The product of two fractions is `9(3)/(5)`. If one of the fractions is `9(3)/(7)`, find the other.

Answer

To solve the problem step by step, we need to find the other fraction when the product of two fractions is given. Here’s how we can do it:

### Step 1: Understand the Problem
We are given that the product of two fractions is \(9 \frac{3}{5}\) and one of the fractions is \(9 \frac{3}{7}\). We need to find the other fraction.

### Step 2: Convert Mixed Numbers to Improper Fractions
First, we convert the mixed numbers into improper fractions.

- For \(9 \frac{3}{5}\):
\[ 9 \frac{3}{5} = \frac{9 \times 5 + 3}{5} = \frac{45 + 3}{5} = \frac{48}{5} \]

- For \(9 \frac{3}{7}\):
\[ 9 \frac{3}{7} = \frac{9 \times 7 + 3}{7} = \frac{63 + 3}{7} = \frac{66}{7} \]

### Step 3: Set Up the Equation
Let the other fraction be \(x\). According to the problem, we have:
\[ \frac{66}{7} \times x = \frac{48}{5} \]

### Step 4: Solve for \(x\)
To find \(x\), we can rearrange the equation:
\[ x = \frac{48}{5} \div \frac{66}{7} \]
Dividing by a fraction is the same as multiplying by its reciprocal:
\[ x = \frac{48}{5} \times \frac{7}{66} \]

### Step 5: Simplify the Expression
Now we can simplify:
\[ x = \frac{48 \times 7}{5 \times 66} \]
Calculating the numerator:
\[ 48 \times 7 = 336 \]
Calculating the denominator:
\[ 5 \times 66 = 330 \]
So we have:
\[ x = \frac{336}{330} \]

### Step 6: Reduce the Fraction
Now we simplify \(\frac{336}{330}\):
Both numbers can be divided by 6:
\[ \frac{336 \div 6}{330 \div 6} = \frac{56}{55} \]

### Step 7: Convert Back to Mixed Number
Since \(56\) is greater than \(55\), we convert it back to a mixed number:
\[ 56 \div 55 = 1 \quad \text{remainder } 1 \]
Thus,
\[ \frac{56}{55} = 1 \frac{1}{55} \]

### Conclusion
The other fraction is \(1 \frac{1}{55}\).

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