Problem 18 - Algebra 1: Concepts and Skills

Question

Evaluate the expression. $$ 7+8 \div 2 $$

Step-by-Step Solution

Answer

The value of the given expression is 11.

Step 1: Perform the Division

According the BIDMAS/BODMAS rule, division should be performed first. So, let’s divide \(8 \div 2\) which equals to \(4\). Then the expression becomes \(7 + 4\).

Step 2: Perform the Addition

The next step is to add the results of step 1. So, \(7 + 4 = 11\).

Key Concepts

BIDMAS

BIDMAS is a handy acronym to remember the order of operations in mathematics. It stands for Brackets, Indices, Division and Multiplication, Addition and Subtraction. It helps you decide which operations to perform first in a given expression.

• Brackets: Always solve expressions inside brackets first.
• Indices: Next, manage any exponential values or indices.
• Division and Multiplication: Perform these operations from left to right.
• Addition and Subtraction: Finally, solve these, also from left to right.

By following BIDMAS, you ensure that your calculations are consistent and accurate. Remember, Division and Multiplication, as well as Addition and Subtraction, are completed based on their order of appearance from left to right.

BODMAS

Similar to BIDMAS, BODMAS is another mnemonic to remind you of the order of operations. It stands for Brackets, Orders, Division and Multiplication, Addition and Subtraction. Often used interchangeably with BIDMAS, it emphasizes the same rules but uses a different term for indices:

• Brackets: Solve expressions inside brackets first.
• Orders: Evaluate any powers or square roots.
• Division and Multiplication: Process these as you encounter them from left to right.
• Addition and Subtraction: Proceed with these last, also from left to right.

The key takeaway is that both BIDMAS and BODMAS guide you on the sequence to follow when solving mathematical expressions. Adhering to these rules helps prevent errors.

Expression Evaluation

Expression evaluation involves solving mathematical expressions in the correct order, using BIDMAS or BODMAS as a guide. Evaluating an expression requires patience and attention to detail. Let's look at the steps in evaluating the given expression:

• Start with Division or Multiplication. In the expression \(7 + 8 \div 2\), the division \(8 \div 2\) is performed first to get 4.
• Next, move on to Addition or Subtraction. After completing the division, you add the result to the other number in the expression: \(7 + 4 = 11\).

By following the steps dictated by BIDMAS/BODMAS, the final evaluated result of the expression is 11. It’s a systematic approach that ensures precision and reduces confusion when dealing with more complex calculations.