Solving the Fraction Problem
We need to find a fraction based on two conditions.
Setting Up the Equations
Let the fraction be represented as $\frac{x}{y}$, where $x$ is the numerator and $y$ is the denominator.
- Condition 1: The sum of the numerator and denominator is 11. $x + y = 11$
- Condition 2: If the numerator is decreased by 1, the fraction becomes $\frac{1}{4}$. $\frac{x-1}{y} = \frac{1}{4}$
Solving for the Numerator and Denominator
We can solve this system of equations. First, express $y$ from the first equation:
$y = 11 - x$Now, substitute this expression for $y$ into the second equation:
$\frac{x-1}{11-x} = \frac{1}{4}$Cross-multiply to solve for $x$:
$4(x-1) = 1(11-x)$ $4x - 4 = 11 - x$Combine like terms:
$4x + x = 11 + 4$ $5x = 15$ $x = \frac{15}{5}$ $x = 3$Now, find the value of $y$ using $y = 11 - x$:
$y = 11 - 3$ $y = 8$Finding the Fraction
The numerator ($x$) is 3 and the denominator ($y$) is 8. Therefore, the fraction is:
$\frac{3}{8}$Verification
- Sum of numerator and denominator: $3 + 8 = 11$.
- If numerator is decreased by 1: $\frac{3-1}{8} = \frac{2}{8}$, which simplifies to $\frac{1}{4}$.
Both conditions are satisfied.
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 $2$?
- 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?
- 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?
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.
\(\frac{3}{5}\)
