- For \(16 \frac{1}{9}\):
\[ 16 \frac{1}{9} = \frac{16 \times 9 + 1}{9} = \frac{144 + 1}{9} = \frac{145}{9} \]

- For \(4 \frac{2}{7}\):
\[ 4 \frac{2}{7} = \frac{4 \times 7 + 2}{7} = \frac{28 + 2}{7} = \frac{30}{7} \]

### Step 2: Set Up the Equation
Let the other fraction be \(x\). According to the problem:
\[ \frac{30}{7} \times x = \frac{145}{9} \]

### Step 3: Solve for \(x\)
To find \(x\), we can rearrange the equation:
\[ x = \frac{145}{9} \div \frac{30}{7} \]

### Step 4: Division of Fractions
Dividing by a fraction is the same as multiplying by its reciprocal:
\[ x = \frac{145}{9} \times \frac{7}{30} \]

### Step 5: Simplify the Expression
Now, we can multiply the fractions:
\[ x = \frac{145 \times 7}{9 \times 30} \]

Calculating the numerator and denominator:
- Numerator: \(145 \times 7 = 1015\)
- Denominator: \(9 \times 30 = 270\)

So,
\[ x = \frac{1015}{270} \]

### Step 6: Simplify the Fraction
To simplify \(\frac{1015}{270}\), we can find the greatest common divisor (GCD) of 1015 and 270. The GCD is 5.

Now, divide both the numerator and denominator by 5:
\[ x = \frac{1015 \div 5}{270 \div 5} = \frac{203}{54} \]

### Final Answer
The other fraction is:
\[ \frac{203}{54} \]

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