why does subtraction not follow oder property explanation
Answers
Step-by-step explanation:
Subtraction of two whole numbers is not commutative. This means we cannot subtract two whole numbers in any order and get the same result. Let a and b be two whole numbers, then a − b ≠ b − a.
Answer:
Properties of Subtraction
Closure Property
When one whole number is subtracted from another, the difference is not always a whole number. This means that the whole numbers are not closed under subtraction. If a and b are two whole numbers and a − b = c, then c is not always a whole number. Take a = 7 and b = 5, a − b = 7 − 5 = 2 and b − a = 5 − 7 = −2 (not a whole number).
Commutative Property
Subtraction of two whole numbers is not commutative. This means we cannot subtract two whole numbers in any order and get the same result. Let a and b be two whole numbers, then a − b ≠ b − a. Take a = 7 and b = 5, 7 − 5 = 2 ≠ 5 − 7 = −2.
Associative Property
An associative property does not hold for the subtraction of whole numbers. This means that we cannot group any two whole numbers and subtract them first. Order of subtraction is an important factor. If ‘a’, ‘b’, and ‘c’ are the three whole numbers then, a − (b − c) ≠ (a − b) − c. Consider the case when a = 8, b = 5 and c = 2, 8 − (5 − 2) = 5 ≠ (8 − 5) − 2 = 1.
Subtractive Property of Zero
When we subtract zero from a whole number, the value of the whole number remains the same. Take an example, a = 98, a − 0 = 98 − 0 = 98.
Properties of Multiplication
Closure Property
Multiplication of two whole numbers will result in a whole number. Suppose, a and b are the two whole numbers and a × b = c, then c is also a whole number. Let a = 10, b = 5, 10 × 5 = 50 (whole number). The whole number is closed under multiplication.
Commutative Property
The value of the product does not change when the order of multiplication gets changed. This is the commutative property of multiplication. Let the two whole numbers be a and b, then a × b = b × a ⇒ 4 × 9 = 36 = 9 × 4.
Associative Property
When we multiply three or more whole numbers, the value of the product remains the same when they are grouped in any manner. The associative property of multiplication holds for whole numbers. Thus, if ‘a’, ‘b’, and ‘c’ are three whole numbers, then a × (b × c) = (a × b) × c = (a × c) × b. For example, 6 × (7 × 2) = (6 × 7) × 2 = (6 × 2) × 7 = 84.
Multiplicative Identity
When we multiply 1 with any whole number, the product is the number itself. 1 is the multiplicative identity of the whole numbers. If w is a whole number, then w × 1 = 1 × w.
Multiplicative Property of Zero
The product of a whole number and 0 is always 0 i.e., w × 0 = 0 = 0 × w. For example, 813 × 0 = 0 = 0 × 813.
Distributive Property of Multiplication over Addition
This property shows that multiplication of a whole number is distributed over the sum of the whole numbers. If a, b, and c are the three whole numbers. We have, a × (b + c) = (a × b) + (a × c). Let a = 10, b = 20 and c = 5 ⇒ 10 × (20 + 5) = 250 and (10 × 20) + (10 × 5) = 200 + 50 = 250.
Distributive Property of Multiplication over Subtraction
This property tells that multiplication of a whole number is distributed over the difference of the whole numbers. Suppose ‘a’, ‘b’, and ‘c’ are three whole numbers. From this property we have,a × (b − c) = (a × b) − (a × c). Let a = 10, b = 20 and c = 5 ⇒ 10 × (20 − 5) = 150 and (10 × 20) − (10 × 5) = 200 − 50 = 150.
Step-by-step explanation: