Find the equivalent fraction of `(6)/(11)` having
(i) denominater 77
(ii) numerator 60

Answer

To find the equivalent fractions of \( \frac{6}{11} \) for the given conditions, we will solve each part step by step.

### Part (i): Find the equivalent fraction of \( \frac{6}{11} \) with a denominator of 77.

**Step 1:** Identify the relationship between the original denominator and the new denominator.
- The original denominator is 11, and we want to find the equivalent fraction with a denominator of 77.

**Hint:** To find the multiplier, divide the new denominator by the original denominator.

**Step 2:** Calculate the multiplier.
- \( \text{Multiplier} = \frac{77}{11} = 7 \)

**Hint:** This tells us how many times we need to multiply the original fraction.

**Step 3:** Multiply both the numerator and the denominator of the original fraction by this multiplier.
- New numerator = \( 6 \times 7 = 42 \)
- New denominator = \( 11 \times 7 = 77 \)

**Hint:** Ensure that you multiply both parts of the fraction by the same number to keep it equivalent.

**Step 4:** Write the equivalent fraction.
- The equivalent fraction is \( \frac{42}{77} \).

### Part (ii): Find the equivalent fraction of \( \frac{6}{11} \) with a numerator of 60.

**Step 1:** Identify the relationship between the original numerator and the new numerator.
- The original numerator is 6, and we want to find the equivalent fraction with a numerator of 60.

**Hint:** To find the multiplier, divide the new numerator by the original numerator.

**Step 2:** Calculate the multiplier.
- \( \text{Multiplier} = \frac{60}{6} = 10 \)

**Hint:** This multiplier will also be used to find the new denominator.

**Step 3:** Multiply the original denominator by this multiplier.
- New denominator = \( 11 \times 10 = 110 \)

**Hint:** Again, ensure that you multiply both parts of the fraction by the same number to maintain equivalence.

**Step 4:** Write the equivalent fraction.
- The equivalent fraction is \( \frac{60}{110} \).

### Final Answers:
- (i) The equivalent fraction with a denominator of 77 is \( \frac{42}{77} \).
- (ii) The equivalent fraction with a numerator of 60 is \( \frac{60}{110} \).