Problem 73 - Algebra A Combined Function

Question

Perform the indicated operation. \(-9-10\)

Step-by-Step Solution

Answer

-9 - 10 = -19.

Step 1: Understand the Operation

In this exercise, we need to perform a subtraction operation where we subtract 10 from -9. This can be rewritten as adding a negative number, i.e., \(-9 + (-10)\).

Step 2: Adding Negative Numbers

When adding negative numbers, you essentially move further into the negative direction on the number line. Here, add -10 to -9, which gives: \(-9 + (-10) = -19\).

Step 3: Verify the Result

Double-check the calculation: starting at -9 and moving 10 spaces left on the number line results in -19. The math confirms this operation.

Key Concepts

Negative Numbers

Negative numbers are values that are less than zero. They are often used to indicate a deficit or an opposite direction. To identify a negative number, look for the minus sign (-) written before the number. These numbers can be challenging, but with practice, they become easier to manage.
For example, in the exercise, the number -9 is a negative number. When dealing with negative numbers, keep a few key points in mind:

• They are positioned to the left of zero on a number line.
• Negative numbers decrease when added to or subtracted from another negative number.
• The further left a number is on the number line, the smaller its value.

These concepts will help you understand how negative numbers behave in different mathematical operations, including subtraction.

Number Line

A number line is a visual representation of numbers arranged in increasing order from left to right. It is an excellent tool for understanding integer operations, especially with positive and negative numbers.
On a number line, each integer has a specific position relative to zero:

• Zero is the starting or middle point on the line.
• Numbers to the right of zero are positive.
• Numbers to the left of zero are negative.

Using a number line allows you to visually track the addition or subtraction of numbers, aiding in comprehension. For instance, when solving (-9 - 10) , you start at -9 and move 10 spaces to the left. This visual helps confirm that the result is -19. Practicing with a number line can significantly improve your grasp of integer operations.

Subtraction Operation

Subtraction is one of the four basic arithmetic operations, and it involves taking one quantity away from another. It can be especially interesting when working with negative numbers.
To subtract a number, you can also think of it as adding its opposite. For example, instead of subtracting 10 from -9 ( -9 - 10 ), you can view it as -9 + (-10) . This highlights the connection between subtraction and addition, especially with negative values. Key elements of subtraction include:

• Understanding it as reverse addition—adding a negative.
• Recognizing that moving left on a number line indicates subtraction.
• Realizing that subtracting a larger number from a smaller one results in a more negative number.

By practicing these approaches to subtraction, you will find it easier to solve problems involving negative numbers.