[tex]\huge{ \fcolorbox{lime}{black}{ \color{yellow} {AnSwEr:-}}}[/tex]
Let's verify the associative property of addition by substituting the given values:
(a+b)+c = a+ (b+c)
For part (a):
a = 2
b = 12/13
c = 22
Substituting the values into the left side of the equation:
(2 + 12/13) + 22
To simplify, let's find a common denominator for 2 and 12/13, which is 13:
(26/13 + 12/13) + 22
(38/13) + 22
Now, let's simplify the right side of the equation:
a = 2
b = 12/13
c = 22
Substituting the values into the right side of the equation:
2 + (12/13 + 22)
To simplify, let's find a common denominator for 12/13 and 22, which is 13:
2 + (12/13 + 286/13)
2 + (298/13)
Now, let's compare both sides of the equation:
(38/13) + 22 = 2 + (298/13)
To add fractions, we need a common denominator. Let's find the common denominator, which is 13:
(38 + 286)/13 = (26 + 298)/13
Simplifying both sides:
324/13 = 324/13
Since both sides of the equation are equal, we have verified that (a+b)+c = a+ (b+c) for the given values.
Now, let's move on to part (b):
a = -9
b = 3
c = -5
Substituting the values into the left side of the equation:
(-9 + 3) + (-5)
Simplifying:
-6 + (-5)
-11
Now, let's simplify the right side of the equation:
a = -9
b = 3
c = -5
Substituting the values into the right side of the equation:
-9 + (3 + (-5))
Simplifying:
-9 + (-2)
-11
Both sides of the equation simplify to -11, so we can conclude that (a+b)+c = a+ (b+c) is true for the given values of a, b, and c.
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I hope this will help you...✨
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