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Chapter 3: Problem 407

In the following exercises, simplify each expression. $$ -75+25 $$

Short Answer

Expert verified
-50

Step by step solution

01

Identify Numbers

The expression consists of two numbers: -75 25
02

Understand Operation

The operation between these numbers is addition. Therefore, we need to add -75 and 25.
03

Perform Calculation

Start by considering the addition: -75 + 25. Adding a positive number to a negative number is the same as subtracting the positive number from the absolute value of the negative number: -75 + 25 = -50

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Addition with Negative Numbers
Understanding how to add negative numbers can be tricky at first, but let鈥檚 break it down. When you add a negative number to a positive number, it is similar to subtraction. For example, in the exercise, we have -75 + 25 . To solve this, think of it like subtracting the smaller number from the absolute value of the larger number. So, how do you approach this?
  • First, recognize that -75 is negative and 25 is positive.
  • Next, subtract 25 from 75 (the absolute value of -75 ).
  • 75 - 25 = 50.
  • The answer follows the sign of the larger absolute value, thus giving us -50 .
This is why -75 + 25 = -50 . By consistently applying this rule, you鈥檒l handle negative additions with ease!
Basic Arithmetic
Basic arithmetic provides the foundational skills necessary for tackling more advanced math problems. Key operations include addition, subtraction, multiplication, and division. Let鈥檚 focus on addition and subtraction since they are most relevant to our exercise.
  • Addition: Adding two numbers finds their total sum. For example, adding 5 and 3 yields 8 because 5 + 3 = 8 .
  • Subtraction: Subtracting one number from another finds their difference. For example, subtracting 3 from 5 yields 2 because 5 - 3 = 2 .
For dealing with positive and negative numbers together, visualize a number line. When adding a positive number, you move to the right. When adding a negative number, you move to the left. Understanding these basic principles will give you confidence in handling various arithmetic problems.
Prealgebra Operations
Prealgebra serves as your gateway to algebra. It covers concepts like operations with integers, fractions, and basic equations. Let鈥檚 use our exercise as a simple example to understand prealgebra operations.
Given the expression -75 + 25 , follow these steps:
  • Identify the operation: Addition in this case.
  • Handle the sign: Recognize that one number is negative and the other is positive.
  • Solve the operation: As mentioned, subtract the smaller absolute value 25 from the larger absolute value 75 . This gives us 50 , and since the larger number was negative, our answer is -50 .
Mastering how to simplify expressions builds your confidence and prepares you for more complex algebraic expressions. Remember, practice makes perfect!

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