Question

Evaluate the following expression:
((4)/(6))^2+2&3/6÷3&3/4*(4)/(3)=

Answer 1

First, simplify the expression inside the parentheses:

(4/6) = 2/3

Next, convert 2&3/6 to an improper fraction:

2&3/6 = 15/6

Then, convert 3&3/4 to an improper fraction:

3&3/4 = 15/4

Now, evaluate the entire expression:

(2/3)^2 + (15/6) ÷ (15/4) * (4/3)

To simplify the expression, perform the following calculations:

(2/3)^2 = 4/9

(15/6) ÷ (15/4) = (15/6) * (4/15) = 1

(4/3) * 1 = 4/3

Finally, evaluate the expression:

4/9 + 4/3

To add these fractions, find a common denominator, which is 9:

4/9 + 4/3 = (4/9)(3/3) + (4/3)(3/3) = 12/27 + 12/9 = 24/27 + 12/9

Now, find a common denominator, which is 27:

24/27 + 12/9 = (24/27)(1/1) + (12/9)(3/3) = 24/27 + 36/27 = 60/27

This fraction can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3:

60/27 = (3/3)(20/9) = 20/9

Therefore, the evaluated expression is 20/9.