Verify the associative law of addition for rational number 3/5,4/7,-5/9
Answers
Answer:
Step-by-step explanation:
Concept used:
Associative law for addition:
For any three numbers a,b,c
a+(b+c)=(a+b)+c
Given:
Now,
.........(1)
.......(2)
From (1) and (2) we get
Hence associative law verified.
Step-by-step explanation:
Answer:
\frac{3}{5}+(\frac{4}{7}+\frac{(-5)}{9})=(\frac{3}{5}+\frac{4}{7})+\frac{(-5)}{9}
5
3
+(
7
4
+
9
(−5)
)=(
5
3
+
7
4
)+
9
(−5)
Step-by-step explanation:
Concept used:
Associative law for addition:
For any three numbers a,b,c
a+(b+c)=(a+b)+c
Given:
\frac{3}{5},\frac{4}{7},\frac{-5}{9}
5
3
,
7
4
,
9
−5
Now,
\frac{3}{5}+(\frac{4}{7}+\frac{(-5)}{9})
5
3
+(
7
4
+
9
(−5)
)
=\frac{3}{5}+(\frac{4}{7}+\frac{(-5)}{9})=
5
3
+(
7
4
+
9
(−5)
)
=\frac{3}{5}+(\frac{36-35}{63})=
5
3
+(
63
36−35
)
=\frac{3}{5}+(\frac{1}{63})=
5
3
+(
63
1
)
=\frac{189+5}{315}=
315
189+5
=\frac{194}{315}=
315
194
.........(1)
(\frac{3}{5}+\frac{4}{7})+\frac{(-5)}{9}(
5
3
+
7
4
)+
9
(−5)
=(\frac{21+20}{35})+\frac{(-5)}{9}=(
35
21+20
)+
9
(−5)
=\frac{41}{35}+\frac{(-5)}{9}=
35
41
+
9
(−5)
=\frac{369-175}{315}=
315
369−175
=\frac{194}{315}=
315
194
.......(2)
From (1) and (2) we get
\frac{3}{5}+(\frac{4}{7}+\frac{(-5)}{9})=(\frac{3}{5}+\frac{4}{7})+\frac{(-5)}{9}
5
3
+(
7
4
+
9
(−5)
)=(
5
3
+
7
4
)+
9
(−5)
Hence associative law verified.