a= -1,b= -3 and c= -4 (By taking these examples proof that associative property of addition holds and associative property of subtraction does not holds.
Answers
Answer:
Step-by-step explanation:
associative property is -
a + (b + c) = (a + b) + c
Now, given that, a = -1, b = -3, c = -4
So, L.H.S = -1 + (-3 -4) = -8
R.H.S = (-1 -3) -4 = -8 ; so addition holds associative property.
Now, for subtraction,
(a) - (b+c) = (-1) - (-3-4) = -1+7 = 6
(a+b) - (c) = (-1-3) + 4 = 0 ; so subtraction does not hold associative property.
Given numbers :
- a = -1
- b = -3
- c = -4
To find:
Take example of those three given numbers,
- prove that associative property of addition holds
- Prove that associative property of subtraction doesn't hold.
Solution:
Given numbers are (-1),(-3) and (-4). To prove that ( by taking examples of these numbers) the associative property of addition holds but associative property of subtraction doesn't hold.
What is associative property of addition?
- Associative property of addition state that, there will be no any change in our results when we add three or more numbers in any form of group.
Let prove associative property of addition :
{(-1)+(-3)}+(-4) = (-1)+{(-3)+(-4)}
→ (-4)+(-4) = (-1)+(-7)
→ (-8) = (-8)
→ LHS = RHS
Therefore, here we have proved that these three numbers are grouped in two different forms but result that we found is same.
What is associative property of subtraction:
- associative property of subtraction is defined as, if we subtract three or more numbers in two different grouping then our result will not be same.
Let prove associative property of subtraction:
{(-1)-(-3)}-(-4) = (-1)-{(-3)-(-4)}
→ {(-1)+3}+4 = (-1)-{(-3)+4}
→ 2+4 = (-1)-1
→ 6 ≠ -2
→ LHS ≠ RHS
Therefore, we have proved that if we subtract three or more numbers in two or more different grouping then our result will not be same