Fractions - Addition and Subtraction of Like Fractions

Definition of Like Fractions: Like fractions are fractions that have the exact same denominator. Visually, imagine two identical rectangular bars both divided into 8 equal parts. Any fraction representing parts of these bars, such as $\frac{2}{8}$ and $\frac{5}{8}$, are like fractions because the size of each part is the same.

The Role of the Denominator: In the addition and subtraction of like fractions, the denominator tells us the total number of equal parts in one whole. Since the parts are of the same size, the denominator remains unchanged during the calculation.

Adding Like Fractions: To add like fractions, we simply add the numerators together and write the sum over the common denominator. For example, if you have a pizza cut into 6 slices and you take 1 slice ($\frac{1}{6}$) and your friend takes 2 slices ($\frac{2}{6}$), together you have $\frac{1+2}{6} = \frac{3}{6}$ of the pizza.

Subtracting Like Fractions: To subtract like fractions, we subtract the smaller numerator from the larger numerator and keep the common denominator. Visually, if a strip of paper is divided into 5 equal sections and 4 are colored ($\frac{4}{5}$), and you erase the color from 1 section ($\frac{1}{5}$), you are left with $\frac{4-1}{5} = \frac{3}{5}$ colored sections.

Fractions Representing a Whole: When the result of an addition gives a numerator equal to the denominator, it represents one whole unit. For example, $\frac{3}{7} + \frac{4}{7} = \frac{7}{7}$, which is equal to $1$. This is like filling all the empty slots in a container to make it full.

Comparing Numerators: When working with like fractions, we only focus on the numerators to determine the quantity. Adding $\frac{2}{10}$ and $\frac{3}{10}$ is as simple as adding 2 and 3 because the 'units' (tenths) are identical.