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
- $1.236576576...$
can be written in the form of: - 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?
- The value of $\frac{4}{3} + \left( \frac{1}{1 + \frac{5}{6}} \right) - \frac{5}{4}$ is
What is the value of
$\frac{7}{9} - \frac{11}{12} + \frac{13}{16} - \frac{1}{8}$?
- How much does one need to add to $\frac{1}{2}$ to get $2$?
- 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.
- 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.
- Two-fifth of seven-seventeenth of three-fifth of a number is 84. Find 40% of that number.
- A beautician's income includes her salary and the tips she gets for her services. During a particular week, if her tips were $\frac{5}{4}$ of her salary, then what fraction of her income came from the tips?
Important Questions from Fractions
5 \(\frac{3}{4}\) + x + 2 \(\frac{1}{2}\) = 10 \(\frac{1}{8}\) Find the value of x.
Simplify the expression 441 ÷ \(\left[270 \div \frac{3}{7}+\left(17\div \frac{1}{3}\right)-\left(8\frac{1}{2}-\frac{5}{2}\right)\right]\)
Number 0.232323 can be written in rational form as:
Solve: \(\frac{1}{2}\) [{-2(2 + 3)*20}/2]
Match the following.
Column I
Column II
a.
Equivalent fraction of \(\frac{7}{12}\) is
i.
Proper fraction
b.
Equivalent fraction of \(\frac{9}{15}\) is
ii.
Improper fraction
c.
\(\frac{7}{11}\) is
iii.
\(\frac{21}{36}\)
d.
\(\frac{19}{5}\) is
iv.
\(\frac{3}{5}\)
