Problem 130 - Intermediate Algebra

Question

In the following exercises, translate to an algebraic expression and simplify if possible. (a) the difference of -5 and -30 (b) subtract -6 from -13

Step-by-Step Solution

Answer

(a) 25 (b) -7

Step 1: Translate Part (a)

The phrase 'the difference of -5 and -30' means subtract -30 from -5. This translates to the algebraic expression o -5 - (-30)

Step 2: Simplify Part (a)

To simplify the expression o -5 - (-30), replace the subtraction of a negative with addition:o -5 + 30. Now, perform the addition to get: 25

Step 3: Translate Part (b)

The phrase 'subtract -6 from -13' means -13 minus (-6). This translates to the algebraic expression o -13 - (-6)

Step 4: Simplify Part (b)

To simplify the expression o -13 - (-6), replace the subtraction of a negative with addition:o -13 + 6. Now, perform the addition to get: -7

Key Concepts

difference of numbers

When we talk about the 'difference of numbers', we simply mean finding out how much one number is different from another. In algebra, this usually means performing subtraction. For example, in the problem 'the difference of -5 and -30', we translate this to an algebraic expression as -5 minus -30. That looks like this: -5 - (-30)
Remember, whenever we find the difference, we always start with the first number mentioned and subtract the second number from it. In this case, it’s important to understand that working with negative numbers follows specific rules, which we will cover in the next section.

subtracting negative numbers

Subtracting negative numbers can be a little tricky at first, but once you understand the rules, it's straightforward. When you subtract a negative number, it changes to adding the positive version of that number. Think of it as removing a debt. If you owe someone negative \(5 (which means they owe you \)5), it's like adding $5 to your total. So, -5 - (-30) becomes -5 + 30.

• A key point to remember is: - Subtracting a negative is the same as adding a positive.
• Instead of **-a - (-b)**, think of it as **-a + b**.

Let's take another example from the exercise: -13 - (-6). This translates to -13 + 6. The act of subtracting a negative turned into adding the positive version of that number.

simplification

Simplification is about making the expression as straightforward as possible. After translating and rewriting the problem in simpler terms, we perform the arithmetic operation directly. Using our example, -5 - (-30) changed to -5 + 30. Now, we can add the numbers: -5 + 30 equals 25. Another example, -13 - (-6), changed to -13 + 6. Now, perform the addition: -13 + 6 equals -7.

• Simplification helps to reach the final value in the easiest way possible.
• Always follow the rule: Subtracting a negative is adding a positive.
• Perform arithmetic carefully to avoid mistakes.