What is the value of $0.7\overline{54}+0.69\overline{2}$?

Question

What is the value of $0.7\overline{54}$ +$0.69\overline2$?

(a) $\frac{1813}{900}$ (b) $\frac{1783}{910}$ (c) $\frac{14323}{9900} (d) \frac{13243}{9900}$

I get

@edit

$$754-7/990 + 692-69/900$$=$747$/$990$ + $623$/$900$=$1$/$90$($747$/$11$ + $623$/$10$)

=($7470$/$11$ + $623$ . $11$/$10$)=($7470$ + $6853$)=$14323$/$9900$

Thankx for help I did not multiplied by $90$

Can anyone guide me how to solve the problem?

Answer 1

The question is not $0.754+0.692=?$
The question asks $0.7 \overline{54}+0.69\overline2=?$

So the answer will be $0.7 \overline{54}+0.69\overline2=\frac{754-7}{990}+\frac{692-69}{900}=\frac{747}{990}+\frac{623}{900}=1.44\overline{67}=\frac{14323}{9900}$

Answer 2

HINT

Easier to convert to regular fractions: $$ 0.7\overline{54} = \frac{7}{10} + \frac{54}{99 \cdot 10} $$ Can you convert the other one?

Answer 3

(754 - 7)/990 + (692 - 69)/900 = 747/990 + 623/900 = 7470/9900 + 6853/9900 = 14323/9900

Answer 4

0.7545454...(+) 0.6922222...[=] 1.44676767... Now convert this into rational number. I got the answer as 14323/9900. Hope this helps.