write all the properties of addition subtraction multiplication and division of integers with 2 example of each
Answers
The following are the five main properties of operation for integers:
- Closure Property
The closure feature of numbers under addition and subtraction asserts that the sum or difference of any two integers will always be an integer.
Examples:
- 3 – 4 = 3 + (−4) = −1
- (–5) + 8 = 3
- Commutative Property
The commutative property of addition and multiplication states that it makes no difference what order the terms are in; the outcome will be the same. The sum or product will not change if the terms are swapped, whether it be addition or multiplication.
Examples:
- 4 + (−6) = −2 = (−6) + 4
- 10 × (−3) = −30 = (−3) × 10
- Associative Property
The associative property of addition and multiplication states that the order in which numbers are grouped makes no difference; the result is the same. The solution will remain the same regardless of how the numbers are grouped. Regardless of the sequence of terms, parenthesis can be used.
Examples:
- 1 + (2 + (-3)) = 0 = (1 + 2) + (−3)
- 1 × (2 × (−3)) =−6 = (1 × 2) × (−3)
- Distributive Property
The distributive property illustrates how one mathematical operation can distribute over another within a bracket. It can be either a distributive property of addition or a distributive property of subtraction. In this case, integers are first added or removed, then multiplied or multiplied with each number within the bracket, then last added or subtracted.
Examples:
- −5 (2 + 1) = −15 = (−5 × 2) + (−5 × 1)
- Identity Property
The additive identity property of integers states that when any integer is multiplied by zero, the result is the same number. Additive identity refers to a value of zero.
Examples:
- x × 1 = x = 1 × x
- x × 0 = 0 =0 × x
Answer:
Step-by-step explanation:
The following are the five main properties of operation for integers:
Closure Property
The closure feature of numbers under addition and subtraction asserts that the sum or difference of any two integers will always be an integer.
Examples:
3 – 4 = 3 + (−4) = −1
(–5) + 8 = 3
Commutative Property
The commutative property of addition and multiplication states that it makes no difference what order the terms are in; the outcome will be the same. The sum or product will not change if the terms are swapped, whether it be addition or multiplication.
Examples:
4 + (−6) = −2 = (−6) + 4
10 × (−3) = −30 = (−3) × 10
Associative Property
The associative property of addition and multiplication states that the order in which numbers are grouped makes no difference; the result is the same. The solution will remain the same regardless of how the numbers are grouped. Regardless of the sequence of terms, parenthesis can be used.
Examples:
1 + (2 + (-3)) = 0 = (1 + 2) + (−3)
1 × (2 × (−3)) =−6 = (1 × 2) × (−3)
Distributive Property
The distributive property illustrates how one mathematical operation can distribute over another within a bracket. It can be either a distributive property of addition or a distributive property of subtraction. In this case, integers are first added or removed, then multiplied or multiplied with each number within the bracket, then last added or subtracted.
Examples:
−5 (2 + 1) = −15 = (−5 × 2) + (−5 × 1)
Identity Property
The additive identity property of integers states that when any integer is multiplied by zero, the result is the same number. Additive identity refers to a value of zero.
Examples:
x × 1 = x = 1 × x
x × 0 = 0 =0 × x