Verified Answer :
- first make the denominators of the set the same.
E.g. \(\frac{2}{7}+ \frac{4}{3}\) = \(\frac{6}{21} + \frac{28}{21}\) = \(\frac{34}{21}\)
2. Divide the total by the number of fractions added together: In this case it was 2 so:
\(\frac{34}{21} * \frac{1}{2}\) = \(\frac{34}{42}\)
3. Simplify the total: \(\frac{17}{21}\)
Answer:
Average of number is equal to sum of numbers by total no.
i.e., \(Average\,=\,\frac{Sun\,of\,numbers}{Total\,no}\)
Now when numbers/amounts are fraction then there is one extra step which is to add the fractions.
Lets say we have to find average of 2 fractions i.e., \(\frac{3}{4}\,,\,\frac{5}{3}\)
\(\implies\,Average\,=\,\frac{\frac{3}{4}+\frac{5}{3}}{2}\)
Step 1 : First to add the fractions find the LCM of denominator as There are unlike fractions
3 = 1 × 3
4 = 1 × 4
LCM of 3 and 4 = 3 × 4 = 12
Step 2: To make them like fraction we find equivalent fraction of each fraction whose denominator equal to 12
\(\frac{3}{4}\times\frac{3}{3}=\frac{9}{12}\)
\(\frac{5}{3}\times\frac{4}{4}=\frac{20}{12}\)
Step 3: Adding both fractions
\(\frac{9}{12}+\frac{20}{12}=\frac{9+20}{12}=\frac{29}{12}\)
Step 4: put these value in average formula
\(\implies\,Average\,=\,\frac{\frac{29}{12}{2}\)
Step 5: Now we divide \(\frac{29}{12}\) by 2 using fraction division .i.e., multiply the reciprocal of divisor with dividend
here 2 is divisor
Reciprocal = \(\frac{1}{2}\)
\(\imples Average=\frac{29}{12}\times\frac{1}{2}=\frac{29\times1}{12\times2}=\frac{29}{24}\)
Following these steps Average of fractional amount of any no can be found.