Problem 26 - Algebra 1

Question

Evaluate the expression. $$5+8 \cdot 2-4$$

Step-by-Step Solution

Answer

The value of the expression \(5 + 8 \cdot 2 - 4\) is 17.

Step 1: Identify the Operations in the Expression

The exercise has three arithmetical operations: addition, represented by '+', multiplication, represented by '\cdot', and subtraction, represented by '-'. The expression is \(5 + 8 \cdot 2 - 4\).

Step 2: Follow the BIDMAS/BODMAS rule

According to the BIDMAS/BODMAS rule, multiplication should be performed before addition or subtraction. So first, calculate the value of \(8 \cdot 2\), which equals to 16.

Step 3: Substitute the Result into the Equation

Substituting the result into the expression, we obtain: \(5 + 16 - 4\). Now, perform the addition and subtraction operations from left to right.

Step 4: Do the Addition and Subtraction

Start by adding 5 and 16 which gives 21. Then, subtract 4 from 21, which gives 17.

Key Concepts

BIDMAS rules

The BIDMAS rule, sometimes known as BODMAS in certain regions, stands for Brackets, Indices, Division, Multiplication, Addition, and Subtraction. This rule is used to determine the order in which different arithmetic operations should be performed in a mathematical expression. Understanding BIDMAS is crucial for correctly evaluating expressions.

When applying BIDMAS, you first calculate anything in brackets. Next, resolve powers or indices. Division and multiplication are performed from left to right, followed by addition and subtraction, again from left to right. This rule helps avoid errors when working with complex multi-operation expressions.

In the expression given in the exercise, the operations are addition, multiplication, and subtraction. BIDMAS tells us to address the multiplication first before moving on to addition and subtraction.

arithmetic operations

Arithmetic operations are the basic mathematical operations that include addition, subtraction, multiplication, and division. These operations form the foundation of most mathematical calculations and expressions.

In the example expression \(5 + 8 \cdot 2 - 4\), we have three types of operations:

• Addition: Represented by the plus sign '+', used to combine numbers.
• Multiplication: Denoted by '\(\cdot\)', it is a quick way to add the same number multiple times.
• Subtraction: Indicated by the minus sign '-', it involves taking one number away from another.

Each operation has a specific effect on numbers, which is why knowing their function and how to use them accurately is important for evaluating expressions. Multiplication is prioritized over addition and subtraction based on BIDMAS, altering the final result significantly if not followed.

expression evaluation

Expression evaluation involves finding the value of a given mathematical expression by systematically following operation rules like BIDMAS. It is similar to solving a puzzle where each piece must be placed correctly.

Here's how it works in the expression \(5 + 8 \cdot 2 - 4\):

• Step 1: Identify all operations present.
• Step 2: Follow BIDMAS to resolve multiplication first: \(8 \cdot 2 = 16\).
• Step 3: Substitute the outcome back into the expression, resulting in \(5 + 16 - 4\).
• Step 4: Proceed with addition and subtraction from left to right to arrive at the final value: \(5 + 16 = 21\), then \(21 - 4 = 17\).

Following an organized approach ensures accurate results while preventing common mistakes. Mastering expression evaluation is critical in math as it lays the groundwork for more advanced topics.