Difference Calculation: Fraction and Reciprocal
This guide details the calculation for finding the positive difference between a specific fraction and its reciprocal.
Core Concepts
- Reciprocal: For any fraction $ \frac{a}{b} $, its reciprocal is $ \frac{b}{a} $.
- Positive Difference: Calculated by subtracting the smaller value from the larger value.
Calculation Steps
- Identify the given fraction: $ \frac{5}{16} $.
- Determine the reciprocal of the fraction: $ \frac{16}{5} $.
- Compare the values: $ \frac{5}{16} \approx 0.3125 $ and $ \frac{16}{5} = 3.2 $. The larger value is $ \frac{16}{5} $.
- Set up the subtraction for the positive difference: $ \frac{16}{5} - \frac{5}{16} $.
- Find the least common denominator (LCD) for 5 and 16, which is $ 80 $.
- Rewrite the fractions with the LCD: $ \frac{16}{5} = \frac{16 \times 16}{5 \times 16} = \frac{256}{80} $ and $ \frac{5}{16} = \frac{5 \times 5}{16 \times 5} = \frac{25}{80} $.
- Perform the subtraction: $ \frac{256}{80} - \frac{25}{80} = \frac{256 - 25}{80} = \frac{231}{80} $.
- Convert the improper fraction $ \frac{231}{80} $ to a mixed number. $ 231 \div 80 = 2 $ with a remainder of $ 71 $.
- The final result is $ 2\frac{71}{80} $.
Final Result
The positive difference between $ \frac{5}{16} $ and its reciprocal is $ 2\frac{71}{80} $.
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?
- 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.
- Two-fifth of seven-seventeenth of three-fifth of a number is 84. Find 40% of that number.
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:
