Let's go through each property and the corresponding expression step-by-step:
### Identity Property of Addition:
The identity property of addition states that any number plus zero is that number itself.
[tex]\[ 8 + 0 = 8 \][/tex]
Thus, [tex]\( 8 + 0 = 8 \)[/tex].
### Multiplication Property of Zero:
The multiplication property of zero states that any number multiplied by zero is zero.
[tex]\[ 21 \times 0 = 0 \][/tex]
Thus, [tex]\( 21 \times 0 = 0 \)[/tex].
### Associative Property of Multiplication:
The associative property of multiplication states that the way in which numbers are grouped does not change their product.
[tex]\[ (5 \times 2) \times 3 = 5 \times (2 \times 3) \][/tex]
First, calculate each side:
[tex]\[ (5 \times 2) \times 3 = 10 \times 3 = 30 \][/tex]
[tex]\[ 5 \times (2 \times 3) = 5 \times 6 = 30 \][/tex]
Thus, [tex]\( (5 \times 2) \times 3 = 5 \times (2 \times 3) \)[/tex] and both equal 30.
### Identity Property of Multiplication:
The identity property of multiplication states that any number multiplied by one is that number itself.
[tex]\[ 34 \times 1 = 34 \][/tex]
Thus, [tex]\( 34 \times 1 = 34 \)[/tex].
### Inverse Property of Addition:
The inverse property of addition states that any number plus its additive inverse (opposite) is zero.
[tex]\[ 19 + (-19) = 0 \][/tex]
Thus, [tex]\( 19 + (-19) = 0 \)[/tex].
### Commutative Property of Multiplication:
The commutative property of multiplication states that the order in which two numbers are multiplied does not change their product.
[tex]\[ 12 \times 20 = 20 \times 12 \][/tex]
First, calculate each side:
[tex]\[ 12 \times 20 = 240 \][/tex]
[tex]\[ 20 \times 12 = 240 \][/tex]
Thus, [tex]\( 12 \times 20 = 20 \times 12 \)[/tex].
### Distributive Property:
The distributive property states that a number multiplied by the sum of two numbers is equal to the sum of the individual products of the number and each addend.
[tex]\[ 5 \times (2 + 4) = 5 \times 2 + 5 \times 4 \][/tex]
First, calculate the left side:
[tex]\[ 5 \times (2 + 4) = 5 \times 6 = 30 \][/tex]
Then, calculate the right side:
[tex]\[ 5 \times 2 + 5 \times 4 = 10 + 20 = 30 \][/tex]
Thus, [tex]\( 5 \times (2 + 4) = 5 \times 2 + 5 \times 4 \)[/tex] and both equal 30.
Let's consolidate:
- Identity Property of Addition: [tex]\(8 + 0 = 8\)[/tex]
- Multiplication Property of Zero: [tex]\(21 \times 0 = 0\)[/tex]
- Associative Property of Multiplication: [tex]\((5 \times 2) \times 3 = 5 \times (2 \times 3) = 30\)[/tex]
- Identity Property of Multiplication: [tex]\(34 \times 1 = 34\)[/tex]
- Inverse Property of Addition: [tex]\(19 + (-19) = 0\)[/tex]
- Commutative Property of Multiplication: [tex]\(12 \times 20 = 20 \times 12 = 240\)[/tex]
- Distributive Property: [tex]\(5 \times (2 + 4) = 5 \times 2 + 5 \times 4 = 30\)[/tex]
Each expression and property is verified as shown in the step-by-step solutions.
