Solving for the Subtraction: Finding the Number to Subtract from 3/5 to Obtain 2

In mathematical equations, the process of subtracting one number from another is often integral to finding unknown values. This article delves into a specific problem: finding the number that should be subtracted from (frac{3}{5}) to get 2. By following a step-by-step approach, this article aims to guide readers through the process of solving such equations.

Setting Up the Equation

The given problem can be set up as an equation as follows:

[ frac{3}{5} - n 2 ]

This equation represents the scenario where a number (n) is subtracted from (frac{3}{5}), resulting in the value 2. To solve for (n), we can rearrange the equation:

[ n frac{3}{5} - 2 ]

Expressing 2 with a Common Denominator

Next, it is necessary to express 2 with a common denominator of 5. This can be achieved by writing 2 as a fraction with a denominator of 5:

[ 2 frac{10}{5} ]

Substituting this back into our equation yields:

[ n frac{3}{5} - frac{10}{5} frac{3 - 10}{5} frac{-7}{5} ]

Final Answer with Mixed Number Representation

Finally, we can represent the fraction (frac{-7}{5}) as a mixed number:

[ n -1frac{2}{5} ]

To confirm the solution, we can substitute (-1frac{2}{5}) back into the original equation:

[ frac{3}{5} - (-1frac{2}{5}) frac{3}{5} 1frac{2}{5} frac{3}{5} frac{7}{5} frac{10}{5} 2 ] (L.H.S R.H.S)

Hence, the solution is proven correct.

Alternative Method for Solving the Equation

A second approach to solving the problem can be outlined as:

Given the equation: [ 3/5 - x 2 ]

Simplify the subtraction on the left side:

[ x 3/5 - 2 ]

Convert 2 to a fraction with denominator 5:

[ x 3/5 - 10/5 ]

Solve for x:

[ x -7/5 ] or ( -1frac{2}{5} )

This confirms the solution: the number that should be subtracted from 3/5 to get 2 is (-1frac{2}{5}) or (-frac{7}{5}).

Conclusion

The process of solving this equation involves basic algebraic manipulation and careful handling of fractions. By utilizing the principle of common denominators and subtraction, we can arrive at a precise solution. Understanding and practicing these steps can significantly enhance problem-solving skills in algebra.