Properties of Operations

Properties of Operations

Properties of Operations: Vocabulary

• Commutative Property

• Associative Property

• Additive Identity Property

• Multiplicative Identity Property

• Multiplicative Property of Zero

• counterexample

Commutative Property

• the ORDER in which numbers are ADDED or MULTIPLIED does not change the SUM or PRODUCT

• Addition Symbols: x + y = y + x

• Addition Example:  3 + 5 = 5 + 3

• Multiplication Symbols: a * b = b * a

• Multiplication Example:  2 * 4 = 4 * 2

• 
  

Multiple Choice

Which of the following shows the COMMUTATIVE PROPERTY?

• 3 * 6 = 6 * 3

• 2 * 4 = 3 * 4

Multiple Choice

Which of the following show the COMMUTATIVE PROPERTY?

• 4 + 9 = 5 + 8

• 10 + 12 = 12 + 10

Associative Property

• the way in which numbers are GROUPED when they are added or multiplied does not change the SUM or PRODUCT

• Addition Symbols: a + (b + c) = (a + b) + c

• Addition Example: 2 + (3 + 8) = (2 + 3) + 8

• Multiplication Symbols: a * (b * c) = (a * b) * c

• Multiplication Example: 3 * (4 * 5) = (3 * 4) * 5

Multiple Choice

Which of the following shows the ASSOCIATIVE property?

• 2 + ( 3 + 5) = (2 + 3) + 5

• 2 + 4 +8 = (2 + 4) + 8

Multiple Choice

Which of the following shows the ASSOCIATIVE property?

• 2 * 3 = 3 * 2

• (3 * 4) * 9 = 3 * (4 * 9)

Property

• A property is a statement that is true for any number.

Multiplicative Identity

• When any number is multiplied by 1, the product is the number.

• Symbols: x * 1 = x

• Example: 1 * 5 = 5

Multiplicative Property of Zero

• When any number is multiplied by 0, the product is 0.

• Symbols: x * 0 = 0

• Example: 3 * 0 = 0

Multiple Choice

Name the property shown by the statement:

2 * (5 * n) = (2 * 5) * n

• Associative Property of Multiplication

• Associative Property of Addition

• Commutative Property of Multiplication

• Additive Identity Property

Multiple Choice

Name the property shown by the statement:

42 + x + y = 42 + y + x

• Associative Property of Addition

• Additive Identity

• Commutative Property of Addition

Fill in the Blank

Solve the expression: $$-\left(\frac{3}{5}\right)\div\left(\frac{2}{7}\right)\cdot\left(\frac{4}{1}\right)$$

Pay attention to the signs!

Use the associative and commutative properties!

-

/

Fill in the Blank

Solve the expression: $$\frac{\left(-\frac{2}{3}\right)}{\frac{1}{5}}\cdot\left(-\frac{6}{7}\right)$$

Pay attention to the signs!

Use the associative and commutative properties!

/

Fill in the Blank

Solve the expression: $$\frac{\left(-\frac{1}{2}\right)}{\frac{3}{4}}\cdot\frac{5}{6}$$

Pay attention to the signs!

Use the associative and commutative properties!

-

/

Fill in the Blank

Solve the expression: $$\left(-\frac{1}{2}\right)\cdot\left(\frac{3}{4}\right)\cdot\left(-\frac{5}{6}\right)$$

Pay attention to the signs!

Use the associative and commutative properties!

/

Fill in the Blank

Solve the expression: $$\left(-\frac{3}{4}\right)\cdot\left(\frac{4}{5}\right)\cdot\left(-\frac{5}{6}\right)$$

Pay attention to the signs!

Use the associative and commutative properties!

/