Problem 29 - Algebra 1: Concepts and Skills

Question

Evaluate the expression. $$2 \cdot 4+(7-3)$$

Step-by-Step Solution

Answer

The result of the expression \(2 \cdot 4+(7-3)\) is 12.

Step 1: Apply Brackets

According to BIDMAS/BODMAS rule, begin solving inside the brackets. Here we have \(7-3\) inside the brackets, which equals to 4.

Step 2: Division and Multiplication

Next, perform any multiplication operations. Here, we have \(2 \cdot 4 = 8\).

Step 3: Addition and Subtraction

Lastly, add the results of the above two steps. So, we get \(8 + 4 = 12\).

Key Concepts

BIDMAS

The concept of BIDMAS is essential when working with mathematical expressions. BIDMAS stands for Brackets, Indices, Division and Multiplication, Addition and Subtraction. It's a guiding order that helps us decide the sequence in which we solve parts of an expression. This order is crucial because performing operations in the wrong sequence can lead to incorrect answers.

Here's how BIDMAS works in practice:

• Brackets: Solve anything in brackets first. They determine what needs to be calculated upfront.
• Indices: Next, compute any powers or square roots.
• Division and Multiplication: These are on an equal footing, so you solve them as they appear from left to right.
• Addition and Subtraction: Like division and multiplication, these operations are solved as they appear from left to right.

By adhering to BIDMAS, we ensure that mathematical expressions are solved consistently and accurately. This method allows students to break down complex problems into more manageable steps, ensuring an orderly and logical approach.

BODMAS

BODMAS is very similar to BIDMAS, but it is another acronym representing the same order of operations. BODMAS stands for Brackets, Orders, Division and Multiplication, Addition and Subtraction. The term 'Orders' in BODMAS is synonymous with 'Indices' in BIDMAS, referring to powers and roots.

Here's a quick breakdown:

• Brackets: Always tackled first. They simplify the expression by grouping terms.
• Orders (or Indices): Process any exponents or roots before other operations.
• Division and Multiplication: Handle these operations next, proceeding from left to right.
• Addition and Subtraction: Finally, these are also done from left to right.

Understanding BODMAS is vital in accurately solving mathematical problems. It prevents common errors in calculation and allows for a structured approach to math expressions. Using BODMAS, students can predictably handle operations, avoiding mistakes commonly made when processing mathematical sequences.

Mathematical Expressions

Mathematical expressions are statements comprised of numbers, variables, and operations like addition, subtraction, multiplication, and division. They serve as instructions that tell us how to compute a specific value. Knowing how to properly read and solve these expressions is a fundamental skill in mathematics.

Expressions can range from simple to complex, featuring a combination of various elements such as:

• Numbers: The basic counting tools, like 2, 4, 5, etc.
• Variables: Represent unknown values, commonly noted as letters like x, y, etc.
• Operations: Signals to perform calculation steps, including addition, subtraction, multiplication, and division.
• Functions or Brackets: Grouping tools that dictate order of operations and precedence.

In our example, the expression \(2 \cdot 4+(7-3)\) is composed of numbers and operations, with brackets indicating which part to solve first. Mathematics emphasizes precision and order, reflected in how expressions are dissected and solved using concepts like BIDMAS and BODMAS. This structured approach is critical for accuracy and efficiency when working with math problems.