Answer: To solve this expression, we first need to simplify the terms in the denominator:
5 1/3 - 4 2/3 + 1 1/6 x 2
We can convert each fraction to a mixed number:
5 1/3 = 5 + 1/3
4 2/3 = 4 + 2/3
1 1/6 x 2 = 2 x 1/6 + 2 = 2 + 1/3
Now we can perform the subtraction:
(5 + 1/3) - (4 + 2/3) + (2 + 1/3)
= 5 + 1/3 - 4 - 2/3 + 2 + 1/3
= 5 + 1/3 - 4 + 2 + 1/3 + 1/3
= 7
So the denominator simplifies to 7.
Next, we simplify the numerator:
8 - (2/3)^2
We can first square the fraction:
(2/3)^2 = 4/9
Now we can perform the subtraction:
8 - 4/9
= 8 - 4/9
= 8 x 9/9 - 4/9
= 72/9 - 4/9
= 68/9
So the numerator simplifies to 68/9.
Finally, we divide the numerator by the denominator:
68/9 ÷ 7 = 9.71
So, the expression simplifies to 9.71.
Explanation: