verify the following eqality [-3/5+1/6] +9/10=-3/5+[1/6+9/10]
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Answer:
Answer and explanation:
To find : Verify the following equality,
(-\frac{3}{5}+\frac{1}{6})+\frac{9}{10}=-\frac{3}{5}+(\frac{1}{6}+\frac{9}{10})(−
5
3
+
6
1
)+
10
9
=−
5
3
+(
6
1
+
10
9
)
Solution :
Taking LHS,
(-\frac{3}{5}+\frac{1}{6})+\frac{9}{10}(−
5
3
+
6
1
)+
10
9
=\frac{-18+5}{30}+\frac{9}{10}=
30
−18+5
+
10
9
=\frac{-13}{30}+\frac{9}{10}=
30
−13
+
10
9
=\frac{-130+270}{300}=
300
−130+270
=\frac{140}{300}=
300
140
=\frac{7}{15}=
15
7
Taking RHS,
-\frac{3}{5}+(\frac{1}{6}+\frac{9}{10})−
5
3
+(
6
1
+
10
9
)
=-\frac{3}{5}+\frac{10+54}{60}=−
5
3
+
60
10+54
=-\frac{3}{5}+\frac{64}{60}=−
5
3
+
60
64
=\frac{-180+320}{300}=
300
−180+320
=\frac{140}{300}=
300
140
=\frac{7}{15}=
15
7
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