In this lesson, you'll discover what fractions are and why they're an essential part of mathematics. You'll learn to identify the numerator and denominator, understand what they represent, and see how fractions appear in everyday life.
A fraction represents a part of a whole. When you divide something into equal pieces and take some of those pieces, you're working with fractions!
Imagine cutting a pizza into 8 equal slices and eating 3 of them. You've eaten \(\frac{3}{8}\) (three-eighths) of the pizza. The remaining 5 slices represent \(\frac{5}{8}\) of the pizza.
\(\frac{8}{8} = 1\)
\(\frac{3}{8}\)
Fractions are written with two numbers separated by a horizontal line:
The line between the numbers is called the fraction bar
The numerator tells us how many parts we have or are considering.
In \(\frac{3}{8}\), the numerator is 3
The denominator tells us how many equal parts the whole is divided into.
In \(\frac{3}{8}\), the denominator is 8
Let's see how different fractions look visually using bar models:
When we divide something into 2 equal parts and take 1:
1 out of 2 parts = \(\frac{1}{2}\)
When we divide something into 4 equal parts and take 3:
3 out of 4 parts = \(\frac{3}{4}\)
When we divide something into 5 equal parts and take 2:
2 out of 5 parts = \(\frac{2}{5}\)
A unit fraction has 1 as its numerator. Let's compare \(\frac{1}{3}\) and \(\frac{1}{6}\):
\(\frac{1}{3}\) (one-third)
\(\frac{1}{6}\) (one-sixth)
Notice: Even though 6 > 3, we have \(\frac{1}{3} > \frac{1}{6}\) because when you divide something into fewer pieces, each piece is larger!
Fractions are everywhere! Here are common examples you encounter daily:
Congratulations! You've learned the fundamental concepts of fractions:
Next lesson: We'll explore equivalent fractions and learn how different fractions can represent the same amount!