Fraction Operations
Add, subtract, multiply, and divide fractions
lessons (5)
Adding Fractions with the Same Denominator
Learn how to add fractions when they have the same denominator - just add the numerators!
Adding Fractions with Different Denominators
Learn to add fractions when the bottom numbers are not the same by finding a common denominator.
Subtracting Fractions
Learn how to subtract fractions with the same and different denominators using visual models and step-by-step methods.
Multiplying Fractions
Learn how to multiply fractions by multiplying numerators and denominators, and understand what it means to take a fraction of a fraction.
Dividing Fractions
Learn how to divide fractions using the 'Keep, Change, Flip' method and understand why it works.
Fraction operations extend the four basic operations to parts of wholes. Adding and subtracting fractions requires common denominators so you are combining like-sized pieces. Multiplying fractions means finding a fraction of a fraction - multiply numerators and denominators directly. Dividing by a fraction means finding how many of that fraction fit into another, accomplished by multiplying by the reciprocal.
These operations appear everywhere: halving a recipe (dividing by 2), finding three-quarters of a price (multiplying), or combining fractional measurements. Mastering fraction operations builds the foundation for algebra, where variables often represent fractional quantities.
What Students Will Learn
- Add and subtract fractions with like and unlike denominators
- Multiply fractions and mixed numbers
- Divide fractions using the reciprocal method
- Simplify fraction results to lowest terms
- Solve word problems involving fraction operations
Frequently Asked Questions
Why do we need common denominators for addition but not multiplication?
Addition combines parts of the same size - you can not add thirds and fourths directly. Multiplication finds a part of a part, which works directly: 1/2 of 1/3 is 1/6 (half of each third).
How do I divide by a fraction?
Multiply by its reciprocal (flip it). To divide by 2/3, multiply by 3/2. For example: 4/5 ÷ 2/3 = 4/5 × 3/2 = 12/10 = 6/5.
When should I convert to mixed numbers?
Convert improper fractions (numerator larger than denominator) to mixed numbers for final answers in context. Keep improper fractions when continuing calculations.