Sort the equations out according to the property they illustrate.
You have 12 cards in this activity.
-7 . 1 = -7
3 + (7+19) = (3+7)+19
8 . 7 . 6 = 8 7 6
99+0=99
2 (4 . 11) = 2 (4 . 11)
5-3-=3-5
1 (-99) = 99
0.4 + 2.3 = 2.3 + 0.4
which of these are not a property, commutive, identity, and associative
Based on the equations provided, we can sort them out according to the properties they illustrate:
Commutative property:
-7 . 1 = -7 (Multiplication is commutative)
99+0=99 (Addition is commutative)
0.4 + 2.3 = 2.3 + 0.4 (Addition is commutative)
Identity property:
99+0=99 (Addition has an identity element of 0)
4 . 11 = 44 (Multiplication has an identity element of 1)
Associative property:
3 + (7+19) = (3+7)+19 (Addition is associative)
2 (4 . 11) = 2 (4 . 11) (Multiplication is associative)
Not a property:
8 . 7 . 6 = 8 7 6 (This equation does not demonstrate any specific property. It is simply a mathematical equation without any inherent property being illustrated.)
In summary:
Commutative property: -7 . 1 = -7, 99+0=99, 0.4 + 2.3 = 2.3 + 0.4
Identity property: 99+0=99, 4 . 11 = 44
Associative property: 3 + (7+19) = (3+7)+19, 2 (4 . 11) = 2 (4 . 11)
Not a property: 8 . 7 . 6 = 8 7 6
What about 5-3=3-5 and 1 (-99) = 99
Apologies for the oversight. Let's include those equations in the correct categories:
Commutative property:
-7 . 1 = -7 (Multiplication is commutative)
99+0=99 (Addition is commutative)
0.4 + 2.3 = 2.3 + 0.4 (Addition is commutative)
5-3=3-5 (Subtraction is commutative)
Identity property:
99+0=99 (Addition has an identity element of 0)
4 . 11 = 44 (Multiplication has an identity element of 1)
Associative property:
3 + (7+19) = (3+7)+19 (Addition is associative)
2 (4 . 11) = 2 (4 . 11) (Multiplication is associative)
Not a property:
8 . 7 . 6 = 8 7 6
Corrected summary:
Commutative property: -7 . 1 = -7, 99+0=99, 0.4 + 2.3 = 2.3 + 0.4, 5-3=3-5
Identity property: 99+0=99, 4 . 11 = 44
Associative property: 3 + (7+19) = (3+7)+19, 2 (4 . 11) = 2 (4 . 11)
Not a property: 8 . 7 . 6 = 8 7 6
To sort the equations according to the property they illustrate, let's look at each equation:
1. -7 . 1 = -7 - This equation illustrates the identity property of multiplication.
2. 3 + (7+19) = (3+7)+19 - This equation illustrates the associative property of addition.
3. 8 . 7 . 6 = 8 7 6 - This equation does not illustrate any specific property. It is a multiplication operation between three numbers.
4. 99+0=99 - This equation illustrates the identity property of addition.
5. 2 (4 . 11) = 2 (4 . 11) - This equation illustrates the identity property of multiplication.
6. 5-3-=3-5 - This equation does not illustrate any specific property. It is a subtraction operation.
7. 1 (-99) = 99 - This equation illustrates the identity property of multiplication.
8. 0.4 + 2.3 = 2.3 + 0.4 - This equation illustrates the commutative property of addition.
To summarize:
- Identity property of multiplication: Equations 1, 5, and 7.
- Identity property of addition: Equation 4.
- Commutative property of addition: Equation 8.
- Associative property of addition: Equation 2.
- Equations 3 and 6 do not illustrate any specific property.
To identify which equations illustrate the commutative, identity, and associative properties, we need to understand what each property means:
1. Commutative Property: This property states that the order of the operands does not affect the result of addition or multiplication. For example, a + b = b + a and a * b = b * a.
2. Identity Property: This property states that there exist special values (called identity elements) such that when they are combined with any other value through addition or multiplication, the result remains unchanged. For example, a + 0 = a and a * 1 = a.
3. Associative Property: This property states that the grouping of operands does not affect the result of addition or multiplication. For example, (a + b) + c = a + (b + c) and (a * b) * c = a * (b * c).
Now let's examine each equation one by one to determine the property they illustrate:
-7 . 1 = -7: This equation illustrates the identity property for multiplication because any number multiplied by 1 remains unchanged.
3 + (7+19) = (3+7)+19: This equation illustrates the associative property for addition because changing the grouping of the parentheses does not affect the sum.
8 . 7 . 6 = 8 7 6: This equation does not illustrate any specific property. It is simply a multiplication expression.
99+0=99: This equation illustrates the identity property for addition because adding 0 to any number does not change its value.
2 (4 . 11) = 2 (4 . 11): This equation illustrates the commutative property for multiplication because the order of the operands does not affect the result.
5-3-=3-5: This equation does not illustrate any specific property. It is an incorrect equation and does not follow the rules of arithmetic.
1 (-99) = 99: This equation does not illustrate any specific property. It is a multiplication expression.
0.4 + 2.3 = 2.3 + 0.4: This equation illustrates the commutative property for addition because the order of the operands does not affect the sum.
Therefore, to summarize:
- Identity property: -7 . 1 = -7, 99+0=99
- Associative property: 3 + (7+19) = (3+7)+19
- Commutative property: 2 (4 . 11) = 2 (4 . 11), 0.4 + 2.3 = 2.3 + 0.4
- None of the above properties: 8 . 7 . 6, 5-3-=3-5, 1 (-99)