Fractions - Introduction to Fractions

A fraction represents a part of a whole or a part of a collection of objects. For example, if you divide a circular cake into $4$ equal pieces and eat $1$ piece, you have eaten a fraction of the cake. Visually, imagine a circle with one slice shaded out of four equal segments.

Every fraction has two parts separated by a horizontal line called the fraction bar. The number above the line is the Numerator (how many parts we have), and the number below is the Denominator (the total number of equal parts the whole is divided into). In $\frac{3}{5}$, $3$ is the numerator and $5$ is the denominator.

Proper Fractions are fractions where the numerator is smaller than the denominator, such as $\frac{2}{7}$ or $\frac{4}{9}$. These fractions always represent a value less than $1$ whole. Visually, the shaded area is smaller than the entire shape.

Improper Fractions have a numerator that is equal to or greater than the denominator, like $\frac{5}{4}$ or $\frac{8}{3}$. This means the value is equal to or more than $1$ whole. Imagine having two identical squares, one fully shaded and the other having only one part shaded.

Mixed Fractions consist of a whole number and a proper fraction combined together, such as $2 \frac{1}{3}$. This represents $2$ complete wholes and $\frac{1}{3}$ of another whole. Visually, you would see two full circles and one circle with only one-third shaded.

Unit Fractions are fractions that always have $1$ as the numerator, like $\frac{1}{2}$, $\frac{1}{5}$, or $\frac{1}{10}$. These represent exactly one part out of the total equal parts of a whole.

Like Fractions are groups of fractions that have the same denominator, such as $\frac{1}{8}$, $\frac{3}{8}$, and $\frac{5}{8}$. Unlike Fractions have different denominators, such as $\frac{1}{2}$ and $\frac{1}{3}$. Like fractions are easy to compare because the size of each part is the same.

Equivalent Fractions are different fractions that represent the same part of a whole. For example, $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent. Visually, if you shade half of a rectangle and then divide that same rectangle into four parts, you will see that two of those four parts cover the exact same area as the original half.