identify which property is being illustrated.
15.1=15
5.0=0
11.1/11=1
3+2=2+3
7+-7=0
-9.1=-9
6.1/6=1
-1+1=0
5.6=6.5
(2+3)+5=(3+2)+5
7(8+5)=(8+5).7
(3+2)+5=3+(2+5)
3(9+1)=(3.9)+(3.1)
(1+2)(3+4)=(3+4)(1+2)
4(2.6)=(4.2)6
3(5-a)=15-3a
The properties being illustrated are:
1. Reflexive Property of Equality: 15.1 = 15
2. Zero Property of Multiplication: 5.0 = 0
3. Division Property of Equality: 11.1 / 11 = 1
4. Commutative Property of Addition: 3 + 2 = 2 + 3
5. Identity Property of Addition: 7 + (-7) = 0
6. Transitive Property of Equality: -9.1 = -9
7. Division Property of Equality: 6.1 / 6 = 1
8. Additive Inverse Property: -1 + 1 = 0
9. Symmetric Property of Equality: 5.6 = 6.5
10. Associative Property of Addition: (2 + 3) + 5 = (3 + 2) + 5
11. Associative Property of Multiplication: 7(8 + 5) = (8 + 5) . 7
12. Associative Property of Addition: (3 + 2) + 5 = 3 + (2 + 5)
13. Distributive Property: 3(9 + 1) = (3 . 9) + (3 . 1)
14. Commutative Property of Multiplication: (1 + 2)(3 + 4) = (3 + 4)(1 + 2)
15. Associative Property of Multiplication: 4(2 . 6) = (4 . 2)6
16. Distributive Property: 3(5 - a) = 15 - 3a
The property being illustrated in this list of equations is the Commutative Property of Addition, the Commutative Property of Multiplication, and the Distributive Property.
- The Commutative Property of Addition states that changing the order of the addends does not change the sum. For example, in the equation "3+2=2+3," the numbers 3 and 2 can be switched, and the sum will still be the same (equal to 5).
- The Commutative Property of Multiplication states that changing the order of the factors does not change the product. For example, in the equation "7(8+5)=(8+5).7," the numbers 7 and (8+5) can be switched, and the product will still be the same (equal to 91).
- The Distributive Property states that when multiplying a number by a sum or difference, you can distribute the multiplication to each term inside the parentheses. For example, in the equation "3(9+1)=(3.9)+(3.1)," you can distribute the multiplication of 3 to 9 and 1 separately, and then add the products on both sides to get the equality.
These properties are fundamental and hold true in arithmetic and algebraic operations, providing us with helpful rules to manipulate numbers and expressions.