Problem 28 - Elementary Algebra

Question

For the following problems, use the order of operations to find each value. $$6.1(2.2+1.8)$$

Step-by-Step Solution

Answer

Answer: The value of the expression 6.1(2.2+1.8) is 24.4.

Step 1: Evaluate expressions within Parentheses

In the given expression, we have one set of parentheses containing \((2.2+1.8)\). Calculate the value within the parentheses. $$2.2+1.8 = 4$$ So, the expression becomes: $$6.1\cdot4$$

Step 2: Perform multiplication

Now, we have only one operation left, multiplication. We will multiply the two numbers together. $$6.1\cdot4=24.4$$ Thus, the value of the expression $$6.1(2.2+1.8)$$ is $$24.4$$.

Key Concepts

Parentheses

Parentheses are a fundamental part of mathematical expressions used to group numbers and operations. When you see parentheses in an expression, it signals that you should calculate whatever is inside them first before doing anything else. This is in accordance with the order of operations, which is a set of rules that dictates the correct sequence to evaluate a math expression.

In the exercise example, the parentheses contain the expression (2.2 + 1.8). According to the order of operations, we solve this part first:

• Calculate inside the parentheses: 2.2 + 1.8 = 4

Once you've found the value inside the parentheses, you replace the entire parentheses with this new number in the overall expression. This ensures the expression is simplified in the correct order, leading to accurate solutions.

Multiplication

Multiplication is one of the basic arithmetic operations essential in mathematics. After resolving any parentheses in an expression, you will often perform multiplication next — unless other operators have higher precedence. It provides a quick way to add equal groups of numbers together, simplifying calculations and making them more efficient.

In the context of our example, once the evaluation inside the parentheses is complete, the expression simplifies to 6.1 times 4.

This multiplication step looks like this:

• Multiply 6.1 by 4, which equals 24.4

By diligently following the multiplication stage after evaluating any parentheses, you ensure that your computations adhere to the correct order of operations, maintaining mathematical integrity.

Mathematical Expressions

Mathematical expressions consist of numbers, operators (such as addition, subtraction, multiplication, and division), and sometimes variables, combined to represent a value. The challenge often lies in simplifying these expressions using the correct sequence of operations.

For every mathematical expression:

• Identify each component and operation.
• Apply the order of operations — resolve parentheses first, then move to multiplication or division from left to right, followed by addition or subtraction.

In our given expression 6.1(2.2 + 1.8), understanding the structure is vital. The components are:

• Numbers: 6.1, 2.2, 1.8
• Operators: addition within the parentheses, multiplication outside it

By systematically evaluating these expressions, starting with operations within parentheses and following through with multiplication, we simplify the expression correctly, obtaining precise results.