How to Work with Fractions Step by Step

Fractions confuse students for one reason: each operation has its own rule, and mixing them up is easy. Learn one method per operation and the confusion disappears.

Adding and subtracting: common denominator first

You can only add or subtract fractions that share a denominator. If they do not, convert them first.

Example: $\frac{1}{2}+\frac{1}{3}$. The common denominator is $6$: $\frac{1}{2}=\frac{3}{6}$ and $\frac{1}{3}=\frac{2}{6}$. So:

$$\frac{3}{6}+\frac{2}{6}=\frac{5}{6}$$

The same method works for subtraction — convert, then subtract the numerators. Never add the denominators: $\frac{1}{2}+\frac{1}{3}$ is not $\frac{2}{5}$.

Multiplying: straight across, then simplify

Example: $\frac{2}{3}\times \frac{9}{4}$. Multiply numerators together and denominators together:

$$\frac{2\times 9}{3\times 4}=\frac{18}{12}=\frac{3}{2}$$

Always simplify at the end — and look for cancellations before multiplying to keep the numbers small. Here $3$ cancels into $9$ before you even start.

Dividing: flip and multiply

Example: $\frac{2}{3}÷\frac{4}{5}$. Flip the second fraction and multiply:

$$\frac{2}{3}\times \frac{5}{4}=\frac{10}{12}=\frac{5}{6}$$

Mixed numbers

Convert mixed numbers to improper fractions before operating. $1\frac{1}{2}=\frac{3}{2}$ and $2\frac{1}{4}=\frac{9}{4}$, so:

$$1\frac{1}{2}+2\frac{1}{4}=\frac{3}{2}+\frac{9}{4}=\frac{6}{4}+\frac{9}{4}=\frac{15}{4}=3\frac{3}{4}$$

Common mistakes

• Adding denominators when adding or subtracting.
• Forgetting to simplify the final answer.
• Flipping the wrong fraction when dividing — always flip the second one.
• Skipping the conversion of mixed numbers before multiplying or dividing.

Practice it

Want to check your work? Try the Fraction Calculator — every answer comes with steps and a simplified result. Then try similar problems on the practice page, or solve anything step by step in the Math Solver.