~ 4.4 ~

Half as Much Again

Learning Targets

  • I can use the distributive property to rewrite an expression like x + ½ x as (1+½) x.

  • I understand that “half as much again” and “multiply by (3/2)” mean the same thing.

Notes

Using the distributive property provides a shortcut for calculating the final amount in situations that involve adding or subtracting a fraction of the original amount.

For example, one day Clare runs 4 miles. The next day, she plans to run that same distance plus half as much again. How far does she plan to run the next day?

Tomorrow she will run 4 miles plus ½ of 4 miles. We can use the distributive property to find this in one step:

1 ⋅ 4 + ½ ⋅ 4 = (1 + ½) ⋅ 4

Clare plans to run 1 ½ ⋅ 4, or 6 miles.

This works when we decrease by a fraction, too. If Tyler spent x dollars on a new shirt, and Noah spent 13 less than Tyler, then Noah spent ⅔ x dollars since x − ⅓ x = ⅔ x.

Activities

4.2 Walking Half as Much Again

  1. Complete the table to show the total distance walked in each case.

      • Jada’s pet turtle walked 10 feet, and then half that length again.

      • Jada’s baby brother walked 3 feet, and then half that length again.

      • Jada’s hamster walked 4.5 feet, and then half that length again.

      • Jada’s robot walked 1 foot, and then half that length again.

  2. A person walked x feet and then half that length again.

  3. Explain how you computed the total distance in each case.

  4. Two students each wrote an equation to represent the relationship between the initial distance walked (x) and the total distance walked (y).

      • Mai wrote y = x + ½x.

      • Kiran wrote y=(3/2)x.

  5. Do you agree with either of them? Explain your reasoning.

4.3 More and Less

  1. Match each situation with a diagram. A diagram may not have a match.

    • Han ate x ounces of blueberries. Mai ate ⅓ less than that.

    • Mai biked x miles. Han biked ⅔ more than that.

    • Han bought x pounds of apples. Mai bought ⅔ of that.

  2. For each diagram, write an equation that represents the relationship between x and y.

    • Diagram A

    • Diagram B

    • Diagram C

    • Diagram D

  3. Write a story for one of the diagrams that doesn't have a match.

Add To Your Notes

We can use the distributive property to create equivalent expressions that make it easier for us to calculate an amount plus (or minus) a fraction of that amount.

e.g. x + ½ x = 1 ½ x

In words, “half as much again” and “multiply by 3/2” mean the same thing. Watch and take notes on the video to the right.

Summary

Assignment

Check Google Classroom!