Problem 80 - Prealgebra

Question

Simplify the given expression. \(8 .5+(3.9-6.98)\)

Step-by-Step Solution

Answer

The simplified expression is 0.92.

Step 1: Perform Multiplication

First, perform the multiplication in the expression. Multiply 8 by 0.5: \(8 \times 0.5 = 4\). The expression becomes \(4 + (3.9 - 6.98)\).

Step 2: Simplify Inside the Parentheses

Next, simplify the expression within the parentheses. Subtract 6.98 from 3.9: \(3.9 - 6.98 = -3.08\). The expression is now \(4 + (-3.08)\).

Step 3: Perform Addition

Finally, add 4 to -3.08: \(4 + (-3.08) = 0.92\).

Key Concepts

Order of Operations

When simplifying expressions in math, it's essential to follow the correct order of operations. This set of rules dictates the sequence in which different operations should be performed in a mathematical expression. The common acronym used to remember this sequence is PEMDAS:

• Parentheses
• Exponents
• Multiplication
• Division
• Addition
• Subtraction

When using PEMDAS, start with operations inside Parentheses. They take priority over everything else. After dealing with the expressions in parentheses, move on to Exponents, if any. Following that, perform Multiplication and Division in the order they appear from left to right.
Finally, complete Addition and Subtraction in the order they appear from left to right. In our example, after doing the multiplication 8 times 0.5, we continue by simplifying the expression within parentheses before adding the final values together.

Parentheses in Math

Parentheses play a crucial role in mathematical expressions as they indicate which operations should be performed first. They essentially "lock in" a specific part of the expression and demand that it be simplified before anything outside the parentheses. This helps prevent any confusion and ensures that everyone simplifies an expression in the same, systematic way.
Consider the expression provided: \(8 \times 0.5 + (3.9 - 6.98)\). In this case, the parentheses around \(3.9 - 6.98\) signal that this subtraction must occur first, once the prior multiplication is completed, regardless of the position of addition or multiplication in the equation.

• Remember, operations inside parentheses have the highest priority.
• Always simplify what's inside them completely, before moving on to other parts of the equation.

This ensures that expressions are calculated accurately and consistently.

Addition and Subtraction of Decimals

Adding and subtracting decimals involves numbers behind a decimal point and requires careful alignment to ensure accuracy. When dealing with these operations, it's important to align decimal points vertically.

• Start from the rightmost digit and proceed leftward.
• Ensure each decimal place corresponds to the digits from the other number involved.

In the example, after simplifying what's inside the parentheses, we are left with \(4 + (-3.08)\). Even though the operations involve working with negative decimals, the focus remains on careful alignment and accurate arithmetic.
Handling decimals correctly is crucial, as a misplaced digit can result in significant errors. This skill is practical for everyday transactions and more complex calculations, ensuring all numbers add up just right. Practice makes perfect, so working through several examples will improve your comfort with decimals.