Solving for m: Equation with Fractions

The problem requires finding the value of '$m$' in the given algebraic equation:

$ m - \frac{2}{3} = \frac{5}{6} + \frac{1}{2} $

Step 1: Simplify the Right-Hand Side (RHS)

First, calculate the sum of the fractions on the right side of the equation. Find a common denominator for $\frac{5}{6}$ and $\frac{1}{2}$, which is 6.

• Convert $\frac{1}{2}$ to an equivalent fraction with a denominator of 6: $ \frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6} $
• Add the fractions: $ \frac{5}{6} + \frac{3}{6} = \frac{5+3}{6} = \frac{8}{6} $
• Simplify the resulting fraction: $ \frac{8}{6} = \frac{8 \div 2}{6 \div 2} = \frac{4}{3} $

The equation now becomes:

$ m - \frac{2}{3} = \frac{4}{3} $

Step 2: Isolate m

To find the value of '$m$', add $\frac{2}{3}$ to both sides of the equation:

$ m = \frac{4}{3} + \frac{2}{3} $

Step 3: Calculate the Final Value of m

Add the fractions on the right side:

$ m = \frac{4+2}{3} = \frac{6}{3} $

Simplify the result:

$ m = 2 $

Therefore, the value of '$m$' is 2.