Write whether the following are equivalent fractions or not.
`7/(11) and 77/(111)`

Answer

To determine whether the fractions \( \frac{7}{11} \) and \( \frac{77}{111} \) are equivalent, we can follow these steps:

### Step 1: Identify the fractions
We have two fractions:
- Fraction 1: \( \frac{7}{11} \)
- Fraction 2: \( \frac{77}{111} \)

### Step 2: Find the Least Common Multiple (LCM) of the denominators
The denominators are 11 and 111. We need to find the LCM of these two numbers.

- The factors of 11 are \( 1, 11 \).
- The factors of 111 are \( 1, 3, 37, 111 \).

Since 11 is a prime number and does not divide 111 evenly, the LCM is \( 11 \times 111 = 1221 \).

### Step 3: Convert both fractions to have the same denominator
Now we will convert both fractions to have the denominator of 1221.

**For \( \frac{7}{11} \):**
- To convert \( 11 \) to \( 1221 \), we multiply by \( 111 \):
\[ \frac{7}{11} \times \frac{111}{111} = \frac{7 \times 111}{11 \times 111} = \frac{777}{1221} \]

**For \( \frac{77}{111} \):**
- To convert \( 111 \) to \( 1221 \), we multiply by \( 11 \):
\[ \frac{77}{111} \times \frac{11}{11} = \frac{77 \times 11}{111 \times 11} = \frac{847}{1221} \]

### Step 4: Compare the numerators
Now we compare the numerators of the two fractions:
- From \( \frac{7}{11} \), we have \( 777 \).
- From \( \frac{77}{111} \), we have \( 847 \).

Since \( 777 \neq 847 \), the two fractions are not equivalent.

### Conclusion
The fractions \( \frac{7}{11} \) and \( \frac{77}{111} \) are **not equivalent**.

---