Problem 58 - Beginning and Intermediate Algebra

Question

Find each difference. $$ -9-4 $$

Step-by-Step Solution

Answer

-13

Step 1: Identify the expression

The given expression is -9 - 4.

Step 2: Simplify subtraction involving negative numbers

To solve -9 - 4, think of it as adding a negative number to another negative number. Rewrite it as -9 + (-4).

Step 3: Add the negative numbers

Now, add -9 and -4. When you add two negative numbers, the sum is also negative. So, -9 + (-4) = -9 - 4 = -13.

Key Concepts

subtraction

Subtraction means taking away a number from another number. It is one of the basic operations in math and is the opposite of addition. When you see a subtraction problem, it involves two main parts: the minuend (the number you start with) and the subtrahend (the number you subtract).
For example, in the problem \(9 - 4\), \(9\) is the minuend and \(4\) is the subtrahend.
Similarly, for negative numbers, consider how subtraction works. If the problem is written as \(-9 - 4\), it helps to think of it as adding a negative number. This is because subtracting a positive number results in moving further into negative territory.

Key Points:
* Subtraction is taking one number away from another.
* The action can be thought of as adding a negative number when dealing with negative values.

negative numbers

Negative numbers represent values less than zero and are written with a minus sign in front of them. Understanding how to work with negative numbers is essential in various math operations, including subtraction and addition.
Let's dive into a few essential properties:
* Negative numbers are found to the left of zero on a number line.
* Adding a negative number is the same as subtracting its positive counterpart: \(-9 + (-4)\) is the same as \(-9 - 4\).
* When subtracting negative numbers, remember that double negatives make a positive: \(a -(-b) = a + b\).
For the problem \(-9 - 4\), we consider adding two negative numbers, which results in moving further left on the number line, hence resulting in \(-13\).

integer operations

Integer operations involve basic mathematical operations like addition, subtraction, multiplication, and division that are done with whole numbers, including both positive and negative numbers. Today, we focus on subtraction involving integers.
Here are a few key principles when working with integer operations:
* When adding two integers with the same sign, add their absolute values and give the sum the same sign.
* When subtracting two integers, convert the subtraction operation into an addition operation: \(a - b\) becomes \(a + (-b)\).
* Use a number line for better visualization. For example, \(-9 - 4\) involves moving \(4\) units to the left from \(-9\), landing on \(-13\).
Grasping these concepts makes solving integer operations quicker and more intuitive.