How to Solve ( frac{11}{12} - x -frac{3}{4} ): A Step-by-Step Guide

Have you ever come across a problem where you need to solve for a missing value in a fraction equation? In this guide, we will walk you through the process of solving the equation ( frac{11}{12} - x -frac{3}{4} ) step-by-step. By following these detailed instructions, you'll be able to tackle similar problems with ease.

Understanding the Problem

The equation in question is ( frac{11}{12} - x -frac{3}{4} ). We are tasked with finding the value of ( x ), which, when subtracted from ( frac{11}{12} ), gives us ( -frac{3}{4} ). This problem involves working with fractions, specifically subtraction and finding a common denominator.

Solving the Equation

First, we start with the original equation:[ frac{11}{12} - x -frac{3}{4} ]

To isolate ( x ), we can add ( x ) to both sides of the equation:[ frac{11}{12} -frac{3}{4} x ]

Now, we need to convert ( -frac{3}{4} ) to a fraction with a denominator of 12 (the common denominator of (frac{11}{12})). We do this by multiplying both the numerator and the denominator of (-frac{3}{4}) by 3:[ -frac{3}{4} -frac{3 times 3}{4 times 3} -frac{9}{12} ]So the equation becomes:[ frac{11}{12} -frac{9}{12} x ]

Add (frac{9}{12}) to both sides to isolate ( x ):[ frac{11}{12} frac{9}{12} x ][ frac{11 9}{12} x ][ frac{20}{12} x ]

Finally, simplify ( frac{20}{12} ) by dividing both the numerator and the denominator by their greatest common divisor, which is 4:[ x frac{20 div 4}{12 div 4} frac{5}{3} ]

Verification

To verify our solution, we substitute ( x frac{5}{3} ) back into the original equation:[ frac{11}{12} - frac{5}{3} -frac{3}{4} ]

Convert ( frac{5}{3} ) to a fraction with a denominator of 12:[ frac{5}{3} frac{5 times 4}{3 times 4} frac{20}{12} ]

Substitute ( frac{20}{12} ) into the equation:[ frac{11}{12} - frac{20}{12} -frac{3}{4} ][ frac{11 - 20}{12} -frac{3}{4} ][ -frac{9}{12} -frac{3}{4} ][ -frac{3}{4} -frac{3}{4} ]

This confirms that our solution is correct.

Conclusion

By following the steps outlined in this guide, we have successfully solved the equation ( frac{11}{12} - x -frac{3}{4} ), finding that ( x frac{5}{3} ). This process involves working with common denominators, algebraic manipulation, and verifying the solution. With practice, you can solve similar problems with ease.