verify whether associative property is satisfied for addition, subtraction, multiplication and division for the following sets of rational numbers. 1/3, 2/5 and –3/7
Answers
Answer:
Step-by-step explanation:
1/3, 2/5 and –3/7
Let a=1/3, b=2/5 and c=-3/7
Addition
associative for addition
a+(b+c)=(a+b)+c
LHS=1/3+(2/5-3/7)
=1/3+(14-15)/35
=1/3-1/35
=(35-3)/105=32/105
RHS =(1/3+2/5) -3/7
=(5+6)/15-3/7
=11/15-3/7
=(77-45)/105=32/105
So LHS =RHS Verifies
=======================
Subtraction
a-(b-c)
=1/3-(2/5-(-3/7))
=1/3-(2/5+3/7)
=1/3-(14+15)/35
=1/3-29/35=(35-87)/35*3
=-52/105
Now (a-b)-c
=(1/3-2/5)-(-3/7)
=(5-6)/15+3/7
=-1/15+3/7
=(-7+45)/7
=38/7
here a-(b-c) ≠ (a-b)-c
so associative property is not applicable for subtraction
MULTIPLICATION:
a x (b x c)=(a x b) x c
a x (b x c)
=1/3 *(2/5 x-3/7))
=1/3 x (-6/35)
=-2/35
Now (a x b) x c
=(1/3 x 2/5) x (-3/7)
=2/15 *(-3/7)
=-2/35
Hence LHS=RHS verified
===========================
DIVISION
a ÷ (b÷c)
=1/3 ÷ ( 2/5 ÷(-3/7)
=1/3 ÷ (-14/15)
=1/2 x (-15/14)
=--15/28
Now (a÷ b) ÷ c
=(1/3 ÷ 2/5) ÷ (-3/7)
=1/3*5/2 ÷(-3/7)
=5/6 x(-7/3)
=-35/18
Here
(a÷ b) ÷ c ≠ a÷( b ÷ c )
So it proves that associative property is not satisfied for division
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