Building Intuitions About Fraction Operations

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• Egg Carton Addition
• Egg Carton Multiplication
• Egg Carton Subtraction
• Egg Carton Division

Fraction subtraction can be modeled by both the take-away and difference models that we saw in lesson 2, "Basic Operations". We can remove 'eggs' from a carton to find out what's left, or we can compare two fraction models and see what the difference is between them. Let's look at a simple problem from both viewpoints. Consider 11/12 - 1/4:

Now, the difference, or comparison model:

You can see that the equivalent fraction answers - 8/12. 4/6, and 2/3 - are evident in both models, the answer is the same, but the situations are quite different. Which model would you use for the following situations?

• Sally had 1 and 1/2 dozen cat's eye marbles in her collection. She gave 1/3 of a dozen to her best friend when she moved.
• Martin has 7/10 of a package of trading cards. His friend Carl has 2/5 of a package.