Solving for the Reciprocal of the Sum of Reciprocals
The problem asks us to find the reciprocal of the sum of the reciprocals of two given fractions: $\frac{5}{7}$ and $\frac{9}{5}$. We can solve this step-by-step:
Step 1: Find the Reciprocals
- The reciprocal of $\frac{5}{7}$ is $\frac{7}{5}$.
- The reciprocal of $\frac{9}{5}$ is $\frac{5}{9}$.
Step 2: Calculate the Sum of Reciprocals
Next, we add the reciprocals found in Step 1:
Sum = $\frac{7}{5} + \frac{5}{9}$
To add these fractions, we find a common denominator, which is $5 \times 9 = 45$.
Sum = $\frac{7 \times 9}{5 \times 9} + \frac{5 \times 5}{9 \times 5}$
Sum = $\frac{63}{45} + \frac{25}{45}$
Sum = $\frac{63 + 25}{45}$
Sum = $\frac{88}{45}$
Step 3: Find the Reciprocal of the Sum
Finally, we find the reciprocal of the sum calculated in Step 2.
The sum is $\frac{88}{45}$.
The reciprocal of the sum is $\frac{45}{88}$.
Conclusion
The reciprocal of the sum of the reciprocals of $\frac{5}{7}$ and $\frac{9}{5}$ is $\frac{45}{88}$.
Similar Questions
- The numerator of a fraction is increased by $20\%$ and the denominator is decreased by $50\%$. If the resultant fraction is $\frac{5}{6}$, then what will be the original fraction?
- $1.236576576...$
can be written in the form of: - What smallest fraction should be added to $3\frac{2}{3} + 6\frac{7}{12} + 4\frac{9}{36} + 5 + 7\frac{1}{12}$ to make the sum a whole number?
- What is the positive difference between $\frac{5}{16}$ and its reciprocal?
- The sum of the numerator and denominator of a fraction is 11. If the numerator is decreased by 1, the fraction becomes $\frac{1}{4}$. Find the fraction.
- How much does one need to add to $\frac{1}{2}$ to get $2$?
- Solve the following:
$(0.\overline{5} + 0.\overline{6} + 0.\overline{7} + 0.\overline{8}) = ?$ - What is the sum of $\frac{1}{3}$, $\frac{4}{3}$ and $\frac{3}{4}$?
- Four persons A, B, C and D completed a task in $\frac{2}{3} \text{ h}, \frac{3}{4} \text{ h}, \frac{4}{5} \text{ h}$ and $\frac{1}{5} \text{ h}$ respectively. Who among the following took the highest amount of time to complete the task?
- If the numerator of a fraction is increased by 30% and its denominator is decreased by 35%, the value of the fraction becomes $\frac{3}{15}$. Find the original fraction.
Important Questions from Fractions
Which fraction among the following is the least ?
\(\frac{5}{11}, \frac{7}{12}, \frac{8}{13}, \frac{9}{17}\)
Find the value of the following expression:
\(\frac{{3 \div 1 \times 2 + 5 - 2}}{{3 \times 3 - 2}}\)
Simplify the expression 441 ÷ \(\left[270 \div \frac{3}{7}+\left(17\div \frac{1}{3}\right)-\left(8\frac{1}{2}-\frac{5}{2}\right)\right]\)
If the sum of two positive numbers is 65 and the square root of their product is 26, then the sum of their reciprocals is:
The value of \(9 \div [\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{6}\div(\frac{3}{4}-\frac{1}{3})\;of\;\frac{2}{9}]\) is:
