Parts and Wholes - Introduction to Fractions

A fraction represents a part of a whole or a part of a collection. Imagine a whole circular chapati divided into 4 equal sectors; each sector represents the fraction $\frac{1}{4}$ of the whole chapati.

The Numerator and Denominator define the fraction. The Denominator (bottom number) tells us how many equal parts the whole is divided into, while the Numerator (top number) tells us how many parts are being considered. For example, in a rectangle with 5 equal horizontal stripes where 2 are colored blue, the fraction of blue stripes is $\frac{2}{5}$.

Equivalent Fractions are different fractions that represent the same value or area. For instance, $\frac{1}{2}$ of a square (cutting it down the middle) covers exactly the same amount of space as $\frac{2}{4}$ of the same square (cutting it into four smaller squares and taking two).

Proper and Improper Fractions describe the size of the part relative to a single whole. A proper fraction like $\frac{3}{8}$ is less than 1 whole because the numerator is smaller than the denominator. An improper fraction like $\frac{5}{3}$ is greater than 1 whole and can be visualized as one full object plus $\frac{2}{3}$ of another identical object.

Mixed Numbers combine a whole number and a proper fraction. For example, $2 \frac{1}{2}$ represents two whole units and one-half of a third unit, often visualized as two full glasses of juice and one glass filled halfway.

Finding a fraction of a collection involves dividing the total group into equal parts. If you have 12 marbles and want to find $\frac{1}{3}$, you arrange them into 3 equal groups of 4; thus, $\frac{1}{3}$ of 12 is 4.

Like and Unlike Fractions: Fractions with the same denominator are called 'Like Fractions' (e.g., $\frac{1}{7}$ and $\frac{4}{7}$), which are easy to compare visually. Fractions with different denominators are called 'Unlike Fractions' (e.g., $\frac{1}{2}$ and $\frac{1}{3}$).