Problem 64 - Algebra 1: Concepts and Skills

Question

Evaluate the expression. $$ 9-2 \cdot 2-3 $$

Step-by-Step Solution

Answer

The result of the expression 9 - 2 * 2 - 3 is 2.

Step 1: Identify Operations

The expression has three operations. They are subtraction and multiplication – 9 - 2 * 2 - 3. According to BIDMAS/BODMAS rule, multiplication should be performed before subtraction.

Step 2: Perform Multiplication

Calculate the multiplication operation first. There is one multiplication operation in the expression: 2 multiplied by 2, which is equal to 4. Now, the expression becomes: 9 - 4 - 3.

Step 3: Perform Subtractions

Now perform the subtraction operations from left to right. Firstly, subtract 4 from 9, which is equal to 5, giving us 5 - 3. Then, subtract 3 from 5, which is equal to 2.

Key Concepts

Order of Operations

Understanding the order of operations is crucial when you want to evaluate expressions in algebra correctly. It dictates the sequence in which you should perform various calculations to ensure that everyone gets the same result for the same mathematical expression. The universal rule prescribed by the order of operations can be remembered using the acronym PEMDAS or BIDMAS/BODMAS, which stands for Parentheses/Brackets, Exponents/Indices, Multiplication, Division, Addition, and Subtraction.

When an expression includes multiple operations, PEMDAS/BODMAS serves as a guideline that multiplication and division should be done first, followed by addition and subtraction. It's important to note that multiplication does not always come before division; they are addressed from left to right in the sequence they appear. Similarly, addition and subtraction are also performed from left to right. In the given exercise, multiplication precedes subtraction, which is why 2 multiplied by 2 was calculated first, resulting in a simplified expression that only required subtraction.

Subtraction in Algebra

Subtraction in algebra follows the same principles as subtraction in basic arithmetic; however, it's encased within a broader range of mathematical concepts and operations. When performing subtraction, it often helps to think of the operation as 'taking away' from or 'adding a negative' to the number you're dealing with.

In the context of algebra, it's also vital to take into account the positioning of numbers and variables, and whether they are associated with other algebraic terms. In the provided exercise, after performing the necessary multiplication, we are left with the task of subtracting numbers in sequence. Working from left to right, as per the order of operations, ensures that we maintain consistency and reach the correct answer.

Multiplication in Algebra

Multiplication in algebra is more than just multiplying numbers; it involves understanding how to manage variables and constants within an expression. The key is to perform multiplication operations before moving on to addition or subtraction, unless grouping symbols such as parentheses indicate otherwise. Multiplication often signifies the 'scaling' or combining of quantities, and it has precedence over addition and subtraction in the order of operations.

In algebra, whenever you encounter a multiplication operation, you must address it before subtracting or adding other terms. This is precisely what we see in the solution to our exercise. Multiplying 2 by 2 reduces our expression, making it simpler to work with. Once you grasp this concept, you'll be able to approach multiplication in algebraic expressions confidently and accurately.