Problem 47 Evaluate each expression. $$ ... [FREE SOLUTION]

Chapter 1: Problem 47

Evaluate each expression. $$ -22-15+3 $$

Short Answer

Expert verified

-34

Step by step solution

Simplify the Negative and Positive Components

Begin with the given expression, \[-22 - 15 + 3.\] First, simplify the expression by combining the negative numbers. Combine \[-22 - 15\] to get \[-37.\] The expression now becomes \[-37 + 3.\]

Add the Remaining Numbers

Now, add \[3\] to \[-37.\] This involves calculating \[-37 + 3,\] which results in \[-34.\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Negative Numbers

Negative numbers are numbers that are less than zero. You can think of them as numbers that go below zero on a number line. When working with negative numbers, it鈥檚 important to pay attention to their signs.
Negative numbers are often used to represent things like debts, temperatures below freezing, or altitudes below sea level.

Example: - If you are 5 meters below sea level, you might represent this as $-5$ meters.
Uses:They help in calculations, especially in scenarios where we need to show decrease or loss.
Arithmetic:When adding or removing negative numbers, treat the negative sign seriously as it influences the operation.

Addition

Addition is one of the basic operations of mathematics. It involves combining two or more numbers to get a total. When handling integers, especially those involving negative numbers, understanding how addition works is crucial.
With integers:

Adding a negative number is the same as subtracting its absolute value.- Example: To solve $-22 + (-15)$, you add $-15$ to $-22$, which moves you deeper into the negatives on the number line, leading to $-37$.
Adding a positive number to a negative number moves you toward or above zero.- Example: In the expression $-37 + 3$, adding $3$ moves you three units toward zero, resulting in $-34$.

Always align the terms properly to ensure accuracy, especially with mixed signs.

Simplifying Expressions

Simplifying expressions involves reducing them to a simpler form. This is commonly the first step in evaluating or solving any mathematical expression. It makes it easier to compute and understand the numbers.

Combining like terms: When given an expression like $-22 - 15 + 3$, first focus on combining terms that are of the same type. Here, $-22$ and $-15$ are both negative, yielding $-37$.
Sequential operations: After combining like terms, handle remaining operations in sequence. In our example, the next step was to add $3$ to $-37$. Proceed step by step to avoid mistakes.
Check your work: After simplifying, double-check to ensure that each step follows the rules of arithmetic accurately.

Simplification is about clarity, transforming an expression into its most understandable form.

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91影视

Evaluate each expression. $$ -22-15+3 $$

Short Answer

Step by step solution

Simplify the Negative and Positive Components

Add the Remaining Numbers

Key Concepts

Negative Numbers

Addition

Simplifying Expressions

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