Parts and Wholes - Addition and Subtraction of Fractions

A fraction represents a part of a whole or a collection. It consists of a Numerator (the top number, indicating how many parts are taken) and a Denominator (the bottom number, indicating the total number of equal parts). Imagine a pizza cut into $8$ equal slices; if you take $3$ slices, you have $\frac{3}{8}$ of the pizza. Visually, the denominator tells you how small the slices are, while the numerator tells you how many you have.

Like Fractions are fractions that have the same denominator, such as $\frac{1}{5}$ and $\frac{4}{5}$. Visually, these fractions represent parts of identical wholes that have been divided into the same number of equal-sized pieces. This makes them easy to compare, add, or subtract because the 'size' of the parts is the same.

Unlike Fractions have different denominators, like $\frac{1}{2}$ and $\frac{1}{3}$. This means the whole is divided into different sized pieces (halves are larger than thirds). To visualize this, imagine one chocolate bar cut into $2$ large blocks and another identical bar cut into $3$ smaller blocks; you cannot simply add '1 block' from each because they are not the same size.

Equivalent Fractions are different fractions that represent the exact same part of a whole. For example, $\frac{1}{2}$, $\frac{2}{4}$, and $\frac{4}{8}$ are all equivalent. If you shade half of a circle, then draw a line to split it into $4$ parts, you will see that $2$ of those $4$ parts cover the same shaded area as the original half.

To perform Addition of Like Fractions, we simply add the numerators and keep the denominator the same. For example, $\frac{2}{6} + \frac{3}{6} = \frac{5}{6}$. If you have $2$ pieces of a $6$-segment orange and your friend gives you $3$ more pieces of the same orange, you now have $5$ out of the $6$ pieces.

To perform Subtraction of Like Fractions, we subtract the second numerator from the first while keeping the denominator constant. If you have $\frac{7}{10}$ of a meter of ribbon and you cut off $\frac{3}{10}$ of a meter, you are left with $\frac{7-3}{10} = \frac{4}{10}$ of a meter.

To add or subtract Unlike Fractions, we must first convert them into Like Fractions by finding a Common Denominator. We usually use the Least Common Multiple (LCM) of the denominators. Visually, this is like taking different-sized slices and cutting them further until all pieces across both wholes are exactly the same size.

The Whole can be represented as a fraction where the numerator and denominator are the same, such as $\frac{4}{4} = 1$ or $\frac{10}{10} = 1$. Visually, this means you have all the pieces that make up the complete object.