Evaluating the Expression: 5/9 + 1/2 × (2/3)^3 in Fraction Form
In this article, we will evaluate the expression 5/9 + 1/2 × (2/3)^3 and simplify it in fraction form.
Step 1: Evaluate the Cubed Expression
First, let's evaluate the cubed expression (2/3)^3:
(2/3)^3 = (2/3) × (2/3) × (2/3) = 8/27
Step 2: Multiply the Result with 1/2
Next, multiply the result with 1/2:
1/2 × 8/27 = 4/27
Step 3: Add 5/9 to the Result
Now, add 5/9 to the result:
5/9 + 4/27
To add these fractions, we need to find the least common multiple (LCM) of 9 and 27, which is 27. So, we can rewrite 5/9 as:
5/9 = 15/27
Now, add the two fractions:
15/27 + 4/27 = 19/27
Therefore, the simplified expression in fraction form is:
5/9 + 1/2 × (2/3)^3 = 19/27
