Solve (0.5 + 2)/5: Adding Decimals in Fractions

To solve the expression $\frac{0.5 + 2}{5}$, we must follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). Here, we need to focus on the addition within the fraction, and then the division that forms the fraction.

Let's break down the steps:

• Start with the expression inside the numerator: $0.5 + 2$.
• Perform the addition: $0.5 + 2 = 2.5$.
• The expression now becomes: $\frac{2.5}{5}$.
• Next, perform the division: divide 2.5 by 5. To do this, consider the division operation:
• $2.5 \div 5$
• Convert 2.5 to a fraction: $\frac{5}{2}$
• Divide by 5: $\frac{5}{2} \times \frac{1}{5}$ (since dividing by a number is the same as multiplying by its reciprocal).
• This becomes: $\frac{5 \times 1}{2 \times 5} = \frac{5}{10}$
• Simplify the fraction $\frac{5}{10}$ to its lowest terms by dividing both the numerator and the denominator by their greatest common divisor (5), resulting in: $\frac{1}{2}$.

Therefore, the value of the expression $\frac{0.5+2}{5}$ is $\frac{1}{2}$, as given.