Find the reciprocal ratio of :
(i) `5 : 8`
(ii) `(x)/(3) : (y)/(7)`

Answer

To find the reciprocal ratio of the given ratios, we will follow these steps:

### Step 1: Find the reciprocal of the first ratio \(5 : 8\).

1. Write the ratio in fraction form:
\[ \frac{5}{8} \]
2. Find the reciprocal by swapping the numerator and denominator:
\[ \text{Reciprocal} = \frac{8}{5} \]

### Step 2: Find the reciprocal of the second ratio \(\frac{x}{3} : \frac{y}{7}\).

1. Write the ratio in a fraction form:
\[ \frac{\frac{x}{3}}{\frac{y}{7}} = \frac{x}{3} \div \frac{y}{7} = \frac{x}{3} \times \frac{7}{y} = \frac{7x}{3y} \]
2. Find the reciprocal by swapping the numerator and denominator:
\[ \text{Reciprocal} = \frac{3y}{7x} \]

### Final Answers:
- The reciprocal of \(5 : 8\) is \(8 : 5\).
- The reciprocal of \(\frac{x}{3} : \frac{y}{7}\) is \(\frac{3y}{7x}\).

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