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Chapter 3: Problem 406

In the following exercises, simplify each expression. $$ -33+(-67) $$

Short Answer

Expert verified
-100

Step by step solution

01

- Identify the operation

The given expression is -33 + (-67). The operation here is addition of two negative numbers.
02

- Recall the rule for adding negative numbers

When adding two negative numbers, the sum is negative. We add the absolute values of the numbers and place a negative sign in front of the result.
03

- Add the absolute values

Find the absolute values of -33 and -67, which are 33 and 67, respectively. Now add these values: 33 + 67 = 100.
04

- Apply the negative sign

Since both original numbers were negative, place a negative sign in front of the result from step 3: -(33 + 67) = -100.
05

- Write the final answer

The simplified form of the expression -33 + (-67) is -100.

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Key Concepts

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

Addition of Negative Numbers
Adding negative numbers may seem tricky at first, but it's quite simple once you understand the process. First, understand that when you add negative numbers, you're essentially combining debts or deficits. Imagine you owe a friend \(33 (an example of -33) and you also owe another friend \)67 (-67). Combining these debts will increase your total debt. Rather than thinking of it as subtraction, think of it as summing up the values but keeping in mind they are negative. This insight helps you see why the sum of two negative numbers is also negative and larger in magnitude.
Absolute Value
The absolute value of a number is its distance from zero on a number line, without considering the direction. For any number x, its absolute value is denoted as \(|x|\). For instance, the absolute values of -33 and -67 are simply 33 and 67, respectively. While the concept of absolute value might seem redundant when dealing with positive numbers or zero, it is extremely useful for negative numbers. By converting a negative number into its positive counterpart, you simplify calculations and can then apply specific rules like the negative sum rule.
Negative Sum Rule
The negative sum rule is a straightforward guideline that helps simplify the addition of negative numbers. According to this rule, when you add two negative numbers, the result is negative. To find the final answer, follow these steps:
  • Find the absolute values of each negative number.
  • Add these absolute values together.
  • Place a negative sign in front of the sum.

For example, with the given numbers -33 and -67, their absolute values are 33 and 67. Adding these gives 100. Placing a negative sign in front, we obtain -100 as the final sum or result.

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