Problem 52 - Prealgebra

Question

Find the value of each expression. $$3+(6 \times 2)-8$$

Step-by-Step Solution

Answer

The value of the expression is 7.

Step 1: Multiply

First, perform the multiplication inside the expression. Multiply 6 by 2: \[6 \times 2 = 12\]

Step 2: Add

Add 3 to the result of the multiplication from Step 1. \[3 + 12 = 15\]

Step 3: Subtract

Subtract 8 from the result obtained in Step 2. \[15 - 8 = 7\]

Key Concepts

Arithmetic Operations

Arithmetic operations form the foundation of mathematics. These operations include addition, subtraction, multiplication, and division. They are essential for manipulating numbers, and understanding them is crucial for tackling more complex problems. Let's break down each of these operations:

• Addition: This operation combines two or more numbers into a single total. It's often represented by the plus sign "+".
• Subtraction: This operation involves taking one number away from another. It's represented by the minus sign "-".
• Multiplication: This operation is a form of repeated addition. If you multiply two numbers, you are essentially adding one of the numbers to itself multiple times. This is indicated by the multiplication sign "×" or "*".
• Division: This operation is essentially the reverse of multiplication. It involves splitting a number into a specified number of parts. The symbol for division is "÷" or "/".

In our exercise, we utilize addition, subtraction, and multiplication to find the value of a mathematical expression. Remember, each operation holds different priorities in mathematical expressions.

Mathematical Expressions

Mathematical expressions are combinations of numbers and operations. They don't have an equals sign and differ from equations. To find the value of an expression, you perform the indicated operations in a certain order. The expression from our original exercise, \(3+(6 \times 2)-8\), is a great example of such a setup. Solving it involves accounting for the order of operations. This set of rules ensures that you perform calculations correctly and uniformly. The commonly used rule is PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). This guides us to perform multiplication before addition and subtraction. That's why, in the solution, the multiplication is done first, followed by addition, and finally subtraction.
Understanding how to manipulate these expressions allows one to solve practical and abstract problems efficiently.

Prealgebra Concepts

Prealgebra is a branch of mathematics that prepares students for algebra by covering basic math skills needed to understand algebra. It involves operations with whole numbers, fractions, decimals, and positive and negative numbers. Among these core concepts is the order of operations, which is fundamental in correctly solving mathematical expressions. Without prealgebra concepts, understanding algebraic principles can become quite challenging.
In the exercise we've tackled, we rely heavily on prealgebra principles, such as understanding that multiplying should be completed before proceeding to addition and subtraction. This ensures we correctly interpret and simplify mathematical expressions. Mastering prealgebra sets a strong foundation for approaching more complex algebraic equations and develops critical thinking skills for solving everyday math challenges.