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Adding/Subtracting Fractions

Overview

You need a common ground.

What is it?

Combining fractions requires matching denominators.

History

Without a common denominator, you're adding apples to oranges.

Key Idea

Butterfly method or LCD (Lowest Common Denominator).

Practice This Topic

Concept Guide

Plain English: You cannot add slices of pizza if they are cut into different sizes. You have to cut them so they match sizes first. You can't add 'Thirds' to 'Fourths' until they both become 'Twelfths'.

Real-world example: Time management. You work 1/2 an hour, then 1/4 of an hour. Total time worked?

Common Pitfall

Adding the denominators! 1/2 + 1/2 is NOT 2/4. It is 2/2 (1 Whole).

Word Problem
"You run 1/2 mile in the morning and 1/3 mile at night. Total distance?"
Reasoning: Common denominator is 6. 1/2 = 3/6. 1/3 = 2/6. Total: 5/6 miles.

Practice Examples

Butterfly
1 1 (3x1) + (2x1) 5 - + - = ------------- = - 2 3 (2x3) 6
Cross multiply tops, multiply bottoms.