2.12.1Name Number Number

PropertiesPropertiesLearning Target:Learning Target: Use number properties. Use number properties.Success Criteria:Success Criteria: • I can identify number properties in equations.• I can identify number properties in equations.• I can use number properties to write equivalent expressions.• I can use number properties to write equivalent expressions.

Explore and Grow

Chapter 2 ⎜ Lesson 1 53

Use all four numbers on the game card below to write an expression that has a value of 24. You can use any number of the four operations:addition, subtraction, multiplication, and division.

Reasoning Write another expression that has a value of 24 using the game card above.

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Think and Grow: Modeling Real LifeThink and Grow: Use Number Properties

54

1. 1. Complete the equation. Identify the property shown.

9 × 15 = 15 ×

2. 2. Use the Distributive Property to find 8 × 49.

Commutative Properties: Changing the order of addends or factors does not change the sum or product.

Associative Properties: Changing the grouping of addends or factors does not change the sum or product.

Addition Property of Zero: The sum of any number and 0 is that number.

Multiplication Properties of Zero and One: The product of any number and 0 is 0.The product of any number and 1 is that number.

Distributive Property: Multiplying a sum (or difference) by a number is the same as multiplying each number in the sum (or difference) by the number and adding (or subtracting) the products.

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Example Complete the equation. Identify the property shown.

Example Use the Distributive Property to find 6 × 38.

3 + 5 = 5 + 33 × 5 = 5 × 3

(2 + 4) + 1 = 2 + (4 + 1)(2 × 4) × 1 = 2 × (4 × 1)

8 + 0 = 8

5 × 0 = 07 × 1 = 7

4 × (3 + 1) = (4 × 3) + (4 × 1)

4 × (3 − 1) = (4 × 3) − (4 × 1)

32 + 29 + 8 = 29 + + 8 Property of Addition

6 × 38 = 6 × ( + ) Write 38 as a sum.

= (6 × ) + (6 × ) Distributive Property

= + Multiply.

= Add.

Key Idea Here are several number properties.

You can also write 38 as a difference.

6 × 38 = 6 × (40 − 2)

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Chapter 2 ⎜ Lesson 1 55

Name

Complete the equation. Identify the property shown.

Use the Distributive Property to find the product.

Use a property to find the sum or product. Identify the property you used.

12. 12. Your friend uses the Distributive Property to find 4 × 46. Is yourfriend correct? Explain.

4 × 46 = 4 × (50 − 4)= (4 × 50) − (4 × 4)= 200 − 16= 184

13. 13. DIG DEEPER Can you use the Associative Property with subtraction? Explain. Use an example to justify your answer.

3. 3. 1 × = 17

7. 7. 5 × 97

9. 9. 4 + (6 + 27)

5. 5. 23 + 145 + 7 = 23 + 7 +

4. 4. 248 + 0 =

8. 8. 83 × 7

10. 10. 5 × 49 × 0 11. 11. 11 + 16 + 89

6. 6. 3 × (10 + 2) = (3 × 10) + (3 × )

Apply and Grow: Practice©

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Think and Grow: Modeling Real Life

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15. 15. DIG DEEPER Tickets for a school play are sold out. The auditorium has 4 sections. Each section has 25 rows with 15 seats in each row. Each ticket costs $2. How much money is raised in ticket sales?

Example There are three types of animals at a shelter. How many animals are there in all?

Find the number of each type of animal at the shelter.

Dogs: 4 = 4 × 4 =

Cats: 5 = 5 × 4 = 1 = So, + = .

Rabbits: 1 =

Add the numbers of dogs, cats, and rabbits.

16 + 22 + 4 = + + Commutative Property of Addition

= + Add.

= Add.

There are animals in all.

14. 14. You play three different video games in an evening. How many minutes do you play video games in all?

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Animals at a Shelter

Dogs Cats Rabbits

Each = 4 pets.

Minutes Playing a Video Game

Dancing Puzzle Racing

Each = 6 minutes.©

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Name 2.12.1Homework

& PracticeLearning Target:Learning Target: Use number properties. Use number properties.

57Chapter 2 ⎜ Lesson 1

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Example Complete the equation. Identify the property shown.

Example Use the Distributive Property to find 9 × 45.

(6 × 25) × 4 = 6 × (25 × ) Property of Multiplication

4

9 × 45 = 9 × ( + ) Write 45 as a sum.

= (9 × ) + (9 × ) Distributive Property

= + Multiply.

= Add.

40

40

360 45

405

5

5

Associative

Complete the equation. Identify the property shown.

Use the Distributive Property to find the product.

Use a property to find the sum or product. Identify the property you used.

1. 1. 687 × = 0

5. 5. 4 × 78

7. 7. 6 × 43

3. 3. 4 × 7 × 25 = 4 × × 7

2. 2. 15 + 13 = 13 +

6. 6. 23 × 8

8. 8. 339 + 0 + 54 9. 9. 25 × 8 × 2

4. 4. 6 × (20 − 3) = (6 × 20) − (6 × )

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10. 10. Number Sense To find 29 + (11 + 16), your friend adds 29 and 11. Then he adds 16 to the sum. Which property did he use and why?

12. 12. Number Sense Newton uses two properties to rewrite the expression (4 × 23) × 25. Identify the properties he uses. Why would Newton use these properties?

11. 11. Writing Explain how using properties can help you mentally find answers to problems.

13. 13. Modeling Real Life Before performing an experiment, students are asked to predict which substance will melt an ice cube the fastest. How many students make a prediction? Identify the property you used.

14. 14. Modeling Real Life An apartment building has 35 floors with 12 apartments on each floor. There are 300 apartments that have 2 bedrooms. The rest of the apartments have 1 bedroom. How many 1-bedroom apartments are in the building? How can you use the Distributive Property to help solve this problem mentally?

Review & RefreshFind the sum. Check whether your answer is reasonable.

16. 16. 17. 17. 15. 15. 8,968+ 4,683

75,310+ 8,596

90,583+ 19,877

(4 × 23) × 25 = 23 × (4 × 25)

Ice Cube Experiment Predictions

Salt Sugar Water

Each = 8 students.

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