Problem 108 - Beginning and Intermediate Algebra

Question

Write a numerical expression for each phrase, and simplify the expression. The difference of 7 and -14

Step-by-Step Solution

Answer

The simplified expression is 21.

Step 1: Translate the Phrase into a Numerical Expression

The phrase 'the difference of 7 and -14' translates to the numerical expression: 7 - (-14).

Step 2: Simplify the Expression

When subtracting a negative number, it is the same as adding the absolute value of that number. Thus, 7 - (-14) simplifies to 7 + 14.

Step 3: Perform the Addition

Now, add 7 and 14 to get the result. 7 + 14 = 21.

Key Concepts

subtracting negative numbers

When we talk about subtracting negative numbers, it can initially seem a bit confusing. However, the rule is quite straightforward. Subtracting a negative number is the same as adding its positive counterpart. In other words, if you see a negative sign followed by another negative sign, they combine to form a positive sign. For instance, consider the expression 7 - (-14). Here, subtraction of -14 is the same as adding +14. Therefore, 7 - (-14) simplifies to 7 + 14. Remember this simple rule, and subtracting negative numbers will become much easier!

simplifying expressions

Simplifying numerical expressions means making them as simple as possible. This involves combining like terms and performing basic arithmetic operations.
Let's consider our example again: 7 - (-14). As we learned, this is equivalent to 7 + 14. The goal now is to perform the addition operation to reach a final answer. Simplified expressions are easier to work with and understand, especially when solving more complex problems. Always try to simplify expressions step-by-step to avoid mistakes and get accurate results.

addition

Addition is one of the most fundamental arithmetic operations. It involves calculating the total of two or more numbers. In our example, after transforming the subtraction of a negative, we get 7 + 14. To perform this addition, you simply combine the numbers:

• Start with 7.
• Add 14 to it:
• 7 + 14 = 21

Therefore, the expression simplifies to 21. Remember, when adding numbers, always line them up properly and take one step at a time. This ensures you don't miss any numbers or make any calculation errors.