IM 7.6.18 Lesson: Subtraction in Equivalent Expressions

Find each sum or difference mentally.

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 that is equivalent to

that uses addition instead of subtraction.

If you wrote the terms of your new expression in a different order, would it still be equivalent? Explain your reasoning.

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 .

Average these four numbers. What do you notice?

Choose a different date that is in a location where it has a date above, below, and to either side. Average these four numbers. What do you notice?

Explain why the same thing will happen for any date in a location where it has a date above, below, and to either side.