Solve: 1/2 - 2/8 + 1/4 | Fraction Operation Challenge

Fractions represent parts of a whole. You can only combine parts when they're the same size! $\frac{1}{2}$ means 1 out of 2 equal pieces, while $\frac{2}{8}$ means 2 out of 8 equal pieces - these are different sized pieces.

Look at the denominators: 2, 8, and 4. Since 8 is already the largest and both 2 and 4 divide evenly into 8, the LCD is 8! For other problems, list multiples of the largest denominator until you find one that all denominators divide into.

That's fine! But always simplify first. In this problem, $\frac{4}{8}$ simplifies to $\frac{1}{2}$. If you get an improper fraction like $\frac{9}{8}$, you can leave it as is or convert to a mixed number.

Yes! Just like with regular arithmetic, follow the order of operations. Since this expression only has addition and subtraction, work from left to right: $\frac{4}{8} - \frac{2}{8} + \frac{2}{8}$.

You could convert to decimals, but be careful! $\frac{1}{2} = 0.5$, $\frac{2}{8} = 0.25$, and $\frac{1}{4} = 0.25$. However, fraction form is often more precise and required for exact answers.

Convert your answer back to the original denominators and verify! $\frac{1}{2} = \frac{4}{8}$. Now check: $\frac{4}{8} - \frac{2}{8} + \frac{2}{8} = \frac{4}{8}$ ✓