Unit 2 structure of expirations lesson 4.The associative properties quick check

Answer 1

It seems like you are asking for information about the associative properties, which are fundamental principles in mathematics related to addition and multiplication. Here’s a brief overview:

Associative Properties

1. Associative Property of Addition: The way numbers are grouped in an addition problem does not change the sum. This can be expressed as: \[ (a + b) + c = a + (b + c) \] For example:

   • If you have numbers 2, 3, and 4, you can group them in different ways:
     • (2 + 3) + 4 = 5 + 4 = 9
     • 2 + (3 + 4) = 2 + 7 = 9
   • Both give the same result: 9

2. Associative Property of Multiplication: The way numbers are grouped in a multiplication problem does not change the product. This can be expressed as: \[ (a \times b) \times c = a \times (b \times c) \] For example:

   • If you have numbers 2, 3, and 4, you can group them in different ways:
     • (2 × 3) × 4 = 6 × 4 = 24
     • 2 × (3 × 4) = 2 × 12 = 24
   • Both give the same result: 24

Quick Check Questions

To reinforce understanding, here are a few quick check questions related to the associative properties:

1. Addition:

   • Calculate: (5 + 7) + 2 and 5 + (7 + 2). Are they equal? What do you find?

2. Multiplication:

   • Calculate: (3 × 6) × 2 and 3 × (6 × 2). What result do you get?

3. True or False:

   • The associative property applies to subtraction. True or False? Explain your answer.

4. Practical Application:

   • If you have to add 10, 5, and 2, how would you group them to simplify the calculation? What is the total?

Feel free to ask any specific questions or indicate if you want more detailed examples or explanations!