Problem 35 - Algebra A Combined Function

Question

Translate each phrase to an expression and simplify. Subtract -5 from 8 .

Step-by-Step Solution

Answer

The simplified expression is 13.

Step 1: Identify the Phrase

The phrase given is "Subtract -5 from 8". This means we are taking the integer -5 and subtracting it from the number 8.

Step 2: Convert the Phrase to an Expression

In mathematical terms, "Subtract -5 from 8" translates to the expression: \[ 8 - (-5) \]

Step 3: Apply the Rule of Subtraction with Negative Numbers

When you subtract a negative number, it is equivalent to adding the absolute value of that number. Therefore, the expression \[ 8 - (-5) \] becomes \[ 8 + 5 \]

Step 4: Simplify the Expression

Add the numbers together: \[ 8 + 5 = 13 \]

Step 5: Write the Final Simplified Expression

The final simplified expression after performing the subtraction is 13.

Key Concepts

Subtraction of Integers

Subtraction can sometimes be confusing, especially when negative numbers are involved. However, understanding subtraction with integers is essential. Subtracting an integer means taking one quantity away from another. Here's a quick rundown to make it simpler:

• Identify the numbers involved. In this problem, we need to subtract -5 from 8.
• Write the numbers in the right order. The first number is where you start, and the second number is what you take away.

When you see two negative signs together, remember that subtracting a negative is the same as adding a positive. This is a crucial point for all algebraic expressions involving integers.Using this rule, our example changes from subtraction to addition: \[ 8 - (-5) \rightarrow 8 + 5 \] This transformation simplifies many problems, making them much more straightforward.

Negative Numbers

Understanding negative numbers is crucial in algebra. These are numbers less than zero, represented with a minus sign (-). Here are a few points to help you grasp negative numbers better:

• Negative numbers represent a "decrease" from zero. For example, -5 means moving 5 steps back from 0.
• Think of them as owing money; if you have -5 dollars, you owe someone 5 dollars.
• When adding negative numbers to positive numbers, you move left on the number line. However, subtracting a negative is like moving right.

Negative numbers follow some unique rules in mathematical operations:- Subtracting a negative: This is equivalent to adding the absolute value.In the context of the exercise, subtracting -5 from 8 actually means adding 5 to 8, because of the double negative rule.This helps transform and simplify expressions like:\[ 8 - (-5) = 8 + 5 \]

Simplifying Expressions

Simplifying expressions is a fundamental skill in algebra. This involves making expressions as concise as possible. When simplifying, we look to combine like terms or make calculations more straightforward. Here's a guide:

• Ensure all subtraction of negative numbers is transformed into addition.
• Combine all the terms you can.

In our example, after identifying the operation \( 8 - (-5) \), we simplify it by turning it into addition: \[ 8 + 5 \]Next, add the numbers to find the simplest form: \[ 13 \]Remember, simplifying isn’t just about combining numbers. It’s about recognizing patterns and using mathematical properties to make problems easier to solve. This practice improves problem-solving skills and helps in understanding complex algebraic expressions comprehensively.