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Chapter 1: Problem 33

In Exercises \(1-66,\) compute the value of each expression. $$-7+3+(-5)$$

Short Answer

Expert verified
-9

Step by step solution

01

Evaluate the first addition

First, add -7 and +3. -7 + 3 = -4 because adding a positive number to a negative number is like subtracting the smaller number from the larger number but keeping the sign of the larger number's absolute value.
02

Evaluate the second addition

Next, add -4 and -5. -4 + (-5) = -9 because adding two negative numbers results in a more negative number. Adding the absolute values of the two negatives (4 + 5) gives 9, but the result is negative since both original numbers were negative.

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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 less than zero. They are represented with a minus sign (-) in front of them. For example, -1, -2, -3, etc. Negative numbers are used to represent values below zero, like cold temperatures, debt, or elevations below sea level.

When working with negative numbers, remember:
  • Adding a negative number to a negative number makes a more negative number.
  • Adding a negative number to a positive number is like subtracting the smaller number from the larger number.
Here, when you added -7 and +3, it was like subtracting 3 from 7, resulting in -4. The sign remained negative because 7 is larger than 3.
Absolute Value
Absolute value refers to the distance a number is from zero on the number line, regardless of direction. It is always a non-negative number.

For example:
  • The absolute value of -5 is 5 (|-5| = 5).
  • The absolute value of 3 is 3 (|3| = 3).
Absolute values are helpful in addition and subtraction involving negative numbers.

For example, in -4 + (-5), the absolute values of -4 and -5 are 4 and 5, respectively. The sum of these absolute values is 9. Finally, since both original numbers were negative, the result is negative (-9).
Addition Rules
Addition rules help simplify working with both positive and negative numbers.

Here are some key rules to remember:
  • Add positive numbers like usual.
  • When adding a positive number to a negative number, subtract and keep the sign of the larger absolute value.
  • When adding two negative numbers, add their absolute values and make the result negative.
In the exercise, the steps are:

Step 1: Add -7 and 3. Think of it as 7 - 3, giving you 4, but with a negative sign (larger absolute value is 7, which is negative).

Step 2: Add -4 and -5. Add the absolute values (4+5=9) and keep the result negative, giving you -9.

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