Verify the Associative property of multiplication for rational numbers: 2/ 3 , −1 /2 and −4 /5 . PLz answer fst
Answers
Answer:
Given numbers are -10/11 , 5/6 and 4/3
To Verify the associative property for addition and multiplication of the rational numbers.
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
The Associative property of multiplication for rational numbers is verified by the given explanation.
Given:
Verify the Associative property of multiplication for rational numbers:
2/ 3, −1 /2, and −4 /5
Solution:
Condition used:
According to the Associative property of multiplication If A, B, and C are any three numbers then it follows
(A × B) × C = A × (B × C)
Let A = 2/3, B = -1/2 and C = -4/5
By using the given condition
(2/3 × -1/2) × (-4/5) = -1/3 × (-4/5) = 4/15
=> (2/3 × -1/2) × (-4/5) = 4/15
2/3 × (-1/2 × -4/5) = 2/3 × 2/5 = 4/15
=> 2/3 × (-1/2 × -4/5) = 4/15
Hence,
(2/3 × -1/2) × (-4/5) = 2/3 × (-1/2 × -4/5) = 4/15
Therefore
The Associative property of multiplication for rational numbers is verified by the given explanation.
Learn more at
https://brainly.in/question/17883235
#SPJ3