Question

express in the form of p/q : 0.38 (bar on 38) + 1.27(bar on 7)

Answer 1

Hope this pic helps you :)

Answer 2

The answer $\bold{\frac{164}{99}}$  is in $\bold{\frac{p}{q}}$.

Solution:

For the first solution of  $0 .\overline{38}$   (bar on 38),  

Let us take x = 0.3838

Shifting the decimal behind first 38 we get 38.38, so  

$x=\frac{38.38}{100}$

100x=38.38  

100x = 38 + 0.38

100x = 38 + x

100x – x = 38

99x = 38

$x=\frac{38}{99}$

For the first solution of   $1 .2\overline{7}$(bar on 7)

Now let us take y = 1.277

Shifting the decimal behind first 27 we get 127.7, so  

$y=\frac{127.7}{100}$

100y=127.7  

100y = 126+ 1.277

100y = 126 + y

100y –y = 126

99y = 126

$y=\frac{126}{99}$

$\bold{0 .\overline{38}}$ (bar on 38) + $\bold{1 .2\overline{7}}$ (bar on 7) = x + y

$\bold{x+y=\frac{38}{99}+\frac{126}{99}=\frac{164}{99}}}$