Simplifying Numerical Expressions

Simplifying Numerical Expressions

A Shopping Problem

Opening

A Shopping Problem

Watch this video about how Karen and Lucy used the distributive property to solve a problem they encountered while shopping.

Here are the steps that Karen and Lucy followed to figure out the total price of the notebooks:

6($1.85)=6($2$0.15)=6($2)6($0.15)=$12$0.90=$11.10

 

Notice that Karen and Lucy distributed multiplication over subtraction.

  • Can you explain why it is possible to use the distributive property in this way?

VIDEO: Girls Buying Notebooks

 

Math Mission

Opening

Use the distributive property to simplify numerical expressions.

Use the Distributive Property

Work Time

Use the Distributive Property

Use the distributive property, as Karen and Lucy did, to help you find each product. Use mental math when you can.

  1. 7 ⋅ $6.12
  2. 12 ⋅ $2.95
  3. 34412

Hint:

Write the second factor in each problem as a sum or a difference and then apply the distributive property.

Kevin’s Work

Work Time

Kevin's Work

Kevin simplified 10 − (6 + 9), but he made a mistake.

10 − (6 + 9) = 10 − 6 + 9

= 4 + 9

= 13

  • What is Kevin’s error?
  • What is the correct value of the expression?

Hint:

If you work within the parentheses first and add 6 + 9 and then subtract this sum from 10, what answer do you get?

Justify

Work Time

Justify

The table shows why 10 − (6 + 9) is equal to 10 − 6 − 9.

  • Work on the table and fill in the missing justifications.
  • Show that 5 − (12 − 4) can be rewritten as 5 − 12 + 4.

HANDOUT: Justifying Equations

Hint:

To show that 5 – (12 – 4) can be rewritten as 5 – 12 + 4, remember that subtracting (12 – 4) is the same as adding the opposite of (12 – 4).

Prepare a Presentation

Work Time

Prepare a Presentation

Use your work to show how you can use the distributive property to help you evaluate expressions with negative numbers.

Challenge Problem

  • For negative values of a, b, and c, is a(b + c) always negative, always positive, or sometimes positive and sometimes negative?
  • Justify your answer.

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about your classmates’ use and explanations of the distributive property.

Hint:

As your classmates present, ask questions such as:

  • How did you figure out how to rewrite the second factor? What property did you use?
  • Can you show where you used the distributive property to show that 5 - (12 - 4) can be rewritten as 12 - 5 + 4?

Simplify Numerical Expressions

Work Time

Simplify Numerical Expressions

Simplify each expression:

  1. 2(12+34)
  2. 131415(3)(4)(5)(6)
  3. 25(375)+67
  4. 2.75(3.25)+2.75(6.75)
  5. (4.8+0.36)÷(6)

The Distributive Property

Formative Assessment

Summary of the Math: The Distributive Property

Read and Discuss

Distributive Property

a ⋅ (b + c) = (ab) + (ac), where a, b, and c can be any numbers, including negative numbers.

Examples:

−5(2 + 3) = (−5 ⋅ 2) + (−5 ⋅ 3)

= −10 + (−15)

= −25

7 − (3 + 5) = 7 + (−1)(3 + 5)

= 7 − 3 − 5

= −1

Hint:

Can you:

  • Give an example that shows how you can use the distributive property to evaluate a multiplication problem?
  • Describe how you can use the distributive property to evaluate expressions, particularly expressions with negative numbers?

Reflect On Your Work

Work Time

Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

An example of a situation in which I used something that I learned in math class is …