Parts and Wholes - Equivalent Fractions

A fraction represents a part of a whole or a collection. For example, if a circular pizza is cut into 4 equal slices, each slice is represented as $\frac{1}{4}$ of the whole pizza.

In any fraction $\frac{a}{b}$, the top number '$a$' is called the Numerator (the number of parts we have) and the bottom number '$b$' is the Denominator (the total number of equal parts the whole is divided into). Visually, if a rectangle is divided into 5 equal strips and 3 are shaded, the fraction is $\frac{3}{5}$.

Equivalent Fractions are different fractions that name the same amount or part of a whole. Imagine two identical chocolate bars: one divided into 2 equal halves (where you eat 1) and another divided into 4 equal quarters (where you eat 2). In both cases, you have eaten the same amount because $\frac{1}{2} = \frac{2}{4}$.

To find an equivalent fraction, multiply both the numerator and the denominator by the same non-zero number. For example, $\frac{2}{3}$ becomes $\frac{4}{6}$ if you multiply both parts by 2. This is like taking a shaded area and cutting all existing parts into smaller equal pieces.

Equivalent fractions can also be found by dividing both the numerator and the denominator by their common factor. For instance, the fraction $\frac{10}{20}$ can be simplified to $\frac{1}{2}$ by dividing both the top and bottom by 10.

You can test if two fractions $\frac{a}{b}$ and $\frac{c}{d}$ are equivalent using cross-multiplication. If the product of $a \times d$ is equal to the product of $b \times c$, the fractions are equivalent.

A fraction is in its simplest form when the only common factor between the numerator and denominator is 1. For example, $\frac{3}{4}$ is in simplest form, whereas $\frac{6}{8}$ is not because both 6 and 8 can be divided by 2.