Question

1. find the number halfway between \\(\frac{3}{7}\\) and \\(\frac{5}{9}\\).

Explanation:

Step1: Recall the formula for the midpoint between two numbers

The number halfway between two numbers \(a\) and \(b\) is the average of \(a\) and \(b\), which is given by \(\frac{a + b}{2}\). Here, \(a=\frac{3}{7}\) and \(b = \frac{5}{9}\).

Step2: Find a common denominator for the fractions

The least common denominator of 7 and 9 is \(7\times9=63\). Convert \(\frac{3}{7}\) and \(\frac{5}{9}\) to fractions with denominator 63:
\(\frac{3}{7}=\frac{3\times9}{7\times9}=\frac{27}{63}\) and \(\frac{5}{9}=\frac{5\times7}{9\times7}=\frac{35}{63}\).

Step3: Add the two fractions

Add \(\frac{27}{63}\) and \(\frac{35}{63}\): \(\frac{27}{63}+\frac{35}{63}=\frac{27 + 35}{63}=\frac{62}{63}\).

Step4: Divide the sum by 2

Now, we need to find the average, so we divide the sum by 2: \(\frac{\frac{62}{63}}{2}=\frac{62}{63}\times\frac{1}{2}=\frac{31}{63}\).

Answer:

\(\frac{31}{63}\)