Adding Fractions with Common Denominators

In this video we look at adding fractions with the same denominator.

Adding fractions with common denominators

Fractions with the same denominators can be added by adding the top numbers (how many parts you have) and keeping the denominators (how many pieces the whole was cut into). Be sure to simplify the answer.

\[\begin{align*}
\frac{3}{8} + \frac{1}{8} &= \frac{4}{8} \\
&=\frac{7}{8} \\
\end{align*}\]

When working with mixed numbers we add the whole numbers and then add the fractions. Then simplify the answer.
\[\begin{align*}
2\frac{3}{5} + 1\frac{1}{5} &= 3\frac{4}{5} \\
\end{align*}\]

Example

Find the perimeter of the hexagon below, if the dimensions of the rectangle $AGON$ are $6\tfrac14$ by $3\tfrac14$.

The trick to this problem is that the area of the hexagon $HEXGON$ is the same as the area of the rectangle $AGON$, so all we need to do is add the distance around the perimeter of the rectangle.

\[\begin{align*}
6\frac{1}{4} + 3\frac{1}{4} + 6\frac{1}{4} + 3\frac{1}{4} &= 18 + \frac{4}{4}\\
&= 18 + 1 \\
&= 19 \\
\end{align*}\]

Transcript:

Today, we are going to be adding fractions with common denominators. If I were to ask myself, what is $\tfrac{3}{10}$ + $\tfrac{4}{10}$ (A tenth is how many pieces we cut the whole into)? This is $\tfrac{3}{10}$. And this is what $\tfrac{4}{10}$ looks like.
We have 7 pieces so, together, we have $\tfrac{7}{10}$. If I didn’t have the fraction pieces, it would look like this on paper.
I’ve got $\tfrac{3}{10}$ + $\tfrac{4}{10}$. Now, if I wanted to figure out how much that makes together, 3 + 4 = 7.
So, the answer is $\tfrac{7}{10}$. And remember, the bottom number (denominator) always stays the same.