2.666 ... + 2.77 ... in fraction form is:

Correct option is C

Solution:

Convert 2.666... into a fraction.

Let x = 2.666...

Multiply both sides by 10 to shift the repeating part:

10x = 26.666...

Now subtract the original equation:

10x - x = 26.666... - 2.666...

9x = 24

x = 24/9 = 8/3

So, 2.666... = 8/3.

Convert 2.77... into a fraction.

Let y = 2.77...

Multiply both sides by 10 to shift the repeating part:

10y = 27.77...

Now subtract the original equation:

10y - y = 27.77... - 2.77...

9y = 25

y = 25/9

So, 2.77... = 25/9.

Add the two fractions 8/3 and 25/9.

Find the least common denominator (LCD) of 3 and 9, which is 9:

8/3 = 24/9

Now add the fractions:

24/9 + 25/9 = (24 + 25)/9 = 49/9

The sum of 2.666... + 2.77... in fraction form is:

49/9.