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Chapter 2: Problem 53

Simplify. $$-19+(-22)$$

Short Answer

Expert verified
-41

Step by step solution

01

Understand the Operation

The given expression is -19 + (-22). This means you need to combine the numbers -19 and -22.
02

Combine the Numbers

Since both numbers are negative, you will add their absolute values and attach a negative sign to the result. So, calculate: 19 + 22 = 41
03

Attach the Negative Sign

After calculating the sum of the absolute values, attach a negative sign to the result. Therefore, -19 + (-22) = -41.

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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 often used to represent opposite directions, loss, or debt. You can recognize negative numbers by the minus sign (-) in front of them. For example, -19 and -22 are negative numbers.
When working with negative numbers, it's important to remember a few key points:
  • Negative numbers are less than positive numbers and zero.
  • On a number line, negative numbers are to the left of zero.
  • Combining two negative numbers involves adding their absolute values, then attaching a negative sign to the result.
Understanding how to handle negative numbers is crucial for simplifying integer expressions correctly.
Absolute Values
The absolute value of a number is the distance of that number from zero on a number line, regardless of direction. It's always a positive value or zero. The absolute value of a number is shown with vertical bars, like this: |x|.
For example, the absolute values of -19 and -22 are:
  • |-19| = 19
  • |-22| = 22
When combining negative numbers, you add their absolute values and then apply a negative sign to the final result. This step is essential for ensuring that your answer is accurate.
In our exercise, we added the absolute values of -19 and -22:
  • 19 + 22 = 41
This gave us the combined magnitude of the two negative numbers.
Addition of Integers
Adding integers can involve positive numbers, negative numbers, or both. The rules for adding integers depend on the signs of the numbers being added:
  • If the numbers have the same sign (both positive or both negative), add their absolute values and keep the common sign.
  • If the numbers have different signs (one positive and one negative), subtract the smaller absolute value from the larger absolute value and take the sign of the number with the larger absolute value.
Let's apply these rules to our exercise:
Given: [-19 + (-22)] Since both numbers are negative:
  • Add their absolute values: 19 + 22 = 41
  • Attach the negative sign: -41
Thus, the simplified result is -41.
Understanding these rules helps simplify integer expressions and solve related mathematical problems accurately.

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