Find the equivalent fraction of `10/(11)` with numerator 40.

Answer

To find the equivalent fraction of \( \frac{10}{11} \) with a numerator of 40, we can follow these steps:

### Step 1: Identify the relationship between the original numerator and the desired numerator.
We start with the original fraction \( \frac{10}{11} \) and want to find an equivalent fraction where the numerator is 40.

### Step 2: Determine the multiplication factor.
To find out what we need to multiply the original numerator (10) by to get 40, we can set up the equation:
\[ 10 \times x = 40 \]
To solve for \( x \), divide both sides by 10:
\[ x = \frac{40}{10} = 4 \]

### Step 3: Multiply both the numerator and the denominator by the same factor.
Now that we know we need to multiply by 4, we can find the new denominator by multiplying the original denominator (11) by 4 as well:
\[ \text{New numerator} = 10 \times 4 = 40 \]
\[ \text{New denominator} = 11 \times 4 = 44 \]

### Step 4: Write the equivalent fraction.
Thus, the equivalent fraction of \( \frac{10}{11} \) with a numerator of 40 is:
\[ \frac{40}{44} \]

### Final Answer:
The equivalent fraction of \( \frac{10}{11} \) with a numerator of 40 is \( \frac{40}{44} \).

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