Commutative property: The order of numbers doesn't change the result in addition or multiplication. For multiplication: a × b = b × a.
- Read the question carefully
- Examine each option for number reordering
- Identify which property is being demonstrated
- Select the correct answer
(5 × 3) × 2 = 5 × (3 × 2)
This changes grouping, not order → Associative property
8 × 1 = 8
This shows multiplication by 1 → Identity property
7 × 4 = 4 × 7
This changes the order of numbers → Commutative property
6 × (9 + 1) = (6 × 9) + (6 × 1)
This distributes multiplication over addition → Distributive property
C) 7 × 4 = 4 × 7 demonstrates the commutative property of multiplication.
• Commutative property: Order doesn't matter in multiplication
• Pattern recognition: Look for numbers switching positions
• Process of elimination: Identify each property in options
Associative property: The grouping of numbers doesn't change the result in addition or multiplication. For addition: (a + b) + c = a + (b + c).
(a + b) + c = a + (b + c)
The property allows us to regroup numbers without changing the result
(15 + 7) + 3 = __ + (7 + 3)
On the left side: 15 and 7 are grouped together
On the right side: 7 and 3 are grouped together
For the equation to be true, the number that pairs with (7 + 3) must be 15
So (15 + 7) + 3 = 15 + (7 + 3)
Left side: (15 + 7) + 3 = 22 + 3 = 25
Right side: 15 + (7 + 3) = 15 + 10 = 25
Both sides equal 25 ✓
The number 15 goes in the blank: (15 + 7) + 3 = 15 + (7 + 3).
• Associative property: Grouping doesn't matter in addition
• Pattern matching: Identify corresponding elements on both sides
• Verification: Always check that both sides are equal
Distributive property: Multiplying a number by a sum equals multiplying the number by each addend separately and then adding the results: a × (b + c) = (a × b) + (a × c).
9 × (6 + 3) = (9 × 6) + (9 × 3)
Multiply 9 by each number inside the parentheses
Option A: 9 × 6 + 3 = 54 + 3 = 57 (Incorrect)
Option B: (9 × 6) + (9 × 3) = 54 + 27 = 81 (Correct)
Option C: 9 × (6 × 3) = 9 × 18 = 162 (Incorrect)
Option D: (9 + 6) × (9 + 3) = 15 × 12 = 180 (Incorrect)
Original: 9 × (6 + 3) = 9 × 9 = 81
Option B: (9 × 6) + (9 × 3) = 54 + 27 = 81
Both equal 81 ✓
a × (b + c) = (a × b) + (a × c)
9 × (6 + 3) = (9 × 6) + (9 × 3)
B) (9 × 6) + (9 × 3) is equivalent to 9 × (6 + 3) using the distributive property.
• Distributive property: Multiply the outside number by each term inside
• Pattern matching: Match the structure of the property
• Verification: Check that both expressions equal the same value
Identity properties: Special numbers that don't change other numbers when combined. Multiplicative identity: a × 1 = a.
24 × 1 = 24
Any number multiplied by 1 equals itself
This is the multiplicative identity property
One is the identity element for multiplication
A) Commutative: Would involve switching order
B) Associative: Would involve grouping
D) Distributive: Would involve distribution over addition
Only the identity property explains why multiplying by 1 gives the same number
C) Identity property is illustrated by 24 × 1 = 24.
• Multiplicative identity: One is the identity element for multiplication
• Pattern recognition: Look for multiplication by 1
• Process of elimination: Rule out other properties
Mixed properties application: Problems requiring identification of which property is being used in specific contexts.
Left side: 8 × (5 + 3)
Right side: 8 × (3 + 5)
Outside the parentheses: 8 remains the same
Inside the parentheses: 5 + 3 became 3 + 5
Inside the parentheses: 5 + 3 = 3 + 5
This is the commutative property of addition
Left side: 8 × (5 + 3) = 8 × 8 = 64
Right side: 8 × (3 + 5) = 8 × 8 = 64
Both sides equal 64 ✓
A) Commutative property is used in 8 × (5 + 3) = 8 × (3 + 5).
• Commutative property: Order of addition changed inside parentheses
• Pattern recognition: Look for numbers switching positions
• Verification: Confirm both sides are equal
Commutative property: The order of numbers doesn't change the result in addition or multiplication
Associative property: The grouping of numbers doesn't change the result in addition or multiplication
Distributive property: Multiplication can be distributed over addition or subtraction
Identity property: Special numbers that preserve the identity of other numbers when combined
Zero property: Multiplication by zero always results in zero
- Look for order changes: If numbers switch places but result stays same → Commutative
- Look for grouping changes: If parentheses move but result stays same → Associative
- Look for distribution: If multiplication is spread across addition → Distributive
- Look for 0 or 1: If 0 or 1 appears → Identity or Zero property
• Commutative: a + b = b + a and a × b = b × a
• Associative: (a + b) + c = a + (b + c) and (a × b) × c = a × (b × c)
• Distributive: a × (b + c) = (a × b) + (a × c)
• Identity: a + 0 = a and a × 1 = a
• Zero: a × 0 = 0
Commutative, Associative, Distributive, and Identity properties
Analysis: The chart shows performance on different property types in the quizizz.
- Commutative property: Understanding of order changes
- Associative property: Grasp of grouping concepts
- Distributive property: Application of distribution
- Identity property: Recognition of neutral elements
- Overall quizizz score: Comprehensive understanding