2. If $$ a $$ is an integer, $$ b $$ is an integer and $$ c $$ is irrational, which of the following are rational numbers? (a) $$ \frac{5}{6} $$ (b) $$ \frac{a}{3} $$ (c) $$ \frac{-2}{b} $$ (d) $$ \frac{1}{c} $$

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Let's analyze each option to determine whether it's a rational number.

1. **Option (a): $$ \frac{5}{6} $$**
   - **Rationality**: $$\frac{5}{6}$$ is a fraction of two integers (5 and 6), so it is **rational**.

2. **Option (b): $$ \frac{a}{3} $$**
   - **Given**: $$a$$ is an integer.
   - **Rationality**: Dividing an integer by another integer (3) results in a rational number. So, $$ \frac{a}{3} $$ is **rational**.

3. **Option (c): $$ \frac{-2}{b} $$**
   - **Given**: $$b$$ is an integer.
   - **Rationality**: Dividing an integer (-2) by another integer ($$b$$) results in a rational number (assuming $$b 
eq 0$$). So, $$ \frac{-2}{b} $$ is **rational**.

4. **Option (d): $$ \frac{1}{c} $$**
   - **Given**: $$c$$ is irrational.
   - **Rationality**: The reciprocal of an irrational number is also **irrational**. Therefore, $$ \frac{1}{c} $$ is **irrational**.

**Summary:**
- **Rational Numbers**: (a) $$ \frac{5}{6} $$, (b) $$ \frac{a}{3} $$, and (c) $$ \frac{-2}{b} $$.
- **Irrational Number**: (d) $$ \frac{1}{c} $$.

**Therefore, options (a), (b), and (c) are rational numbers, while option (d) is not.**

**Answer:** All except option (d) are rational. Only 5⁄6, a⁄3, and –2⁄b are rational numbers.
Options (a), (b), and (c) are rational numbers.

If is an integer, is an integer and is irrational, which of the following
are rational numbers?
(a)
(b)
©
(d)

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