Find four rational number equivalent to each of the following.
(i) `frac(6)(11)`
(ii) `frac(-3)(8)`
(iii) `frac(7)(-15)`
(iv) 8
(v) 1
(vi) -1

Answer

To find four rational numbers equivalent to each of the given rational numbers, we can multiply both the numerator and the denominator of the fraction by the same non-zero integer. This will yield an equivalent fraction. Let's solve the question step by step.

### (i) Find four rational numbers equivalent to `6/11`

1. **Multiply by 2**:
\[ \frac{6 \times 2}{11 \times 2} = \frac{12}{22} \]

2. **Multiply by 3**:
\[ \frac{6 \times 3}{11 \times 3} = \frac{18}{33} \]

3. **Multiply by 4**:
\[ \frac{6 \times 4}{11 \times 4} = \frac{24}{44} \]

4. **Multiply by 5**:
\[ \frac{6 \times 5}{11 \times 5} = \frac{30}{55} \]

**Equivalent rational numbers for `6/11` are:**
\[ \frac{12}{22}, \frac{18}{33}, \frac{24}{44}, \frac{30}{55} \]

### (ii) Find four rational numbers equivalent to `-3/8`

1. **Multiply by 2**:
\[ \frac{-3 \times 2}{8 \times 2} = \frac{-6}{16} \]

2. **Multiply by 3**:
\[ \frac{-3 \times 3}{8 \times 3} = \frac{-9}{24} \]

3. **Multiply by 4**:
\[ \frac{-3 \times 4}{8 \times 4} = \frac{-12}{32} \]

4. **Multiply by 5**:
\[ \frac{-3 \times 5}{8 \times 5} = \frac{-15}{40} \]

**Equivalent rational numbers for `-3/8` are:**
\[ \frac{-6}{16}, \frac{-9}{24}, \frac{-12}{32}, \frac{-15}{40} \]

### (iii) Find four rational numbers equivalent to `7/-15`

1. **Multiply by 2**:
\[ \frac{7 \times 2}{-15 \times 2} = \frac{14}{-30} \]

2. **Multiply by 3**:
\[ \frac{7 \times 3}{-15 \times 3} = \frac{21}{-45} \]

3. **Multiply by 4**:
\[ \frac{7 \times 4}{-15 \times 4} = \frac{28}{-60} \]

4. **Multiply by 5**:
\[ \frac{7 \times 5}{-15 \times 5} = \frac{35}{-75} \]

**Equivalent rational numbers for `7/-15` are:**
\[ \frac{14}{-30}, \frac{21}{-45}, \frac{28}{-60}, \frac{35}{-75} \]

### (iv) Find four rational numbers equivalent to `8`

1. **Write as a fraction**:
\[ 8 = \frac{8}{1} \]

2. **Multiply by 2**:
\[ \frac{8 \times 2}{1 \times 2} = \frac{16}{2} \]

3. **Multiply by 3**:
\[ \frac{8 \times 3}{1 \times 3} = \frac{24}{3} \]

4. **Multiply by 4**:
\[ \frac{8 \times 4}{1 \times 4} = \frac{32}{4} \]

**Equivalent rational numbers for `8` are:**
\[ \frac{16}{2}, \frac{24}{3}, \frac{32}{4} \]

### (v) Find four rational numbers equivalent to `1`

1. **Write as a fraction**:
\[ 1 = \frac{1}{1} \]

2. **Multiply by 2**:
\[ \frac{1 \times 2}{1 \times 2} = \frac{2}{2} \]

3. **Multiply by 3**:
\[ \frac{1 \times 3}{1 \times 3} = \frac{3}{3} \]

4. **Multiply by 4**:
\[ \frac{1 \times 4}{1 \times 4} = \frac{4}{4} \]

**Equivalent rational numbers for `1` are:**
\[ \frac{2}{2}, \frac{3}{3}, \frac{4}{4} \]

### (vi) Find four rational numbers equivalent to `-1`

1. **Write as a fraction**:
\[ -1 = \frac{-1}{1} \]

2. **Multiply by 2**:
\[ \frac{-1 \times 2}{1 \times 2} = \frac{-2}{2} \]

3. **Multiply by 3**:
\[ \frac{-1 \times 3}{1 \times 3} = \frac{-3}{3} \]

4. **Multiply by 4**:
\[ \frac{-1 \times 4}{1 \times 4} = \frac{-4}{4} \]

**Equivalent rational numbers for `-1` are:**
\[ \frac{-2}{2}, \frac{-3}{3}, \frac{-4}{4} \]