If a = -$\frac{3}{4}$ and b = $\frac{5}{6}$, then which of the following does not lie between a and b ?

Question

Accepted Answer

To determine which of the given options does not lie between $ a = -\frac{3}{4} $ and $ b = \frac{5}{6} $, we need to compare each option with the values of $ a $ and $ b $.

1. **Option 1: 0**

- $ a = -\frac{3}{4} $ is less than 0, and 0 is less than $ b = \frac{5}{6} $.
   - Therefore, 0 lies between $ a $ and $ b $.

2. **Option 2: -\frac{1}{2}**

- $ a = -\frac{3}{4} $ is less than $-\frac{1}{2}$, and $-\frac{1}{2}$ is less than $ b = \frac{5}{6} $.
   - Therefore, $-\frac{1}{2}$ lies between $ a $ and $ b $.

3. **Option 3: -\frac{2}{5}**

- $ a = -\frac{3}{4} $ is less than $-\frac{2}{5}$, and $-\frac{2}{5}$ is less than $ b = \frac{5}{6} $.
   - Therefore, $-\frac{2}{5}$ lies between $ a $ and $ b $.

4. **Option 4: -\frac{7}{9}**

- To compare $-\frac{7}{9}$ with $ a = -\frac{3}{4} $, we convert both to a common denominator:
     - $-\frac{3}{4} = -\frac{27}{36}$
     - $-\frac{7}{9} = -\frac{28}{36}$
   - Since $-\frac{28}{36}$ is less than $-\frac{27}{36}$, $-\frac{7}{9}$ is less than $-\frac{3}{4}$.
   - Therefore, $-\frac{7}{9}$ does not lie between $ a $ and $ b $.

In conclusion, Option 4, $-\frac{7}{9}$, is the correct answer because it does not lie between $ a = -\frac{3}{4} $ and $ b = \frac{5}{6} $. The other options (0, $-\frac{1}{2}$, and $-\frac{2}{5}$) all lie within the range defined by $ a $ and $ b $.