Addition and Subtraction of Fractions with Common Denominators

When adding and subtracting fractions, we need the denominators to be the same, 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

$\displaystyle \frac{1}{5}+\frac{2}{5}$ (
Solution

x

Solution: $\dfrac{3}{5}$
Details: The fraction bar shows one part shaded in green out of a total of five parts.
$This image shows a rectangle that is divided into five equal bars and one out of five bars is shaded in green. There is a fraction, 1 over 5, shown to the right of the rectangle.$

This fraction bar shows two parts shaded in blue out of a total of five parts.
$This image shows a rectangle that is divided into five equal bars and two out of five bars are shaded in blue. There is a fraction, 2 over 5, shown to the right of the rectangle.$

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.
$This image shows a rectangle that is divided into five equal bars. Two out of five bars are shaded in blue and one out of five bars is shaded in green. There is a fraction, 3 over 5, shown to the right of the rectangle.$
$\displaystyle \frac{1}{5}+\frac{2}{5}=\frac{3}{5}$

)
$\displaystyle \frac{2}{7}+\frac{4}{7}$ (
Solution

x

Solution: $\dfrac{6}{7}$
Details: The fraction bar shows two green parts out of seven parts.
$This image shows a rectangle that is divided into seven equal bars and two out of seven bars are shaded in green. There is a fraction, 2 over 7, shown to the right of the rectangle.$

This fraction bar shows four orange parts out of seven parts.
$This image shows a rectangle that is divided into seven equal bars and four out of five bars are shaded in orange. There is a fraction, 4 over 7, shown to the right of the rectangle.$

Combine the two fraction bars to get $\dfrac{6}{7}$.
$This image shows a rectangle that is divided into seven equal bars. Four out of seven bars are shaded in orange and two out of seven bars are shaded in green. There is a fraction, 6 over 7, shown to the right of the rectangle.$
$\displaystyle \frac{2}{7}+\frac{4}{7}=\frac{6}{7}$

)
$\displaystyle \frac{4}{5}+\frac{2}{5}$ (
Video Solution

x

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)

)
$\displaystyle \frac{5}{6}-\frac{3}{6}$ (
Video Solution

x

Solution: $\dfrac{1}{3}$
Details:

(Video Source | Transcript)

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$ \displaystyle\frac{4}{9}-\frac{5}{9}$ (
Solution

x

Solution:
$\displaystyle -\frac{1}{9}$

)
$\displaystyle \frac{11}{5}-\frac{7}{5}$ (
Solution

x

Solution:
$\dfrac{4}{5}$

)

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