Problem 113 - Beginning and Intermediate Algebra

Question

Write a numerical expression for each phrase, and simplify the expression. 12 less than the difference of 8 and -5

Step-by-Step Solution

Answer

1

Step 1: Define the Phrase

Identify the key components in the phrase. The phrase given is '12 less than the difference of 8 and -5.'

Step 2: Find the Difference

The difference between 8 and -5 is found by subtracting -5 from 8. So, calculate: Equation: 8 - (-5)

Step 3: Simplify the Difference

Simplify the equation from Step 2 by recognizing that subtracting a negative is the same as adding a positive: 8 - (-5) = 8 + 5 = 13

Step 4: Subtract 12 from the Result

Now, take 12 less than the result from Step 3, which means 13 - 12. Calculate this: 13 - 12 = 1

Key Concepts

Understanding Numerical Expressions

A numerical expression is a mathematical sentence involving numbers and operation signs, but no equal sign. In simple terms, it's a combination of numbers and math operations like addition, subtraction, multiplication, or division that represents a value.
For example, in our exercise, we encountered the phrase '12 less than the difference of 8 and -5'. This phrase can be represented as a numerical expression which we need to simplify.
Working with numerical expressions is fundamental in math as it helps to translate real-world situations into mathematical language. This skill is crucial for solving problems efficiently.

• Identify numbers and operations involved
• Translate the phrase into an expression
• Simplify step by step

The key to mastering numerical expressions is practice and understanding the order of operations.

Subtracting Negative Numbers

Subtracting negative numbers can be tricky at first, but it's essential to grasp this to simplify expressions correctly.
Here's a simple rule: Subtracting a negative number is the same as adding its positive counterpart. So, when you encounter a subtraction of a negative number, you actually perform an addition.
Let's look at an example from the exercise: 8 - (-5).

• Recognize that subtracting -5 is like adding 5
• The expression 8 - (-5) can be rewritten as 8 + 5

Following that rule, 8 - (-5) becomes 8 + 5, which equals 13. This simplification step is straightforward but fundamental for solving more complex expressions correctly. Always remember the rule: subtracting a negative is adding a positive.

Basic Algebra Steps

Algebra often involves simplifying expressions by following systematic steps. Understanding these basic algebra steps is crucial:

• Define the problem and identify terms
• Perform operations step by step following the correct order
• Simplify the expression to find the solution

In our exercise, we used these steps:
1. **Identify the Phrase**: First, break down the phrase '12 less than the difference of 8 and -5'.
2. **Find the Difference**: Calculate the difference between 8 and -5, which translates into 8 - (-5).
3. **Simplify**: Recognize that 8 - (-5) simplifies to 8 + 5, resulting in 13.
4. **Subtract 12**: Finally, subtract 12 from 13 to get 1.
By understanding and applying these simple algebra steps, you can tackle a wide range of problems efficiently. Practice makes perfect, so keep working through problems step by step.