Question

Evaluate the expression. $$2(11-7) \div 3$$

Short answer

The result of the given expression \(2(11-7) \div 3\) is approximately \(2.67\).

Step-by-step solution

Simplify Expression Inside the Brackets

Calculate the value inside the brackets first, which is \(11-7\). So the expression becomes \(2 \times 4 \div 3\).

Perform Multiplication

Next operation to be performed according to BIDMAS/BODMAS rule is multiplication. Multiply \(2 \times 4\) to get \(8\), the expression now is \(8 \div 3\).

Perform Division

Finally perform the division operation \(8 \div 3\) which equals \(2.67\) (approximately, to two decimal places).

Key concepts

Order of Operations

When evaluating expressions in algebra, it is essential to follow the correct order of operations. This predetermined set of rules dictates the sequence in which the mathematical operations should be performed to ensure consistent and accurate results. Without following this order, different people could interpret and solve the same expression differently, leading to multiple answers. In the provided example, Evaluate the expression: \(2(11-7) \div 3\), the order of operations tells us to simplify what's inside the brackets first before moving on to multiplication or division. After simplifying the expression inside the brackets, then tackling the operations from left to right according to their hierarchy.

BIDMAS/BODMAS Rule

The BIDMAS/BODMAS rule is a mnemonic to help remember the correct order in which to solve mathematical problems: Brackets, Indices/Orders (powers and square roots, etc.), Division and Multiplication (from left to right), and Addition and Subtraction (from left to right). In our example, Evaluate the expression: \(2(11-7) \div 3\), we start by solving the Brackets (11-7), followed by Multiplication (2 \times 4), and finally the Division (8 \div 3). Adhering to the BIDMAS/BODMAS rule guarantees that we always approach the problem with a consistent method, which is crucial for obtaining the correct answer.

Simplifying Expressions

To simplify expressions, we combine like terms and carry out operations to reduce the expression to a simpler form or a single number. Simplification lies at the heart of solving algebraic expressions and equations efficiently. In the example Evaluate the expression: \(2(11-7) \div 3\), simplification occurs in several stages: first by calculating the contents of the brackets, then by performing the multiplication, and finally by dividing. Simplifying each step as far as possible before proceeding to the next ensures that the final result is as straightforward as possible, rendering the expression to a single numerical value.

Arithmetic Operations

Basic arithmetic operations include addition, subtraction, multiplication, and division. These are foundational to all levels of math and are used not just individually but often in combination, as seen in algebraic expressions. In our standard problem, Evaluate the expression: \(2(11-7) \div 3\), we apply multiplication (2 \times 4) and division (8 \div 3) once we have simplified the initial subtraction (11-7). Mastery of these arithmetic operations, along with the understanding of when and how they should be applied, is essential for solving mathematical expressions accurately and efficiently.