VERIFY THE ASSOCIATIVE PROPERTY FOR ADDITION AND MULTIPLICATION FOR 5/7,-3/8,3/-11
Answers
Answer:
Associative Property for addition of the rational numbers is as follows
( a + b ) + c = a + ( b + c )
Associative Property for multiplication of the rational numbers is as follows
( a × b ) × c = a × ( b × c )
let a = -10/11 , b = 5/6 and c = 4/3
So, First Associative property of addition:
LHS = ( a + b ) + c = ( -10/11 + 5/6 ) + 4/3
=(\frac{-60+55}{66})+\frac{4}{3}=(
66
−60+55
)+
3
4
=\frac{-5}{66}+\frac{4}{3}=
66
−5
+
3
4
=\frac{-5+88}{66}=\frac{83}{66}=
66
−5+88
=
66
83
RHS = a + ( b + c ) = -10/11 + ( 5/6 + 4/3 )
=\frac{-10}{11}+(\frac{5+8}{6})=
11
−10
+(
6
5+8
)
=\frac{-10}{11}+\frac{13}{6}=
11
−10
+
6
13
=\frac{-60+143}{66}=\frac{83}{66}=
66
−60+143
=
66
83
LHS = RHS
Hence Verified
Second, Associative property of multiplication:
LHS = ( a × b ) × c = ( -10/11 × 5/6 ) × 4/3
=(\frac{-50}{66})\times\frac{4}{3}=(
66
−50
)×
3
4
=\frac{-200}{198}=\frac{-11}{99}=
198
−200
=
99
−11
RHS = a × ( b × c ) = -10/11 × ( 5/6 × 4/3 )
=\frac{-10}{11}\times(\frac{20}{18})=
11
−10
×(
18
20
)
=\frac{-200}{198}=\frac{-100}{99}=
198
−200
=
99
−100
LHS = RHS
Hence Verified