Number Calculation: Solving Fraction Problems
Let the unknown number be represented by $x$. We will translate the problem statement into a mathematical equation and solve for $x$.
Step 1: Initial Fraction Operations
First, calculate the values of the fractional expressions given in the problem.
- Calculate the difference: $ \frac{1}{3} - \frac{1}{4} = \frac{4}{12} - \frac{3}{12} = \frac{1}{12} $
- Calculate the product ($\frac{1}{3}$ of $\frac{1}{4}$): $ \frac{1}{3} \times \frac{1}{4} = \frac{1}{12} $
- Calculate the target remainder sum: $ \frac{1}{3} + \frac{1}{4} = \frac{4}{12} + \frac{3}{12} = \frac{7}{12} $
Step 2: Formulate the Algebraic Equation
Now, construct the equation based on the problem description.
The problem states that to the number ($x$), $(\frac{1}{3} - \frac{1}{4})$ is added. From this sum, $\frac{1}{3}$ of $\frac{1}{4}$ is subtracted, and the result is $\frac{1}{3} + \frac{1}{4}$.
Using the calculated values:
$ (x + \frac{1}{12}) - \frac{1}{12} = \frac{7}{12} $Step 3: Solve for the Unknown Number
Simplify the equation to find the value of $x$.
The equation simplifies as follows:
$ x + (\frac{1}{12} - \frac{1}{12}) = \frac{7}{12} $ $ x + 0 = \frac{7}{12} $ $ x = \frac{7}{12} $The number is $\frac{7}{12}$.
Similar Questions
- What is the value of the following expression? $(14 \div 7) \times [8 + \{3 + 8 - 2\}] - (5 - 2)$
- If $\frac{121}{0.121} = \frac{12.1}{x}$, then the value of $x$ will be:
- Select the option that will replace the question mark (?) in the given equation.
$? + \frac{18}{24} + 3\frac{3}{4} = 23\frac{13}{24}$ - Select the number that can replace the question mark (?) in the following equation.
$? + \frac{18}{24} + 3\frac{3}{4} = 23\frac{13}{24}$ - The value of $987 \times 999$ is:
- Solve the following. $\frac{3}{\sqrt{0.0009}} + \frac{4}{\sqrt{0.0016}} = ?$
- Solve the following.$$8.75 \times 8.75 - 135.625 + 7.75 \times 7.75 = ?$$
- Simplify the following.
$\frac{1}{5} \div \left(\frac{5}{3} \times \frac{3}{25}\right)$ - Solve the following.
$\frac{0.6 \times 0.6 \times 0.6 + 0.7 \times 0.7 \times 0.7}{0.6 \times 0.6 - 0.42 + 0.7 \times 0.7} = ?$ - Find the value of $[868 \div \{26 + 6 \times (3 - 7)\}]$.
Important Questions from Simplification
Simplify
6 × {28 ÷ 84 × {36 × 49 ÷ (6 × 7)}}.
Simplify.
- A bag contains ₹5, 2 and 1 coins in the ratio of 3 : 4 : 5. The total value of all the coins is ₹2,100. How many coins of ₹5 are there in the bag?
- \(\frac{6}{2}\times\frac{10}{2}\div\frac{6}{2}\times6^2+5\times4=?\)
- Find the value of 2.\(\overline {36} \) + 3.\(\overline {21} \) - 1.\(\overline {05} \)
