Fractions:

Addition and Subtraction of Fractions with Common Denominators

When adding and subtracting fractions, we need the denominators to be the same, and then we can add or subtract the numerators.

Video Source (04:57 mins) | Transcript

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.

Additional Resources

Khan Academy: Adding Fractions with Like Denominators (03:17 mins, Transcript)
Khan Academy: Subtracting Fractions with Like Denominators (02:25 mins, Transcript)

Practice Problems

Combine and simplify the following fractions:

$\frac{1}{5}+\frac{2}{5}$

$\frac{2}{7}+\frac{4}{7}$

$\frac{4}{5}+\frac{2}{5}$

$\frac{5}{6}-\frac{3}{6}$

$\frac{4}{9}-\frac{5}{9}$

$\frac{11}{5}-\frac{7}{5}$

Solutions

$\frac{3}{5}$ (Written Solution)

The fraction bar shows 1 part shaded in green out of a total of 5 parts.

$This image shows a rectangle that is divided into five equal bars and one out of five bars is shaded in green. There is a fraction one over five to the right of the rectangle.$

This fraction bar shows 2 parts shaded in blue out of a total of 5 parts.

$This image shows a rectangle that is divided into five equal bars and two out of five bars are shaded in blue. There is a fraction: two over five on the right of the rectangle.$

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

$This image shows a rectangle that is divided into five equal bars. Two out of five bars are shaded in blue and one out of five bars is shaded in green. There is a fraction, three over five, listed on the right of the rectangle.$

$\frac{1}{5}+\frac{2}{5}=\frac{3}{5}$
$\frac{6}{7}$ (Written Solution)

The fraction bar shows, 2 green parts out of 7 parts.

$This image shows a rectangle that is divided into seven equal bars and two out of seven bars are shaded in green. There is a fraction, two over seven, listed on the right of the rectangle.$

This fraction bar shows 4 orange parts out of 7 parts.

$This image shows a rectangle that is divided into seven equal bars and four out of seven bars are shaded in orange. There is a fraction: four over seven on the right of the rectangle.$

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

$This image shows a rectangle that is divided into seven equal bars. Four out of seven bars are shaded in orange and two out of seven bars are shaded in green. There is a fraction, six over seven, listed on the right of the rectangle.$

$\frac{2}{7}+\frac{4}{7}=\frac{6}{7}$
$\frac{6}{5}$ (Solution Video | Transcript | Written Solution)

This is the same as $1\frac{1}{5}$, but for now, we will represent this as an improper fraction. An improper fraction just means that the numerator is bigger than the denominator.
$\frac{1}{3}$ (Solution Video | Transcript)
$-\frac{1}{9}$
$\frac{4}{5}$