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 will the value of the following expression be?
$\left(\frac{6+3}{3}\right) - 5 \times (4+5)$
- What is the value of the following expression?
$\frac{\sqrt{225}}{14} \times \frac{\sqrt{196}}{22} \times \frac{\sqrt{484}}{15}$ - The value of $\frac{(5.4)^3 - 0.064}{(5.4)^2 + 2.16 + 0.16}$ is:
- The value of $\sqrt{10 + \sqrt{221 + \sqrt{12 + \sqrt{16}}}}$ is:
- Solve the following.
$(1 + \frac{1}{x})(1 + \frac{1}{x+1})(1 + \frac{1}{x+2})(1 + \frac{1}{x+3}) = ?$ - The value of $\sqrt{0.04} + \sqrt{1.44} + \sqrt{1.69} + \sqrt{0.0009}$ is:
- The value of $\sqrt{196} + \sqrt{0.0361} - \sqrt{7.29}$ is ____.
- The value of $\frac{32 \div 4 - 5 \times 8 \div 3}{5 \times 3 - \{6 + 3\}}$ is:
- What is the value of $x$, if $-3 \times \sqrt{196} + \sqrt{x} = 8 \times 3 - 2$?
- What is the value of $\sqrt{\frac{1.21 \times 0.9}{1.1 \times 0.11}}$?
Important Questions from Simplification
What will come in the place of the question mark ‘?’ in the following question?
(15 + 24) × 3 ÷ 13 + 18 – 5 = ?
What should come in place of the question mark '?' in the following question?
\n13 × 3 of 5 ÷ 26 = ? + 2.5What should come in place of the question mark '?' in the following question?
10% of 450 - (8 × 5) = ? × 5
What will come in the place of the question mark ‘?’ in the following question?
(66)2 - (34)2 + ?2 = (60)2
What will come in the place of the question mark ‘?’ in the following question?
3 × ? ÷ 9 = ∛729 × √121
