verify : 2/3(8/9+1/6)=2/3×8/9+2/3×1/6
Answers
Answer:
To verify
Let LHS =
\begin{gathered}\frac{2}{3} ( \frac{8}{9} + \frac{1}{6} ) \\ = \frac{2}{3}( \frac{16 + 3}{18} ) \\ = \frac{2}{3} \times \frac{19}{18} \\ = \frac{38}{54} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \huge = \green{ \frac{19}{27} }\end{gathered}
3
2
(
9
8
+
6
1
)
=
3
2
(
18
16+3
)
=
3
2
×
18
19
=
54
38
=
27
19
and RHS =
\begin{gathered}\frac{2}{3} \times \frac{8}{9} + \frac{2}{3} \times \frac{1}{6} \\ = \frac{16}{27} + \frac{1}{9} \: \: or \: \: \frac{2}{3} ( \frac{8}{9} + \frac{1}{6} ) \\ = \frac{16 + 3}{27} \: \: or \: \: \frac{2}{3} (\frac{16 + 3}{18} ) \\ = \huge \: \pink{\frac{19}{27} }\end{gathered}
3
2
×
9
8
+
3
2
×
6
1
=
27
16
+
9
1
or
3
2
(
9
8
+
6
1
)
=
27
16+3
or
3
2
(
18
16+3
)
=
27
19
\begin{gathered}here \: \blue{LHS} = \green{RHS} \\ hence \: verified ✓\end{gathered}
hereLHS=RHS
henceverified✓