Properties of Numbers

Show your work for each problem.

1.
Which property does demonstrate?
1. a)Commutative Property
2. b)Associative Property
3. c)Identity Property
4. d)Distributive Property
Answer: Commutative Property
The commutative property states that changing the order of numbers in addition or multiplication doesn't change the result. Here, .
2.
Which property shows that ?
1. a)Commutative Property
2. b)Identity Property
3. c)Associative Property
4. d)Zero Property
Answer: Identity Property
The identity property of multiplication states that any number multiplied by 1 equals itself. Here, . The number 1 is the multiplicative identity.
3.
Using the commutative property, if , what does equal?
Answer: 36
The commutative property of multiplication states . Therefore, .
4.
What number makes this true using the identity property:
Answer: 0
The identity property of addition states that . Zero is the additive identity because adding it doesn't change the number. So .
5.
Which property does demonstrate?
1. a)Distributive Property
2. b)Associative Property
3. c)Identity Property
4. d)Commutative Property
Answer: Associative Property
The associative property states that changing how numbers are grouped doesn't change the result. The numbers stay in the same order, only the parentheses move. Both and equal 12.
6.
Use the distributive property to calculate:
Answer: 50
Using the distributive property: . You can verify: .
7.
Which equation does NOT demonstrate the commutative property?
1. a)
2. b)
3. c)
4. d)
Answer:
, but . These are not equal! Subtraction is NOT commutative. The other equations correctly show the commutative property for addition and multiplication.
8.
Use the distributive property to calculate . Hint: Write 13 as .
Answer: 52
1. Rewrite as . What do you get when you distribute? 4 * 10 + 4 * 3
2. Calculate 40
3. Calculate 12
4. Add the results: 52
9.
Use properties to calculate mentally. Hint: .
Answer: 200
1. Rewrite as . What is ? 100
2. Now multiply the result by 2: 200
10.
Add these numbers mentally using properties:
Answer: 70
1. Which two numbers add to make a round number? ( or ) 17 + 3
2. What is ? 20
3. What is ? 50
4. What is ? 70
11.
Use the distributive property:
Answer: 686
. The distributive property also works with subtraction!
12.
Which statement is TRUE about the associative property?
1. a)It works for addition and multiplication only
2. b)It changes the order of numbers
3. c)It only works for addition
4. d)It works for all four operations
Answer: It works for addition and multiplication only
The associative property only works for addition and multiplication. For subtraction: , but . For division: , but . Neither gives the same result!
13.
Calculate using the distributive property by writing .
Answer: 180
1. Rewrite as . Apply the distributive property. 15 * 10 + 15 * 2
2. Calculate 150
3. Calculate 30
4. Add the results: 180
14.
Identify the property used in each step:
Answer: 180
1. From to : Which property changes the order? commutative
2. From to : Which property groups numbers? associative
3. What is ? 12
4. What is ? 180
15.
Use the distributive property to factor:
Answer: 12 * (3 + 2)
1. What is ? 3
2. What is ? 2
3. So . What is ? 5
4. Verify: What is ? 60