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.
What Are Fractions and Their Uses
A fraction is made up of two parts, separated by a fraction bar:
- Numerator (top number) - indicates how many parts are taken
- Denominator (bottom number) - shows how many equal parts the whole is divided into
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
Types of Fractions
Proper Fractions
The numerator is smaller than the denominator.
The fraction’s value is less than 1.
Improper Fractions
Mixed Numbers
Combines a whole number and a proper fraction.
The value is greater than 1.
Converting an Improper Fraction to a Mixed Number:
- Divide the numerator by the denominator: \( 17 \div 5 = 3 \) (remainder \( 2 \))
- The quotient is the whole number: \( 3 \)
- The remainder is the new numerator: \( 2 \)
- The denominator stays the same: \( 5 \)
Simplifying and Expanding Fractions
Simplifying Fractions
Simplifying involves dividing the numerator and denominator by their greatest common divisor (GCD).
- Find the GCD of the numerator and denominator
- Divide both by the 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 Fractions
Expanding involves multiplying the numerator and denominator by the same number.
- Choose a number to multiply by
- Multiply both the numerator and denominator
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!
Comparing Fractions
To compare fractions:
- Convert the fractions to a common denominator
- Compare the numerators - a larger numerator means a larger fraction
Solution:
- Find the least common multiple (LCM) of 4 and 3 = 12
- Convert: \( \large \frac{3}{4} = \frac{9}{12} \) and \( \large \frac{2}{3} = \frac{8}{12} \)
- Compare numerators: 9 > 8
- Conclusion: \( \large \frac{3}{4} > \frac{2}{3} \)
Operations with Fractions
Adding Fractions
1. Same denominators - add the numerators
2. Different denominators - find a common denominator
Subtracting Fractions
1. Same denominators - subtract the numerators
2. Different denominators - find a common denominator
Multiplying Fractions
Multiply numerator by numerator and denominator by denominator
Dividing Fractions
Multiply the first fraction by the reciprocal of the second
Quick Tips
- Addition and subtraction require a common denominator
- Multiplication and division don’t need a common denominator
- For division, flip the second fraction and multiply
- Always simplify the final result to its lowest terms
Fractions in Everyday Life
In the Kitchen
- \( \large \frac{2}{3} \) cup of flour
- \( \large \frac{1}{4} \) tsp of salt
- \( \large 1\frac{1}{2} \) cups of milk
In Construction
- Board \( \large 2\frac{1}{4} \) meters long
- Nail \( \large \frac{3}{4} \) inch
- Wall \( \large 3\frac{1}{2} \) meters high
In Finance
- \( \large \frac{1}{4} \) of income for savings
- \( \large \frac{1}{3} \) of company shares
- \( \large 3\frac{1}{2} \)% interest rate
Understanding fractions is essential for education and everyday tasks alike.
Dive deeper into specific fraction operations by exploring our other pages!