Problem 97 - Beginning and Intermediate Algebra

Question

Perform each indicated operation. $$ -9.12+[(-4.8-3.25)+11.279] $$

Step-by-Step Solution

Answer

-5.891

Step 1: Identify the Innermost Parenthesis

Locate the innermost parentheses to simplify them first. In this expression, it is \( -4.8-3.25 \).

Step 2: Simplify the Innermost Expression

Calculate \( -4.8 - 3.25 = -8.05 \).

Step 3: Substitute the Simplified Expression

Replace \( -4.8 - 3.25 \) with \( -8.05 \) in the original expression. Now it looks like this: \[ -9.12 + [-8.05 + 11.279] \].

Step 4: Simplify Inside the Square Brackets

What remains inside the square brackets is \[ -8.05 + 11.279 \]. Simplify this by calculating \[ 11.279 - 8.05 = 3.229 \].

Step 5: Substitute Back Again

Replace the simplified part back into the expression: \[ -9.12 + 3.229 \].

Step 6: Final Calculation

Calculate the final part of the expression: \[ -9.12 + 3.229 = -5.891 \].

Key Concepts

order of operations

When working with algebraic expressions, it’s crucial to follow the order of operations to get the correct result. This method ensures we perform calculations in the right sequence. The standard order is often remembered through PEMDAS, which stands for:

• Parentheses
• Exponents
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

When dealing with the given expression, \(-9.12+[-4.8-3.25+11.279]\), we first tackle the innermost parentheses. Simplifying inside these parentheses first guarantees that we respect the defined order, preventing any mistakes in our calculations.

simplifying expressions

Simplifying an expression involves reducing it to its simplest form. To do this, we break down complex parts step-by-step. In the provided expression, we start by simplifying the innermost parentheses \[ (-4.8-3.25) \] as \[ -8.05 \]. This substitution simplifies the expression to \[ -9.12 + [-8.05 + 11.279] \]. Next, we further simplify the expression inside the square brackets. Calculating \[ 11.279 - 8.05 \] results in \[ 3.229 \]. When this is substituted back into the expression, it then reads \[ -9.12 + 3.229 \], which leads us to the final simplified calculation.

addition and subtraction of decimals

Addition and subtraction of decimals require careful attention to align the decimal points. In the given problem, we encounter two main decimal operations:

• Subtracting \(-4.8 - 3.25\) giving \(-8.05\)
• Adding \[ -8.05 + 11.279 \] which simplifies to \[ 3.229 \]

When subtracting \(4.8\) from \(3.25\), we convert both numbers to decimal format and then perform the subtraction. Be sure to place the decimal points directly under each other to avoid errors. Similarly, while adding \: \[ 11.279 - 8.05 \], stacking and aligning the decimals correctly is essential. Ultimately, our final step involves adding \[ -9.12 + 3.229 \], ensuring we respect the negative sign and decimal alignment to find the correct result of \[ -5.891 \].