Let the original fraction be represented as $\frac{x}{y}$.
Adjusting Numerator and Denominator
- The numerator is increased by 20%: The new numerator becomes $x + 0.20x = 1.20x$.
- The denominator is decreased by 50%: The new denominator becomes $y - 0.50y = 0.50y$.
Forming the New Fraction
The new fraction is formed by the adjusted numerator and denominator:
$ \text{New Fraction} = \frac{1.20x}{0.50y} $We are given that this new fraction is equal to $\frac{5}{6}$:
$ \frac{1.20x}{0.50y} = \frac{5}{6} $Solving for the Original Fraction
To find the original fraction $\frac{x}{y}$, we rearrange the equation:
- Simplify the coefficients: $\frac{1.2}{0.5} \times \frac{x}{y} = \frac{5}{6}$.
- Multiply the numerator and denominator of the coefficient by 10 to remove decimals: $\frac{12}{5} \times \frac{x}{y} = \frac{5}{6}$.
- Isolate $\frac{x}{y}$ by dividing both sides by $\frac{12}{5}$ (which is the same as multiplying by its reciprocal, $\frac{5}{12}$): $ \frac{x}{y} = \frac{5}{6} \div \frac{12}{5} $ $ \frac{x}{y} = \frac{5}{6} \times \frac{5}{12} $ $ \frac{x}{y} = \frac{5 \times 5}{6 \times 12} $ $ \frac{x}{y} = \frac{25}{72} $
Therefore, the original fraction is $\frac{25}{72}$.
Similar Questions
- $1.236576576...$
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.
- 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:
