Problem 6 - Elementary Algebra

Question

Use the order of operations to find each value. $$25+8(3)$$

Step-by-Step Solution

Answer

Answer: The value of the expression $$25 + 8(3)$$ is $$49$$.

Step 1: Identify operations in the expression

We are given the expression $$25 + 8(3)$$, and it contains addition and multiplication operations.

Step 2: Perform multiplication

Apply the order of operations, starting with multiplication: $$ 25 + 8 \cdot 3 $$ $$ 25 + 24 $$

Step 3: Perform addition

Now that we have completed the multiplication, we can perform the addition: $$ 25 + 24 $$ $$ 49 $$ The value of the expression $$25 + 8(3)$$ simplifies to $$49$$.

Key Concepts

Multiplication

Multiplication is one of the fundamental operations in mathematics. It simplifies the process of adding a number to itself repeatedly. For example, instead of writing 3 + 3 + 3, you can use multiplication to express it as 3 \times 3. In the context of our given expression \(25 + 8(3)\), multiplication is indicated next to the number 8 and follows the rules of order of operations. In this expression, 8 is multiplied by 3 first. This process follows what we often remember by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). Multiplying 8 by 3 gives us 24, which simplifies the original expression before moving on to the next step.

Addition

Addition is another basic operation in mathematics and involves combining numbers to get a total sum. After handling any multiplication in a mathematical expression, we turn our focus to addition. In our step-by-step solution to the expression \(25 + 8(3)\), after finding the result of the multiplication (24), addition is the next operation performed. We add the number 25 and the result of 8 multiplied by 3, which is 24. Doing so gives the final value:

• \(25 + 24 = 49\)

Thus, the sum of 25 and 24 completes the solution to the expression.

Mathematical Expressions

A mathematical expression is a combination of numbers, operations, and sometimes variables that together represent a particular value or statement. Understanding how to simplify these expressions by using the correct order of operations is crucial.For our expression \(25 + 8(3)\), there are a few key steps in simplifying it:- Identify each operation involved (in this case, addition and multiplication).- Follow the order of operations (PEMDAS) so multiplication is done before addition.- Simplify step by step to find the final value.Mathematical expressions like this one are solved efficiently when approached methodically. By recognizing the operation hierarchy, you ensure accurate and reliable results.