Problem 11 In Exercises $1-66,$ compute t... [FREE SOLUTION]

91影视

Understanding Elementary Algebra with Geometry

Lewis Hirsch, Arthur Goodman

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 1: Problem 11

In Exercises $1-66,$ compute the value of each expression. $$-7+(-3)$$

Short Answer

Expert verified

-10

Step by step solution

- Understanding the expression

The given expression is $-7 + (-3)$. This means you need to add -3 to -7.

- Adding negative numbers

Adding two negative numbers involves adding their absolute values and then applying a negative sign to the result. $\text{Absolute value of -7: } 7$ $\text{Absolute value of -3: } 3$. Thus, add $7 + 3 = 10$.

- Applying the negative sign

After finding the sum of the absolute values, apply a negative sign to the result. So, $ -(7 + 3) = -10 $. Therefore, the value of the expression \ -7 + (-3) \ is -10.

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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. They are represented with a minus sign (-) in front of them. For example, -1, -2, and -3 are all negative numbers. In real life, negative numbers can represent things like debt or temperatures below zero. When working with negative numbers in arithmetic, it's essential to understand how they interact with positive numbers and each other. One key point to remember is that subtracting a negative number is the same as adding its absolute value.

absolute value

The absolute value of a number is the distance of that number from zero on the number line, regardless of direction. It is always a positive value or zero. For example, the absolute value of -7 is 7, and the absolute value of 3 is 3. The absolute value is denoted by two vertical bars surrounding the number, like this: $|-7| = 7$. When adding or subtracting negative numbers, finding their absolute values can make the calculations easier. It's also useful for comparing the size of numbers without worrying about their sign.

addition of negative numbers

Adding negative numbers can seem tricky at first, but with practice, it becomes more intuitive. When you add two negative numbers, you first look at their absolute values. Then, you add these absolute values together and apply a negative sign to the result. Let's look at an example: If you have -7 and -3, you first find their absolute values, which are 7 and 3. Then, you add these absolute values to get 10. Finally, you apply a negative sign to the result, resulting in -10. This process works because adding negative numbers means you're going further in the negative direction on the number line.

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91影视

In Exercises \(1-66,\) compute the value of each expression. $$-7+(-3)$$

Short Answer

Step by step solution

- Understanding the expression

- Adding negative numbers

- Applying the negative sign

Key Concepts

negative numbers

absolute value

addition of negative numbers

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