Examples of Order Of Operations

1. INTRODUCTION

The order of operations is a set of rules that dictates the order in which mathematical operations should be performed when there are multiple operations in an expression. This set of rules is often remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. Following the order of operations ensures that mathematical expressions are evaluated consistently and accurately.

2. EVERYDAY EXAMPLES

In everyday life, the order of operations is used in a variety of situations. For example, a student named Alex is planning a road trip from New York to Los Angeles. The total distance is 2,796 miles, and Alex's car gets 32 miles per gallon. To calculate how many gallons of gas Alex will need, the student must first divide the total distance by the miles per gallon: 2,796 miles / 32 miles/gallon = 87.375 gallons. In this case, the division operation is performed before the result is rounded to the nearest whole number.

Another example is a cook named Maya who is making a recipe that calls for 3/4 cup of sugar plus 1/2 cup of honey. To add these two quantities, Maya must first find a common denominator, which is 4. So, 3/4 cup of sugar plus 1/2 cup (or 2/4 cup) of honey equals 5/4 cup of sweetener. In this case, the fraction 1/2 is converted to have a denominator of 4 before the addition operation is performed.

A third example is a person named Jack who is saving money for a new bike. Jack has $120 in his savings account and wants to add $45 that he earned from mowing lawns. However, he must also subtract $25 that he spent on a new video game. To calculate the new total, Jack must first add the $120 and $45, then subtract the $25: $120 + $45 = $165, then $165 - $25 = $140. In this case, the addition operation is performed before the subtraction operation.

3. NOTABLE EXAMPLES

One well-known example of the order of operations is the expression 12 / 3 * 4. Using the PEMDAS rules, the division operation is performed first: 12 / 3 = 4. Then, the multiplication operation is performed: 4 * 4 = 16. Therefore, the final result is 16.

Another classic example is the expression 18 - 3 + 12. In this case, the subtraction and addition operations have the same precedence, so they are performed from left to right. First, 18 - 3 = 15, then 15 + 12 = 27. Therefore, the final result is 27.

A third example is the expression 9 - 3 * 2. Using the PEMDAS rules, the multiplication operation is performed first: 3 * 2 = 6. Then, the subtraction operation is performed: 9 - 6 = 3. Therefore, the final result is 3.

4. EDGE CASES

One unusual example of the order of operations is the expression 12 + 3 * (4 - 2). In this case, the expression inside the parentheses is evaluated first: 4 - 2 = 2. Then, the multiplication operation is performed: 3 * 2 = 6. Finally, the addition operation is performed: 12 + 6 = 18. Therefore, the final result is 18.

5. NON-EXAMPLES

Some people may think that the order of operations applies to situations where there are no mathematical operations, such as following a recipe or assembling furniture. However, in these cases, the order of steps is determined by the specific task or process, rather than a set of mathematical rules.

Another example of something that is not an example of the order of operations is a situation where there are no multiple operations, such as calculating the area of a rectangle. In this case, there is only one operation (multiplication), so the order of operations does not apply.

A third example is a situation where the operations are not mathematical, such as prioritizing tasks or making decisions. In these cases, the order of operations is not relevant, and other factors such as importance, urgency, or personal preference determine the order of steps.

6. PATTERN

All valid examples of the order of operations have one thing in common: they involve multiple mathematical operations that must be performed in a specific order to obtain the correct result. Whether it is a simple expression like 2 + 3 * 4 or a complex expression like 12 + 3 * (4 - 2), the order of operations provides a set of rules for evaluating mathematical expressions consistently and accurately. By following these rules, individuals can ensure that they are performing mathematical operations in the correct order, which is essential for obtaining accurate results in a wide range of contexts and scales.