Problem 99 - Prealgebra

Question

Simplify. $$4 \cdot 3+2(5-3)$$

Step-by-Step Solution

Answer

The expression simplifies to 16.

Step 1: Simplify Inside the Parentheses

First, look at the expression inside the parentheses: \(5 - 3\). Simplify this by subtracting 3 from 5, which gives \(2\). The expression now reads \(4 \cdot 3 + 2(2)\).

Step 2: Perform Multiplication

Next, perform the multiplications in the expression: \(4 \cdot 3\) and \(2(2)\). Calculate \(4 \cdot 3 = 12\) and \(2 \times 2 = 4\). Substitute these results back into the expression: \(12 + 4\).

Step 3: Add the Results

Finally, add the results together. Calculate \(12 + 4\), which equals \(16\). This is the simplified result of the expression.

Key Concepts

Simplifying Expressions

Simplifying expressions in math is like tidying up a room. You aim to make the expression as simple and understandable as possible. To simplify, you follow a set of rules that help clarify the calculations. In math, these rules are known as 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 the context of the exercise, simplifying means applying these rules to break down the expression step-by-step. By simplifying, you reduce the complexity of the expression, making it easier to solve. Always simplify inside parentheses first, then perform any multiplication or division, and finally move on to addition or subtraction. This structured approach ensures you arrive at the correct simplified result.

Parentheses in Math

Parentheses are crucial in mathematical expressions as they indicate which calculations should be performed first. They serve as a way to group parts of an expression and establish priority.
The presence of parentheses in a problem like this one, 4 \cdot 3 + 2(5-3), means you should first focus on simplifying whatever is inside them. So, you start with:

• Calculate the expression inside the parentheses: \(5 - 3\).
• Result is \(2\), so you replace \((5 - 3)\) with \((2)\).

Parentheses ensure clarity and prevent mistakes in calculations. By simplifying expressions within parentheses first, you're following the appropriate order of operations which prevents errors and confusion later.

Multiplication in Arithmetic

Multiplication is a fundamental arithmetic operation used to find the total of equal groups. In the given expression, after simplifying the parentheses, you're left with multiplications to execute:

• First, \(4 \, \cdot \, 3\) tells you to take four groups of three, which is \(12\).
• Second, you have \(2(2)\), representing two groups of two, equaling \(4\).

After calculating these products, you incorporate them back into the expression for the next operations. Make sure to perform all multiplication parts of an expression before moving on to addition or subtraction, following the order of operations. This ensures accurate results and allows you to solve math problems efficiently and effectively.