From the given options, find the rational number between the range `(2)/(4)` and 0.6.

Options

A. `(11)/(25)`
B. `(21)/(40)`
C. `(3)/(4)`
D. `(11)/(4)`

Answer

To find a rational number between \( \frac{2}{4} \) and \( 0.6 \), we can follow these steps:

### Step 1: Convert \( 0.6 \) to a Fraction
First, we need to convert \( 0.6 \) into a fraction.
\[ 0.6 = \frac{6}{10} \]
We can simplify this fraction:
\[ \frac{6}{10} = \frac{3}{5} \]

### Step 2: Identify the Two Rational Numbers
Now we have two rational numbers:
\[ \frac{2}{4} \quad \text{and} \quad \frac{3}{5} \]
We can simplify \( \frac{2}{4} \) as well:
\[ \frac{2}{4} = \frac{1}{2} \]

### Step 3: Find a Common Denominator
To find a rational number between \( \frac{1}{2} \) and \( \frac{3}{5} \), we need a common denominator. The least common multiple (LCM) of the denominators 2 and 5 is 10.

### Step 4: Convert Both Fractions to Have the Same Denominator
Convert \( \frac{1}{2} \) to a fraction with a denominator of 10:
\[ \frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10} \]
Convert \( \frac{3}{5} \) to a fraction with a denominator of 10:
\[ \frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10} \]

### Step 5: Identify Rational Numbers Between the Two Fractions
Now we have:
\[ \frac{5}{10} \quad \text{and} \quad \frac{6}{10} \]
The rational numbers between \( \frac{5}{10} \) and \( \frac{6}{10} \) can be:
\[ \frac{21}{40}, \frac{22}{40}, \frac{23}{40} \]
For example, \( \frac{21}{40} \) is a rational number that lies between these two fractions.

### Step 6: Check the Options
Now we check the options provided to see if \( \frac{21}{40} \) or any of the other fractions are present.

### Conclusion
The rational number \( \frac{21}{40} \) is between \( \frac{2}{4} \) and \( 0.6 \).

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