Concept and Types of Fractions
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What is a Fraction?
A fraction represents a part of a whole. When we divide a whole object or set into equal parts and take some of those parts, we get a fraction.
For example, $\frac{1}{2}$ means one part out of two equal parts.
Components of a fraction:
Numerator
(shows how many parts we take)
In $\frac{3}{4}$, the numerator is $3$
Denominator
(shows into how many parts the whole is divided)
In $\frac{3}{4}$, the denominator is $4$
Fraction Line
(indicates division of numerator by denominator)
Types of Fractions
Proper Fractions
Numerator is less than denominator (a < b)
Represent a part less than 1
Examples: $\frac{1}{2}$, $\frac{3}{4}$, $\frac{2}{5}$
Means less than a whole (e.g., half a pizza)
Improper Fractions
Numerator is greater than denominator (a > b)
Represent an amount greater than 1
Examples: $\frac{5}{3}$, $\frac{7}{4}$, $\frac{11}{5}$
Means more than a whole (e.g., 1½ pizzas)
Unit Fractions
Numerator equals denominator (a = b)
Represent exactly one whole
Examples: $\frac{1}{1}$, $\frac{2}{2}$, $\frac{5}{5}$
Exactly one whole (e.g., a complete pizza)