Question

\(30+20-4 \times 6\) is equal to (a) 156 (b) 276 (c) 330 (d) none of these

Short answer

Question: Solve the expression \(30+20-4 \times 6\) and select the correct option: a) 20 b) 30 c) 40 d) none of these Answer: d) none of these

Step-by-step solution

Identify the Operations

First, observe the given expression and identify the operations present. In this case, we have addition, subtraction, and multiplication.

Perform Multiplication

According to the order of operations, we should perform multiplication before addition or subtraction. In this expression, we have one multiplication: \(4 \times 6\). Multiply these numbers together: \(4 \times 6 = 24\). Now the expression becomes: \(30 + 20 - 24\)

Perform Addition

Next in the order of operations is addition. The only addition in the expression is \(30 + 20\). Add these numbers together: \(30 + 20 = 50\). Now the expression becomes: \(50 - 24\)

Perform Subtraction

Finally, we have subtraction in the expression as the last step: \(50 - 24\). Subtract 24 from 50: \(50 - 24 = 26\)

Compare the Result With the Options

The result of the expression is \(26\). However, this number does not match any of the available options. Therefore, the correct answer is: (d) none of these.

Key concepts

Mathematical Expressions

In mathematics, the term "mathematical expression" refers to a combination of numbers, variables, and operators that collectively represent a particular value or concept. This can include anything from simple arithmetic calculations to complex algebraic expressions. In the exercise, the expression given is: \(30+20-4 \times 6\). Expressions can include operations like addition, subtraction, multiplication, division, and more. Understanding how to evaluate these expressions involves recognizing the different components and operators present within them.

Mathematical expressions are often used to solve problems, compute values, and understand relationships between numbers. They are essential in both basic arithmetic and advanced mathematics.

• Components: These are the numbers or values being manipulated.
• Operators: These tell us what action to take, such as add (+), subtract (-), multiply (×), etc.
• Order of Operations: This rule dictates the sequence in which operations should be conducted.

Mastering mathematical expressions is crucial for problem-solving and for applying mathematical reasoning in practical scenarios.

Arithmetic Operations

Arithmetic operations are fundamental to mathematics. They form the basis of most calculations, computations, and problem-solving processes. The primary arithmetic operations include addition, subtraction, multiplication, and division. In the given expression \(30+20-4 \times 6\), we encounter all but division.

Recognizing these operations and knowing when and how to apply them is crucial:

• Addition (+): This operation involves combining numbers to find a total sum. For example, adding \(30 + 20\) yields \(50\).
• Subtraction (-): This finds the difference between numbers, such as \(50 - 24\), which equals \(26\).
• Multiplication (×): This involves scaling one number by another. In our example, \(4 \times 6\) equals \(24\).

Each of these operations has properties and rules, like associative, commutative, and distributive laws that help us simplify and solve expressions. For successful problem-solving, understanding these operations and their priority in the order of operations is vital.

Problem Solving

Problem-solving in mathematics involves a systematic approach to find solutions to given challenges or questions. It requires observation, logical thinking, and the application of mathematical rules and concepts. For the exercise involving \(30+20-4 \times 6\), problem-solving starts by recognizing the operations and applying them in the correct sequence according to the order of operations—often remembered using the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

Here is a simplified framework to tackle such problems:

• Identify Operations: First, determine what operations are involved. This could include addition, subtraction, multiplication, etc.
• Order of Operations: Always perform operations in the correct order. This avoids mistakes and ensures your calculations are correct.
• Simplify the Expression: Break down the operations one step at a time, simplifying the expression as you solve it.
• Check Your Work: Verify your calculations to confirm that you've arrived at the correct result, and compare it with the given options (if applicable).

Successful problem-solving in mathematics often involves breaking down complex expressions into manageable steps and applying mathematical principles at each stage to find the solution.