Problem 98 - Prealgebra

Question

Simplify. $$4 \cdot 6+3$$

Step-by-Step Solution

Answer

27

Step 1: Understand the Order of Operations

When simplifying expressions, you must follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). In this expression, there is multiplication and addition.

Step 2: Perform the Multiplication

According to the order of operations, multiplication comes before addition. So first, multiply 4 by 6.\[ 4 imes 6 = 24 \]

Step 3: Perform the Addition

Now that the multiplication is done, add the result to 3.\[ 24 + 3 = 27 \]

Key Concepts

PEMDAS

When you are working on simplifying expressions, it's essential to follow the order of operations. In mathematics, this order is remembered using the acronym PEMDAS. PEMDAS stands for:

• Parentheses – Always handle operations within parentheses first.
• Exponents – Simplify powers or roots next.
• Multiplication and Division – Work from left to right across these operations.
• Addition and Subtraction – Again, perform these from left to right.

This set of rules ensures that everyone solves math problems in the same way, getting the same answer every time. So, when you see an expression like \(4 \cdot 6 + 3\), you multiply first before you add.

Simplifying Expressions

Simplifying expressions might sound like a fancy term, but it's just the way we make mathematical expressions easier to understand or solve. Take the expression \(4 \cdot 6 + 3\) for instance. Simplifying means performing all possible calculations so the expression becomes clearer.

First, identify the operations you need to perform. Start with multiplication, as it comes before addition according to PEMDAS. So, calculate \(4 \cdot 6\), which gives you 24. Once multiplication is done, move to the addition: 24 plus 3. This results in 27. Now, you've turned the original, more complicated expression into a single, simple number.

You're not changing the value, but making it so we can easily know the result.

Mathematical Operations

Mathematical operations are the building blocks for simplifying expressions and solving equations. The core operations include addition, subtraction, multiplication, and division. Each operation has a specific role and a unique effect on numbers.

In the exercise \(4 \cdot 6 + 3\), you deal with two operations: multiplication and addition.

• Multiplication: This operation combines groups of numbers into a bigger total. Multiply 4 by 6 to find out what 4 lots of 6 equals, which is 24.
• Addition: This collects numbers together to find their total amount. After multiplying, add 3 to the result (24), leading to a total of 27.

Understanding how each operation works and how they operate together is key to mastering math problems and simplifying expressions.