Problem 39 - Prealgebra

Question

Perform the following operations according to the rule for order of operations. $$3.08-0.2(5+0.03)$$

Step-by-Step Solution

Answer

The result of the operation is 2.074.

Step 1: Parentheses

First, solve the operation inside the parentheses: \(5 + 0.03 = 5.03\). The expression becomes \(3.08 - 0.2(5.03)\).

Step 2: Multiplication

Next, perform the multiplication: \(0.2 \times 5.03 = 1.006\). The expression now is \(3.08 - 1.006\).

Step 3: Subtraction

Finally, perform the subtraction: \(3.08 - 1.006 = 2.074\).

Key Concepts

Understanding Parentheses in Order of Operations

When solving math problems, parentheses are pivotal. They indicate which part of the equation should be tackled first.
In the order of operations, parentheses are the very first step. This means any calculations within them have priority.
For instance, if you see an expression like \(5 + 0.03\) inside a pair of parentheses, your first task is to solve that portion.
Think of parentheses as a "do this first!" tag. They help organize complex equations, breaking them down into manageable steps.
In the given exercise, we first tackle \((5 + 0.03)\), resulting in \(5.03\), before moving on to other operations.

Delving into Multiplication in Equations

Once parentheses are dealt with, multiplication is usually the next operation. This step solidifies the progression of simplifying an expression.
When we encounter a number directly outside parentheses, like \(0.2(5.03)\), it indicates multiplication. This means 0.2 is multiplied by the entire result of \((5+0.03)\).
So, our task is to calculate \(0.2 \times 5.03\), which equals \(1.006\). Accomplishing this step efficiently pushes the equation closer to its final simplified form.
Multiplication in these scenarios is carried out with precision. Rounding errors can be risky, so it's essential to pay attention to details.

Exploring Subtraction in Mathematical Operations

The last operation in the order of operations for this exercise is subtraction. This step helps bring the equation to a close.
In the context of this exercise, after completing the multiplication, we obtain the expression \(3.08 - 1.006\).
Subtraction requires careful attention, especially when dealing with decimals. Align numbers by their decimal points to ensure accuracy.
Subtract \(1.006\) from \(3.08\) precisely, and you'll find it equals \(2.074\).
This final step brings the equation to completion, offering a sense of resolve to the mathematical operations.