Problem 116 - Prealgebra

Question

Simplify \(24+4 \cdot 6\)

Step-by-Step Solution

Answer

The simplified expression is 48.

Step 1: Identify the Operations

First, identify the different operations in the expression. In the expression \(24 + 4 \cdot 6\), there is an addition and a multiplication.

Step 2: Apply the Order of Operations

According to the order of operations (PEMDAS/BODMAS), multiplication comes before addition. Therefore, start by performing the multiplication: \(4 \cdot 6\).

Step 3: Perform the Multiplication

Calculate the result of the multiplication operation: \(4 \cdot 6 = 24\).

Step 4: Simplify the Expression

Replace \(4 \cdot 6\) in the original expression with its result \(24\). The expression becomes \(24 + 24\).

Step 5: Perform the Addition

Evaluate the addition: \(24 + 24 = 48\).

Key Concepts

PEMDAS

The term PEMDAS is an acronym that represents the order of operations used in mathematics to solve expressions. The letters in PEMDAS stand for:

• P - Parentheses
• E - Exponents
• M - Multiplication
• D - Division
• A - Addition
• S - Subtraction

The rule helps students to determine which part of an expression to calculate first. For example, in the expression \(24 + 4 \cdot 6\), the PEMDAS rule tells us to perform the multiplication before the addition.
Understanding and applying PEMDAS is crucial since performing operations out of order can lead to incorrect results. Always remember to start with operations inside Parentheses, follow with Exponents, and then proceed with Multiplication and Division, which are on the same level of priority and should be addressed from left to right. Finally, tackle Addition and Subtraction, also moving from left to right.

BODMAS

BODMAS is another acronym similar to PEMDAS, used primarily in countries like the UK and Australia. It stands for:

• B - Brackets
• O - Orders (meaning powers and roots, like exponents)
• D - Division
• M - Multiplication
• A - Addition
• S - Subtraction

As with PEMDAS, BODMAS guides you on which operations to carry out first when simplifying expressions. The main difference lies in the terms used, such as 'Brackets' instead of 'Parentheses', and 'Orders' instead of 'Exponents'.
Using the expression \(24 + 4 \cdot 6\), BODMAS also insists on the multiplication being handled before the addition, leading to a similar simplification process. It's essential to understand both terms for global mathematical literacy, as different regions may use one system exclusively.

simplification of expressions

Simplifying expressions involves a systematic approach of reducing expressions to their simplest form. This means performing all possible operations to arrive at a single numerical value or a simplified expression.
The simplification process requires an understanding of the correct order of operations (PEMDAS/BODMAS) to avoid mistakes. Each step involves substituting parts of the expression with their calculated values until you achieve a simple form.
In the exercise provided, \(24 + 4 \cdot 6\), simplification involves:

• Identifying the operations: addition and multiplication.
• Applying the rules of order of operations, performing multiplication first to obtain 24 from \(4 \cdot 6\).
• Replacing \(4 \cdot 6\) with 24, giving the expression \(24 + 24\).
• Finally, performing the addition to simplify the expression to 48.

Simplification aims to make mathematics more manageable and helps in solving problems accurately and efficiently. Always work step-by-step according to the rules to avoid confusion.