Lesson 1.12
Fraction Operations
Fractions are the gatekeepers of algebra. If you can add, subtract, multiply, and divide fractions with confidence, you can handle any algebraic expression that comes your way.
Introduction
In this final lesson of Unit 1, we bring together everything: sign rules, order of operations, and number properties — all applied to fractions. Master these and you're ready for Unit 2.
Past Knowledge
You know integer operations, sign rules, and how to find common denominators.
Today's Goal
Add, subtract, multiply, and divide fractions — including those with negative signs.
Future Success
Solving equations often produces fractional answers. These skills are non-negotiable.
Key Concepts
1. Multiplying Fractions
Multiply straight across — tops with tops, bottoms with bottoms. Simplify after (or cross-cancel before).
2. Dividing Fractions
Keep, Change, Flip: Keep the first fraction, change ÷ to ×, flip the second fraction.
3. Adding & Subtracting Fractions
Find a common denominator (LCD).
Rewrite each fraction with the LCD.
Add/subtract the numerators only.
Simplify if possible.
Worked Examples
Example 1: Multiply Fractions
BasicEvaluate .
Multiply Across
No common factors between 10 and 21, so is already simplified.
Example 2: Divide Fractions
IntermediateEvaluate .
Keep, Change, Flip
Cross-Cancel & Multiply
(3 and 9 share factor 3; 4 and 8 share factor 4)
Example 3: Add with Different Denominators
AdvancedEvaluate .
LCD of 5 and 3
Convert
Add Numerators
Common Pitfalls
Adding Across the Denominators
. You must find a common denominator, not add tops and bottoms separately.
Forgetting "Keep, Change, Flip"
When dividing, you must flip the second fraction and change the operation to multiplication. Flipping the first fraction gives the wrong answer.
Real-Life Applications
Recipes are built on fractions. If a recipe calls for cup of flour and you want to make batches, you need cups of flour. Fraction skills power every kitchen and workshop.
Practice Quiz
Loading...