Question

find a rational number halfway in between the two numbers.
\\(\frac{6}{11}\\) and \\(\frac{1}{2}\\)

Explanation:

Step1: Recall the formula for the midpoint of two numbers

To find a number halfway between two numbers \( a \) and \( b \), we use the formula for the average: \( \frac{a + b}{2} \). Here, \( a=\frac{6}{11} \) and \( b = \frac{1}{2} \).

Step2: Find a common denominator for addition

The common denominator of 11 and 2 is \( 11\times2 = 22 \). Convert \( \frac{6}{11} \) to \( \frac{6\times2}{11\times2}=\frac{12}{22} \) and \( \frac{1}{2} \) to \( \frac{1\times11}{2\times11}=\frac{11}{22} \).

Step3: Add the two fractions

Add \( \frac{12}{22} \) and \( \frac{11}{22} \): \( \frac{12}{22}+\frac{11}{22}=\frac{12 + 11}{22}=\frac{23}{22} \).

Step4: Divide the sum by 2

Divide \( \frac{23}{22} \) by 2, which is the same as multiplying by \( \frac{1}{2} \): \( \frac{23}{22}\times\frac{1}{2}=\frac{23}{44} \).

Answer:

\( \frac{23}{44} \)