Problem 66 - Algebra 1: Concepts and Skills

Question

Evaluate the expression. $$ 14-2 \cdot 5-3 $$

Step-by-Step Solution

Answer

The evaluated result of the expression \(14 - 2 \cdot 5 - 3\) is \(1\).

Step 1: Apply the Order of Operations - BIDMAS/PEMDAS

The arithmetic operations in the expression are subtraction and multiplication. According to the order of operations, it is necessary to perform multiplication before subtraction. So, Multiply 2 by 5 first. This results in \(14 - 2 \cdot 5 - 3\) = \(14 - 10 - 3\)

Step 2: Continue Applying the Order of Operations - BIDMAS/PEMDAS

Now, you have the expression \(14 - 10 - 3\). Here, only subtraction is left. The subtraction operation is performed from left to right. So, first subtract 10 from 14, and then subtract 3 from the result. So, \(14 - 10 - 3\) = \(4 - 3\)

Step 3: Finish the calculation

Now, subtract 3 from 4 which results in \(1\).

Key Concepts

Multiplication

Multiplication is one of the fundamental operations in arithmetic. It involves calculating the total of one number added repeatedly. In the expression given in the original exercise, we have the operation \(2 \cdot 5\). This tells us to take the number 2 and add it to itself 5 times, which results in 10.
Multiplication is a crucial step in the order of operations, as it usually takes precedence over addition and subtraction. In many expressions, handling multiplication correctly is vital for accuracy.

• Consider what numbers are being multiplied: In this case, it was 2 and 5.
• Recognize that multiplication can simplify expressions greatly before you move on to other operations.

By understanding multiplication's role, solving mathematical problems becomes much clearer and more straightforward.

Subtraction

Subtraction is the arithmetic operation that involves taking away a number from another, which gives us the difference. In the step-by-step solution of the original exercise, subtraction appeared multiple times. After performing the multiplication, the expression was simplified to \(14 - 10 - 3\).
When dealing with subtraction:

• Subtract numbers in the order they appear from left to right.
• Always simplify the expression after each subtraction to make the process easier.

First, you subtract 10 from 14, leading to 4, and then 3 from 4, resulting in 1. Ensuring each subtraction step is done carefully helps to avoid errors.

BIDMAS/PEMDAS

BIDMAS or PEMDAS is an acronym to help remember the order of operations: Brackets, Indices (or Exponents), Division and Multiplication, Addition and Subtraction. This order dictates the priority of operations to solve an expression correctly.
For the expression in the exercise, BIDMAS/PEMDAS tells us to deal with multiplication before subtraction.
Key points to remember include:

• Multiplication comes before subtraction, so 2 times 5 is calculated first, giving 10.
• After the multiplication, subtraction operations are performed from left to right.

By following BIDMAS/PEMDAS, the expression \(14 - 2 \cdot 5 - 3\) is simplified accurately to 1, ensuring you don't end up with incorrect answers due to neglecting the correct order.