Problem 69 - Prealgebra

Question

Simplify the given expression. \(-19.1-(1.51-(-17.35))\)

Step-by-Step Solution

Answer

The simplified expression is -37.96.

Step 1: Identify the Expression

First, we need to identify the arithmetic expression that needs to be simplified. The given expression is: \(-19.1 - (1.51 - (-17.35))\).

Step 2: Remove Parentheses

Notice the expression inside the parentheses: \(1.51 - (-17.35)\). The minus sign in front of \(-17.35\) changes to a plus:\(1.51 + 17.35\).

Step 3: Simplify Inside the Parentheses

Now calculate the sum inside the parentheses: \(1.51 + 17.35 = 18.86\).

Step 4: Substitute Back and Simplify Further

Substitute the simplified value back into the main expression:\(-19.1 - 18.86\).

Step 5: Final Calculation

Now perform the subtraction:\(-19.1 - 18.86 = -37.96\).

Key Concepts

Simplification

When we're simplifying an arithmetic expression, our main goal is to make the expression as simple as possible without changing its value. Simplification involves combining like terms and performing basic arithmetic operations. In the case of our given expression \(-19.1 - (1.51 - (-17.35))\), we start by breaking down complex parts into simpler components. This means dealing with operations inside the parentheses first, then moving outward. Simplification also involves being mindful of the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

• Rearrange and simplify terms.
• Always perform operations inside parentheses first.
• Follow order of operations to avoid mistakes.

Simplifying expressions makes them easier to understand and solve. This is particularly useful in algebra where expressions become more complex.

Parentheses

In the world of arithmetic, parentheses \(()\) hold a special place. They help us understand which operations to perform first in an expression. In our problem \(-19.1 - (1.51 - (-17.35))\), the parentheses tell us to focus on \(1.51 - (-17.35)\) first. It's crucial to solve any operations inside parentheses before moving to the rest of the equation. When you see parentheses:

• Recognize that operations inside them take priority.
• Simplify everything inside them before handling the rest of the expression.

Parentheses not only structure arithmetic expressions but also help make calculations clearer.

Negative Numbers

Negative numbers represent values less than zero, displaying an essential part of arithmetic. They can initially be tricky since they follow different rules compared to positive numbers. In our expression, we see negative numbers like \(-19.1\) and \(-17.35\). Handling negative signs requires careful attention, especially when they appear close to one another or in pairs as in \(-(-17.35)\).Guidelines when working with negatives:

• A negative sign in front of another negative makes a positive.
• Be cautious when adding and subtracting negative numbers to avoid mistakes.

Understanding how to manage negative numbers helps in avoiding errors and ensures accurate results.

Subtraction

Subtraction is an essential arithmetic operation that indicates the difference between two numbers. In an expression like \(-19.1 - 18.86\), subtraction involves removing the second number from the first. It's crucial to pay attention to the signs of the numbers involved, especially when dealing with negatives. When subtracting, keep in mind:

• You are effectively adding the opposite.
• Always double-check your signs when subtracting negative numbers.

Mastering subtraction ensures you can perform calculations correctly, yielding the right outcomes in arithmetic expressions.