Fractions represent parts of a whole. They consist of a numerator (top number) and a denominator (bottom number). Below, you’ll find everything you need to know about fractions.
A fraction is made up of two parts, separated by a fraction bar:
For example, the fraction \( \large \frac{3}{4} \) means the whole is divided into 4 equal parts, and we’re taking 3 of them.
Fractions in Everyday Life:
In the Kitchen
\( \large \frac{1}{2} \) cup of flour, \( \large \frac{3}{4} \) tsp of salt
In Construction
A board \( \large 2\frac{1}{4} \) meters long
In Finance
\( \large \frac{1}{4} \) percentage point, \( \large \frac{1}{3} \) of the budget
The numerator is smaller than the denominator.
The fraction’s value is less than 1.
Combines a whole number and a proper fraction.
The value is greater than 1.
Converting an Improper Fraction to a Mixed Number:
Simplifying involves dividing the numerator and denominator by their greatest common divisor (GCD).
For \( \large \frac{8}{12} \): GCD(8, 12) = 4, so \( \large \frac{8}{12} = \frac{8 \div 4}{12 \div 4} = \frac{2}{3} \)
Expanding involves multiplying the numerator and denominator by the same number.
For \( \large \frac{2}{3} \): Multiply by 4 to get \( \large \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \)
Note: Simplifying or expanding does NOT change the value of a fraction!
To compare fractions:
Solution:
1. Same denominators - add the numerators
2. Different denominators - find a common denominator
1. Same denominators - subtract the numerators
2. Different denominators - find a common denominator
Multiply numerator by numerator and denominator by denominator
Multiply the first fraction by the reciprocal of the second
Understanding fractions is essential for education and everyday tasks alike.
Dive deeper into specific fraction operations by exploring our other pages!