if a,b,c are three rational numbers where a=2/3,b=4/8,c=-5/6, verify
a) a×(b+c)=(a+b)+c (associative property of multiplication)
please give correct answer
Answers
Answer:
FORMULA FOR ASSOCIATED PROPERTY OF ADDITION :
A+(B+C) = (A+B)+C
FORMULA FOR ASSOCIATED PROPERTY OF MULTIPLICATION :
A×(B×C) = (A×B)×C
GIVEN:
d=2/3
b=4/8
C= -5/6
ASSOCIATIVE PROPERTY OF ADDITION
LHS = a+(b+c)
(b+c) = 4/8 +(-5/6) { +(×)- = - }
= 4/8 - 5/6
= 4×3/8×3 - 5×4/6×4
[IN ORDER TO GET THE SAME DENOMINATOR]
{multiplying by 3 in the numerator and denominator}
{multiplying by 4 in the numerator and denominator}
= 12/24 - 20/24
= 12 - 20 / 24
= -8/24
= -1/3
a+(b+c) = 2/3 - 1/3
= 1/3
LHS = 1/3
RHS = (a+b)+c
(a+b) = (2/3 + 4/8)
= (2×8/3×8 + 4×3/8×3)
[IN ORDER TO GET THE SAME DENOMINATOR]
{multiplying by 8 in numerator and denominator}
{multiplying by 3 in numerator and denominator}
= (16/24 + 12/24)
= (16+12/24)
= 28/24 simplified by 2 table
= 14/12
(a+b)+c = (14/12) + (-5/6) { +(×)- = - }
= 14/12 - 5/6
= 14/12 - 5×2/6×2
[IN ORDER TO GET THE SAME DENOMINATOR]
{multiplying by 2 in numerator and denominator}
= 14/12 - 10/12
= 14 - 10/12
= 4/12
= 1/3
RHS = 1/3
HENCE ASSOCIATIVE PROPERTY OF ADDITION HAS BEEN PROVED
ASSOCIATIVE PROPERTY OF MULTIPLICATION
A×(B×C) = (A×B)×C
LHS = A×(B×C)
(B×C) = 4/8×(-5/6)
= -20/48 simplified by 4 table
= -5/12
A×(B×C) = 2/3×(-5/12)
= -10/36 simplified by 2 table
= -5/18
LHS = -5/18
RHS = (A×B)×C
(A×B) = 2/3 × 4/8
= 8/24
= 1/3
(A×B)×C = 1/3×(-5/6)
= -5/18
RHS = -5/18
HENCE ASSOCIATIVE PROPERTY OF MULTIPLICATION HAS BEEN PROVED