Evaluate the following expressions:
The problem asks us to evaluate three distinct arithmetic expressions following the standard order of operations (PEMDAS/BODMAS): Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). The expressions are:
We will evaluate each sequentially by applying these rules.
For the first expression, \(1 \times 9 + 9 + 9\), we perform the multiplication first:
\(1 \times 9 = 9\).
Then, we perform the additions from left to right:
\(9 + 9 + 9 = 18 + 9 = 27\).
Thus, the value of the first expression is \(27\).
For the second expression, \(24 - 1\), we perform the subtraction directly:
\(24 - 1 = 23\).
Thus, the value of the second expression is \(23\).
For the third expression, \(5 + 9(1 + 2)^2\), we follow the order of operations:
First, simplify the expression inside the parentheses: \((1 + 2) = 3\).
Second, apply the exponent to the result: \(3^2 = 9\).
Third, perform the multiplication: \(9 \times 9 = 81\).
Finally, perform the addition: \(5 + 81 = 86\).
Thus, the value of the third expression is \(86\).
Arithmetic operations are foundational in daily life, such as when calculating a final bill. Imagine you are buying several items at a store: if you purchase one item for \$9, and two other items for \$9 each, your total is calculated as \(1 \times 9 + 9 + 9 = 27\). Similarly, if you have a budget of \$24 and spend \$1, you have \(24 - 1 = 23\) left. Mastering the order of operations ensures that you correctly calculate costs, discounts, and distributions every time.