By what fraction should `9/25` be multiplied to get `7/15`

Answer

To solve the problem of finding the fraction by which \( \frac{9}{25} \) should be multiplied to obtain \( \frac{7}{15} \), we can follow these steps:

### Step 1: Set up the equation
Let the unknown fraction be \( x \). We can express the relationship as:
\[ \frac{9}{25} \times x = \frac{7}{15} \]

### Step 2: Isolate \( x \)
To isolate \( x \), we can multiply both sides of the equation by the reciprocal of \( \frac{9}{25} \), which is \( \frac{25}{9} \):
\[ x = \frac{7}{15} \times \frac{25}{9} \]

### Step 3: Multiply the fractions
Now, we can multiply the fractions on the right side:
\[ x = \frac{7 \times 25}{15 \times 9} \]

### Step 4: Simplify the multiplication
Calculating the numerator and the denominator:
- Numerator: \( 7 \times 25 = 175 \)
- Denominator: \( 15 \times 9 = 135 \)

So we have:
\[ x = \frac{175}{135} \]

### Step 5: Simplify the fraction
Now, we can simplify \( \frac{175}{135} \). We can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 5:
\[ x = \frac{175 \div 5}{135 \div 5} = \frac{35}{27} \]

### Final Answer
Thus, the fraction by which \( \frac{9}{25} \) should be multiplied to get \( \frac{7}{15} \) is:
\[ \frac{35}{27} \]

---