Problem 36 - Elementary and Intermediate Algebra

Question

Add. Do not use the number line except as a check. \(-15+(-7)\)

Step-by-Step Solution

Answer

-22

Step 1: Identify the Operation

Determine that the problem is asking to add two negative numbers, \( -15 + (-7) \).

Step 2: Understand Adding Negative Numbers

When adding two negative numbers, the result is a negative number. You combine the absolute values of the numbers and then apply the negative sign to the result.

Step 3: Add the Absolute Values

Add the absolute values of \( 15 \) and \( 7 \): \( 15 + 7 = 22 \).

Step 4: Apply the Negative Sign

Since both numbers are negative, the result will be negative: \( -22 \).

Key Concepts

negative numbers

Negative numbers are numbers less than zero. They are usually shown with a minus sign (-) in front. For example, -3 is a negative number. Negative numbers represent values that are less than zero and can be thought of as opposites of positive numbers.

Think of negative numbers as a way to describe things like temperature below freezing or money owed.

• For instance, if you owe $5, you could write that as -5.
• On a thermometer, -10 degrees is colder than 0 degrees.

Knowing how negative numbers work is important for understanding more complex math concepts.

absolute value

Absolute value refers to the distance a number is from zero on a number line, regardless of direction. It is always a nonnegative value. For any given number, its absolute value is shown as \(|number|\), and it is always positive.

For example:

• \(|-5| = 5\)
• \(|7| = 7\)

When adding negative numbers, we often need to consider their absolute values to simplify the calculation. This helps determine how large the combined negative result will be.

addition of integers

When adding integers, you might encounter positive and negative numbers. The rules for adding these can vary slightly based on their signs.

For adding two negative numbers:

• Add their absolute values.
• Apply a negative sign to the result.

As shown in the exercise:
\(-15 + (-7)\)

Step-by-step example:

• Identify the numbers and their signs: -15 and -7.
• Follow the rules for adding negative numbers: Add the absolute values, \(15 + 7 = 22\).
• Apply the negative sign to the result: \(-22\).

Understanding these steps makes it easier to handle any addition of integers.