Adding Fractions with Like Denominators

How to Add Fractions with the Same Denominator 

Adding fractions with the same denominator (Sometimes, it is called adding fractions with like denominators) is straightforward. Follow these simple steps:

Steps to Add Fractions

1. Check the Denominators: Ensure the fractions have the same denominator.
   For example, $$\frac{3}{8}+\frac{1}{8}$$
   Both terms have the same denominator, which is 8.
2. Add the Numerators:  Keep the denominator the same and add the numerators.
   $$\frac{3}{8}+\frac{1}{8}=\frac{3+1}{8}=\frac{4}{8}$$
3. Simplify the fraction if Necessary: If the resulting fraction can be simplified, do so.
   $$\frac{3}{8}+\frac{1}{8}=\frac{3+1}{8}=\frac{4}{8}=\boxed{\frac{1}{2}}$$

Graphical Explanation

Consider the fractions $\dfrac{3}{8} $ and $\dfrac{1}{8} $

1. Visual Representation: Each fraction represents parts of a whole divided into 8 equal parts.

   $\dfrac{3}{8} $	$\dfrac{1}{8} $
   3 parts of a whole divided into 8 equal parts.	1 parts of a whole divided into 8 equal parts.

2. Adding the Numerators

$\dfrac{3}{8} $	$+$	$\dfrac{1}{8} $	$=$	$\dfrac{4}{8} $	$=$	$\dfrac{1}{2} $
	$+$		$=$		$=$

When adding fractions with the same denominator, maintain the same denominator and add the numerators. The same denominator means that the two fractions represent equal parts of a single whole, which is why they can be combined (since each fractional piece is the same size) as shown above.

Glimpse into our exercises on this topic