Simplify:
5+ 1/3 x 1/3 x 1/3-(1/9+1/9)
To simplify this expression, we will follow the order of operations (also known as PEMDAS).
Step 1: Simplify the expression inside the parentheses.
1/9 + 1/9 = 2/9
Step 2: Simplify the multiplication before addition and subtraction.
1/3 x 1/3 = 1/9 x 1/3 = 1/27
Step 3: Simplify the addition and subtraction.
5 + 1/27 - 2/9
To combine the fractions, we need a common denominator. In this case, the least common denominator (LCD) is 27.
Convert 5 to a fraction with a denominator of 27: (5 x 27/27) = 135/27
Convert 1/27 to an equivalent fraction with a denominator of 27: (1 x 1/1) = 1/27
Convert 2/9 to an equivalent fraction with a denominator of 27: (2 x 3/3) = 6/27
Now that all the fractions have the same denominator, we can combine them:
135/27 + 1/27 - 6/27
To simplify the addition and subtraction, we combine the numerators and keep the denominator the same:
(135 + 1 - 6)/27 = 130/27
Therefore, the simplified expression is 130/27.