Lin and Kiran are trying to calculate . Here is their conversation:
Lin: “I plan to first add and , so I will have to start by finding equivalent fractions with a common denominator.”
Kiran: “It would be a lot easier if we could start by working with the and . Can we rewrite it like ?”
Lin: “You can’t switch the order of numbers in a subtraction problem like you can with addition. is not equal to .”
Kiran: “That’s true, but do you remember what we learned about rewriting subtraction expressions using addition? is equal to .”
Write an expression with three terms that is equivalent to and uses only addition.
If you wrote the terms of your new expression in a different order, would it still be equivalent? Explain your reasoning.
18.3
Activity
Write two expressions for the area of the big rectangle.
Use the distributive property to write an expression that is equivalent to . The boxes can help you organize your work.
Use the distributive property to write an expression that is equivalent to .
Student Lesson Summary
In previous lessons, we learned that subtracting a number gives the same result as adding its opposite. We can apply this relationship to rewrite an expression with subtraction so it uses only addition. Then we can make use of the properties of addition that allow us to add and group in any order. This can make calculations simpler. Example:
We can also organize the work of multiplying signed numbers in expressions. The product can be found by drawing a rectangle with the first factor, , on one side, and the three terms inside the parentheses on the other side:
Multiply by each term across the top:
Reassemble the parts to get the expanded version of the original expression:
Terms are the parts of an expression that are added together. They can be a single number, a variable, or a number and a variable that are multiplied together.
