Problem 84 - Prealgebra

Question

Use the rule for order of operations to combine the following. \(8 \cdot 3-2\)

Step-by-Step Solution

Answer

The result is 22.

Step 1: Review the Order of Operations

First, recall the order of operations, often remembered using PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Step 2: Identify Operations in the Expression

In the expression \(8 \cdot 3 - 2\), identify that there is multiplication (\(8 \cdot 3\)) and subtraction (\(-2\)).

Step 3: Perform Multiplication First

According to the order of operations, perform multiplication before subtraction. Compute \(8 \cdot 3\), which equals 24.

Step 4: Perform Subtraction

After multiplication, perform the subtraction. Subtract 2 from 24, resulting in \(24 - 2 = 22\).

Key Concepts

PEMDAS

When solving mathematical expressions, it's essential to follow the correct order of operations. To remember this sequence, we often use the acronym PEMDAS.
PEMDAS stands for:

• **P**arentheses: Solve expressions inside parentheses first.
• **E**xponents: Calculate powers or square roots.
• **M**ultiplication and **D**ivision: Work from left to right, performing any multiplication or division.
• **A**ddition and **S**ubtraction: Finally, handle addition and subtraction from left to right.

This sequence ensures that everyone solves expressions the same way and gets the same answer. It's crucial, especially with complex problems, to always start with operations in parentheses and move through the list in order.

multiplication

In the given expression, multiplication plays a key role. The operation comes before subtraction according to PEMDAS.
With the expression given as:
- Multiply 8 by 3, which gives 24. This step is crucial because if you don't handle multiplication first, you'll end up with the wrong result. Always remember to multiply or divide before tackling any addition or subtraction operations. This principle makes your calculations accurate and consistent.

subtraction

Subtraction is one of the basic arithmetic operations and comes after multiplication in the order of operations.
Note the expression after tackling multiplication:
- You start with 24 after completing the multiplication step.
- Now, subtract 2 from 24, which leaves you with 22.
This demonstrates why it's essential to handle operations in their proper order. By focusing on subtraction last, as indicated by PEMDAS, you ensure the integrity and accuracy of your solution.
Always remember, once you've completed operations like multiplication, move on to subtraction to wrap up your expression.