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Addition and Subtraction of Fractions with Common Denominators
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When adding and subtracting fractions, we need the denominators to be the same, then we can add or subtract the numerators.

Addition and Subtraction of Fractions with Common Denominators

After doing the addition or subtraction, check to see if the fraction can be simplified! Find the prime factorization of the numerator and the denominator and see if anything can cancel out.

### Practice Problems

Combine and simplify the following fractions:
1. $$\displaystyle \frac{1}{5}+\frac{2}{5}$$ (
Solution
Solution: $$\dfrac{3}{5}$$
Details: The fraction bar shows one part shaded in green out of a total of five parts.

This fraction bar shows two parts shaded in blue out of a total of five parts.

Combine $$\dfrac{1}{5}$$ and $$\dfrac{2}{5}$$ to get $$\dfrac{3}{5}$$. Notice how moving the green part with the two blue parts results in a total of three parts out of five parts.

$$\displaystyle \frac{1}{5}+\frac{2}{5}=\frac{3}{5}$$
)
2. $$\displaystyle \frac{2}{7}+\frac{4}{7}$$ (
Solution
Solution: $$\dfrac{6}{7}$$
Details: The fraction bar shows two green parts out of seven parts.

This fraction bar shows four orange parts out of seven parts.

Combine the two fraction bars to get $$\dfrac{6}{7}$$.

$$\displaystyle \frac{2}{7}+\frac{4}{7}=\frac{6}{7}$$
)
3. $$\displaystyle \frac{4}{5}+\frac{2}{5}$$ (
Video Solution
Solution: $$\dfrac{6}{5}$$
Details: This is the same as $$\displaystyle 1\frac{1}{5}$$, but for now, we will represent this as an improper fraction. An improper fraction just means that the numerator is bigger than the denominator.

(Video Source | Transcript)
)
4. $$\displaystyle \frac{5}{6}-\frac{3}{6}$$ (
Video Solution
Solution: $$\dfrac{1}{3}$$
Details:

(Video Source | Transcript)
)
5. $$\displaystyle\frac{4}{9}-\frac{5}{9}$$ (
Solution
Solution:
$$\displaystyle -\frac{1}{9}$$
)
6. $$\displaystyle \frac{11}{5}-\frac{7}{5}$$ (
Solution
Solution:
$$\dfrac{4}{5}$$
)

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