what do you mean by associative property and communicative property and distributive property and closure property too
Answers
Required answer :-
Associative means 'to connect or combine'. Suppose you have add three numbers, 9, 13 and 17, then which of the following will you add first?
Study the following:
(9+13)+17
= 22+17
= 39
Now, 9+(13+17)
= 9+30
= 39
You see that addends may be used in any order. This is called associative property of addition.
Associative property also applies for multiplication.
4×5 = 5×4 = 20.
Therefore, associative property applies with addition and multiplication only.
When you add a pair of numbers, you get the same number no matter what order you use in adding them.
Thus, 4+3 = 3+4 = 7
This property is known as the commutative property of addition.
This applies to multiplication as well.
4×5 = 5×4 = 20
Therefore, commutative property applies with addition and multiplication.
When you add two whole numbers, the sum will always be a whole number. This is called closure property and is one of the special properties of addition.
Closure property applies with multiplication also.
Therefore, whole numbers are said to be closed under multiplication and addition.
Distributive property:
Suppose, you have to multiply 38 by 4. You can do it in two ways.
First way: multiply directly 38 by 4, which is equal to 152.
Second way: Write 38 as 30+8 and then multiply by 4.
4×38 = 4×(30+8) = 4×30+4×8
= 120 + 32
= 152
The product obtained by working out in both ways is the same, i.e., 152, but the second way which states distributivity of multiplication over addition is more easy.
You can also apply this property for multiplication over subtraction.
Let us examine it:
5×(9-3) = 5×6 = 30
Also, 5×(9-3) = 5×9-5×3 = 45-15 = 30
Therefore, 5×(9-3) = 5×9-5×3
Thus, multiplication is distributive over subtraction.