Problem 68 - Algebra 1: Concepts and Skills

Question

Determine whether the statement is true or false. Use the subtraction rule or a number line to support your answer. $$ 4 \cdot(12 \div 6)-5 $$

Step-by-Step Solution

Answer

The value of the given mathematical expression is 3, therefore the initial statement is true assuming it expected this result.

Step 1: Resolve the operation inside the brackets

According to the BIDMAS/BODMAS rule, operations inside brackets have the highest priority. Here, \( 12 \div 6 = 2 \) inside the brackets.

Step 2: Perform multiplication

Next, we have the multiplication operation. Multiply the outcome from step 1 by 4: \( 4 \cdot 2 = 8 \).

Step 3: Subtraction operation

The final operation is subtraction. Subtract 5 from the result of the multiplication: \( 8 - 5 = 3 \).

Key Concepts

Subtraction Rule

The subtraction rule is a fundamental arithmetic operation. It is used to find the difference between numbers by removing the value of one number from another. When you see a subtraction sign, it tells you to take away the second number from the first. For example, if you start with 8 and need to subtract 5, you are essentially taking 5 from 8 to determine how much remains. In this case, using the subtraction rule, the answer is 3.

• Subtraction is essential when balancing equations or solving problems requiring a decrease.
• It helps in determining how much remains or how much has changed.

In the solved example, after performing multiplication, the result was 8, and by applying the subtraction rule correctly, 5 was subtracted from 8, yielding 3. Understanding this rule is key to correctly executing operations involving differences.

Number Line

A number line is a visual tool that helps to illustrate the position and relationship of numbers. It is essentially like a map for numbers, where you can see where each number stands in relation to another. A number line extends infinitely in both directions, but for simplicity, we often draw them in a focused segment. This tool is useful for understanding addition and subtraction as you can move left for subtraction and right for addition.

• Start at the point of the initial number.
• Move left if subtracting to reach the final position.

In the exercise example, if depicted on a number line, you would start at 8 and move five steps to the left to reach the answer, 3. This visual representation reinforces arithmetic operations and ensures accurate calculations.

BIDMAS/BODMAS

BIDMAS/BODMAS is an acronym that stands for Brackets, Indices, Division and Multiplication, Addition and Subtraction. It is a rule that indicates the order in which operations should be carried out to ensure consistent results across mathematical problems. This rule is crucial because it prevents confusion in math operations by defining a standard sequence.

• First, solve operations inside Brackets.
• Then address any Indices (exponents).
• Perform Division and Multiplication, from left to right.
• Finally, execute Addition and Subtraction, also from left to right.

In the provided problem, BIDMAS/BODMAS ensures that division within the bracket is solved first: \(12 \div 6 = 2\). Then, multiplication follows: \(4 \times 2 = 8\), and finally, subtraction concludes the calculation: \(8 - 5 = 3\). Understanding BIDMAS/BODMAS is essential to solve problems methodically and accurately.