Problem 10 In Exercises $1-72$, compute t... [FREE SOLUTION]

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Understanding Elementary Algebra with Geometry

Lewis Hirsch, Arthur Goodman

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 1: Problem 10

In Exercises $1-72$, compute the value of each expression. $$-7+(+5)$$

Short Answer

Expert verified

-2

Step by step solution

Identify the terms

Observe that the expression consists of the terms $-7$ and $+5$.

Understand the operation

Note that the operation between the terms is addition. The expression is $-7 + 5$.

Perform the addition

When adding $-7$ and $+5$, treat $-7$ as moving 7 units to the left of zero, and then moving 5 units to the right. The result of $-7 + 5$ is $-2$.

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Key Concepts

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

Addition of Integers

Addition of integers can initially seem tricky, but it's actually quite simple once you understand the rules. When you add two positive integers, the result is positive. When you add two negative integers, the result is negative. The tricky part is when you add a positive integer and a negative integer. Here are the key points to remember:

When adding a positive number and a negative number, you actually subtract the smaller number from the larger one and keep the sign of the larger number.
In the problem $-7 + 5$, you treat $-7$ as 7 units to the left of zero and $+5$ as 5 units to the right.

After subtracting 5 from 7, you get 2. Since 7 (from $-7$) is larger, the result is negative. That's why $-7 + 5 = -2$. This understanding simplifies many algebra problems as you progress.

Negative Numbers

Negative numbers are a fundamental concept in mathematics. They are numbers less than zero and are represented with a minus sign (-). Negative numbers have some unique properties:

Adding a negative number is the same as subtracting its positive counterpart. For instance, $-3$ added to $+2$ results in the same value as $+2 - 3$.
When visualizing on a number line, moving left indicates subtraction or the negative direction, and moving right indicates addition or the positive direction.
Subtraction of negative numbers can be tricky. For example, subtracting a negative number is equivalent to adding its positive counterpart. For instance, \-(-4)\After performing these basic operations, you'll find that working with negative numbers becomes intuitive. Keep practicing, and you'll master them in no time.

Basic Arithmetic Operations

Basic arithmetic operations form the foundation of algebra and include addition, subtraction, multiplication, and division. Here is a quick recap of how each works:

Addition: Combining two or more numbers to get a total sum. For example, $ 2 + 3 = 5 $.
Subtraction: Finding the difference between two numbers by removing the value of one from another. For example, $ 5 - 2 = 3 $.
Multiplication: Adding a number to itself a certain number of times. For instance, $ 4 \times 3 = 12 $.
Division: Splitting a number into equal parts. For example, $ 12 梅 3 = 4 $.

Being comfortable with these operations is essential. Remember, practice is key. Working through examples, like our exercise with $ -7 + 5 $, strengthens your understanding and ability to handle more complex algebraic expressions. Don't rush; take your time to understand each concept thoroughly.

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91影视

In Exercises \(1-72\), compute the value of each expression. $$-7+(+5)$$

Short Answer

Step by step solution

Identify the terms

Understand the operation

Perform the addition

Key Concepts

Addition of Integers

Negative Numbers

Basic Arithmetic Operations

One App. One Place for Learning.

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