Evaluate 1/2(1-0.82)
The question is asking you to calculate the value of the mathematical expression 1/2 multiplied by the difference between 1 and 0.82. Essentially, you are to perform a subtraction operation within the parentheses first, then divide the result by 2 to obtain the final answer.
$\frac{1}{2} \left(\right. 1 - 0.82 \left.\right)$
Answer
Solution:
Calculation Process
Step 1:
First, we need to perform the subtraction inside the parentheses: $1 - 0.82$. This gives us $0.18$.
Step 2:
Next, we multiply the result by $\frac{1}{2}$. This is equivalent to dividing $0.18$ by $2$.
Step 3:
Finally, we carry out the division: $\frac{0.18}{2}$, which equals $0.09$.
Knowledge Notes:
To solve the given problem, we need to understand the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). This rule dictates that operations within parentheses are performed first.
In this problem, we first address the operation within the parentheses, which is subtraction. Once we have the result of the subtraction, we then proceed to the multiplication step. However, since we are multiplying by a fraction, specifically $\frac{1}{2}$, this is the same as dividing the number by 2.
In mathematical terms, the given expression can be rewritten as follows:
$$ \frac{1}{2}(1 - 0.82) = \frac{1}{2} \times (1 - 0.82) = \frac{1}{2} \times 0.18 = \frac{0.18}{2} = 0.09 $$
The division of a decimal by an integer follows the same rules as the division of whole numbers. You can think of the decimal $0.18$ as $18$ hundredths, and when you divide by $2$, you are finding how many hundredths are in half of that amount, which is $9$ hundredths or $0.09$.
