Questions: (a) Name a fraction between 4/5 and 5/6.

$(a) Name a fraction between 4/5 and 5/6.$

Transcript text: (a) Name a fraction between $\frac{4}{5}$ and $\frac{5}{6}$.

Solution

Solution Steps

To find a fraction between $\frac{4}{5}$ and $\frac{5}{6}$, we can convert both fractions to have a common denominator and then find a fraction that lies between them.

Step 1: Define the Fractions

We start with the fractions $ \frac{4}{5} $ and $ \frac{5}{6} $.

Step 2: Find a Common Denominator

The least common multiple of the denominators $ 5 $ and $ 6 $ is $ 30 $. We convert both fractions to have this common denominator: \[ \frac{4}{5} = \frac{4 \times 6}{5 \times 6} = \frac{24}{30} \] \[ \frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30} \]

Step 3: Identify a Fraction Between Them

To find a fraction between $ \frac{24}{30} $ and $ \frac{25}{30} $, we can take the average of the numerators: \[ \text{Mid numerator} = \frac{24 + 25}{2} = 24.5 \] However, since we are looking for a fraction, we can choose $ \frac{24}{30} $ and $ \frac{25}{30} $ and find a simple fraction like $ \frac{24.5}{30} $ or $ \frac{24 + 1}{30} = \frac{25}{30} $.

Final Answer

The fraction between $ \frac{4}{5} $ and $ \frac{5}{6} $ can be expressed as: \[ \boxed{\frac{24.5}{30}} \]

Alternatively, a simple fraction could be: \[ \boxed{\frac{24}{30}} \text{ or } \boxed{\frac{25}{30}} \]

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