Properties of Mathematics

1.9 properties

by Amber Clemens

​Commutative property of Addition

• ​format: a+b=b+a

• ​description: changing the order doesn't change the answer

• ​example: 5+3=3+5

Multiple Choice

What is the missing number?

6 + ____ = 7 + 6

• 4

• 13

• 7

• 9

Multiple Choice

Which one of the following illustrates the Commutative Property of Addition?

• 5 + 7 = 7 + 5

• 5 + 7 = 4 + 8

• 5 + 7 = 3 + 9

• 5 + 7 = 10 + 2

​Associative property of Addition

• ​format: (a+b)+c = a+(b+c)

• ​description: changing the grouping doesn't change the answer

• ​example: (3+5)+25= 3+(5+25)

Multiple Choice

What is the missing number?

4 + (____ + 5) = (4 + 7) + 5

• 4

• 5

• 16

• 7

Multiple Choice

Which one of the following illustrates the Associative Property of addition?

• 3 + ( 2 + 4) = (4 + 4) + 1

• 3 + (2 + 4) = (3 + 2) + 4

• 3 + (2 + 4) = (5 + 2) + 2

• 3 + (2 + 4) = (2 + 6) + 1

​Additive Identity

• ​format: a +0 = a

• ​description: adding zero doesn't change the value

• ​example: 5+0=5

Multiple Choice

Pick the answer that is an example of the additive identity

• a + (-a) = 0

• 1 + 1 = 2

• a + 0 = a

• a + b = b + a

​Additive Inverse

• ​format: a+ -a = 0

• ​description: a number and its opposite equal zero

• ​example: 8+ -8 = 0

Multiple Choice

What is the additive inverse of 2/3?

• -2/3

• 3/2

• 2/3

• -3/2

Multiple Choice

What is the ADDITIVE INVERSE of -7

• -7

• ^-1/₇

• ¹/₇

• 7

​Commutative property of mulitplication

• ​format: ab=ba

• ​description: changing the order doesn't change the answer

• ​example: 5(3)=3(5)

Multiple Choice

Which of the following illustrates the Commutative Property of Multiplication?

• 3 x 4 = 6 x 2

• 3 x 4 = 12 x 1

• 3 x 4 = 2 x 6

• 3 x 4 = 4 x 3

​Associative Property of multiplication

• ​format: (ab)c= a(bc)

• ​description: changing the grouping doesn't change the answer

• ​example: (5*2)*4 = 5*(2*4)

Multiple Choice

5 × (2 × 9) is also equal to:

• 5 x (2 - 9)

• 5 x (2 + 9)

• (5 x 2) x 9

• (5 x 2) + 9

Multiple Choice

Which of the following illustrates the Associative Property of multiplication?

• 4 × (3 × 6) = (3 × 12) × 2

• 4 × (3 × 6) = (6 × 6) × 2

• 4 × (3 × 6) = (4 × 3) × 6

• 4 × (3 × 6) = (3 × 8) × 3

​Multiplicative Identity

• ​format: a*1=a

• ​description: a number multiplied by one doesn't change the number

• ​example: 4*1=4

Multiple Choice

What property is this? 1a = a

• Commutative Property of Multiplication

• Multiplicative Inverse

• Multiplicative Identity

• Distributive Property

​Multiplicative Inverse

• ​format:

​

• ​description: a number times it's reciprocal equals

• ​example:

Multiple Choice

Find the reciprocal of 7

• $$\frac{1}{7}$$

• $$\frac{7}{1}$$

• 1 $$\frac{1}{7}$$

• $$\frac{7}{7}$$

Multiple Choice

Find the reciprocal of $$\frac{7}{11}$$  

• 1 $$\frac{1}{7}$$  

• $$\frac{11}{11}$$  

• $$\frac{11}{7}$$  

• $$\frac{7}{7}$$  

​Distributive property of multiplication over addition

• ​format: a(b+c)= ab+ac

• ​description: multiply the outside value by each term inside the parenthesis

• ​example: 4(2+3)= 4(2) + 4(3)

Multiple Choice

2(c - 8)

• 2c - 16

• 2c + 16

• 2c - 8

• c - 16

Multiple Choice

e(f + g) is equivalent to:

• ef + g

• f + g

• f + eg

• ef + eg