Problem 34 - Introductory Algebra for College Students

Question

In Exercises \(29-72,\) use the order of operations to simplify each expression. $$8 \cdot 6 \div 2$$

Step-by-Step Solution

Answer

The simplified form of the expression \(8 \cdot 6 \div 2\) is 24

Step 1: Perform the multiplication operation

According to the Order of operations (PEMDAS), multiplication and division operations should be processed from left to right. So, you should first perform the multiplication operation in the expression. That is \(8 \cdot 6 = 48\)

Step 2: Perform the Division operation

Next, perform the division operation on the result from step 1. That is \(48 \div 2 = 24\)

Key Concepts

Understanding PEMDAS

When tackling math problems like \(8 \cdot 6 \div 2\), it's essential to understand the order of operations, often remembered by the acronym PEMDAS. This handy rule guides us in solving expressions accurately. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

• Parentheses: Handle anything inside parentheses first.
• Exponents: Solve these after parentheses.
• Multiplication and Division: Work these out next, moving from left to right.
• Addition and Subtraction: Finally, deal with these, also moving from left to right.

The left-to-right rule for multiplication and division is crucial. You don't necessarily multiply first; instead, you follow the order as they appear in the expression. This ensures consistency and accuracy in reaching the solution.

Performing Multiplication

Multiplication, symbolized by \(\cdot\), combines quantities. For example, in the expression \(8 \cdot 6 \div 2\), start by multiplying 8 and 6.

How to multiply:

• Identify the numbers to be multiplied: Here, it's 8 and 6.
• Calculate the product: \(8 \cdot 6 = 48\).
• This product becomes the new number used in further calculations.

Multiplication is often faster than adding the same number multiple times. It reduces complexity, particularly in lengthy calculations. Remember that multiplication doesn't necessarily precede division unless it appears first when moving left to right in the expression.

Executing Division

Division, shown by \(\div\), splits a quantity into equal parts. In \(8 \cdot 6 \div 2\), the division follows the multiplication due to the left-to-right rule.

Steps for division:

• Take your previous result (from multiplication): Here, it's 48.
• Divide this result by the next number in the expression: \(48 \div 2\).
• Calculate the quotient: 48 divided by 2 equals 24.

Division is key for breaking down numbers, helping to determine how many times one fits into another. Always remember to divide only after any preceding multiplication unless division appears first in the expression following the order of operations.