Simplify the expression:
$13-42 \div 7+2$
To simplify the arithmetic expression \(13 - 42 \div 7 + 2\), we must follow the order of operations, often referred to as PEMDAS or BODMAS. This rule dictates the sequence in which mathematical operations should be performed: Parentheses, Exponents, Multiplication and Division (from left to right), and finally Addition and Subtraction (from left to right). Our expression contains subtraction, division, and addition. According to the order of operations, we must prioritize the division before addressing addition and subtraction.
We start by calculating the division part of the expression: \(42 \div 7\). Performing this division gives us \(6\). Now, substitute this result back into the original expression to get:
\[13 - 6 + 2\]
With the division completed, we are left with subtraction and addition. Following the rule that these operations are performed from left to right, we first perform the subtraction:
\[13 - 6 = 7\]
Next, we add the final term to this result:
\[7 + 2 = 9\]
Therefore, the simplified value of the expression is \(9\).
Understanding the order of operations is crucial in everyday life, especially when managing finances. For example, if you are calculating the total cost of a project where you receive a discount and then add a shipping fee, you must apply the correct order of operations to ensure your accounting is accurate. If you calculate the components in the wrong sequence, your final budget projection could be significantly incorrect, potentially leading to financial errors. By applying these rules consistently, you ensure that complex transactions are calculated accurately, whether you are balancing a budget, shopping, or working on professional project estimates.