7.44…+3.77…-2.55…=

Correct option is A

Given:

7.44…+3.77…-2.55…=

Formula Used:

Solution:

Convert each repeating decimal to fraction:

let $$x$$ = 7.444...

Multiply by 100 to shift the repeating part:

100$$x$$​  =7.444×100 = 100$$x$$ = 744.4..

Subtract the original equation

100$$x$$-$$x$$ = 744.4.. - 7.44.. = 99$$x$$ = 737

$$x$$ = $$\frac{737}{99}$$ 

Again Convert repeating decimal to fraction:

$$y$$ = 3.777..

Multiply by 100 to shift the repeating part:

100$$y$$ = 377.7..×100 = 100$$y$$ = 377.7..

Subtract the original value

100$$y$$-$$y$$= 377.7- 3.777 = 99$$x$$ =374

$$y$$ = $$\frac{374}{99}$$ 

Again Convert repeating decimal to fraction:

$$z$$ = 2.55

Multiply by 100 to shift the repeating part:

100$$z$$ = 2.55×100 = 100$$z$$ = 255.5..

Subtract the original equation:

100$$z$$ - $$z$$ = 255.5..-2.55 = 99$$z$$ = 253

$$z$$ = $$\frac{253}{99}$$​

According to question combine and simplify the all fraction:

$$x+y-z$$ 

= $$\frac{737}{99}$$+$$\frac{374}{99}$$- $$\frac{253}{99}$$   

= $$\frac{737+374-253}{99}$$ 

=$$\frac{858}{99}$$ 

= $$\frac{78}{9}$$ 

Thus the correct answer is (A)