Lesson 1: What is a Fraction?

Property

A fraction is written $\frac{a}{b}$, where $a$ and $b$ are integers and $b \neq 0$. In a fraction, $a$ is called the numerator and $b$ is called the denominator. A fraction is a way to represent parts of a whole. The denominator $b$ represents the number of equal parts the whole has been divided into, and the numerator $a$ represents how many parts are included. The denominator, $b$, cannot equal zero because division by zero is undefined.

Examples

• A chocolate bar is split into 12 equal squares. If you eat 5 squares, you have eaten $\frac{5}{12}$ of the bar.
• A class has 25 students. If 14 are girls, then $\frac{14}{25}$ of the class consists of girls.
• An hour has 60 minutes. If you spend 20 minutes on homework, you have used $\frac{20}{60}$ of the hour.

Explanation

Think of a pizza! The denominator is how many equal slices you cut it into, and the numerator is how many of those slices you get to eat. It's all about representing parts of a complete item or group.

Property

A fraction represents division. The fraction $\frac{a}{b}$ means "$a$ divided by $b$" or "$a \div b$". The numerator (top number) is what we are dividing, and the denominator (bottom number) is what we are dividing by.

Examples

Property

Division of Zero: For any real number $a$, $a \neq 0$

Zero divided by any real number, except itself, is zero.

Division by Zero: For any real number $a$,

Division by zero is undefined.

Examples

• The expression $\frac{0}{15}$ simplifies to $0$, as zero divided by any non-zero number is zero.
• The expression $\frac{-8}{0}$ is undefined, because division by zero is not a defined operation in mathematics.
• For any non-zero value of $k$, the expression $0 \div k$ will always equal $0$.