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Chapter 15: Problem 33

Simplify. $$ 2+(-3)+7+10 $$

Short Answer

Expert verified
The simplified expression is 16.

Step by step solution

01

Identify the Numbers

Look at the expression to identify all the numbers involved: 2, -3, 7, and 10.
02

Add the Positive Numbers

Add all the positive numbers together first:2 + 7 + 10 = 19
03

Add the Negative Number

Now, add the negative number to the result from Step 2:19 + (-3) = 16

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Key Concepts

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

Integer Addition
Integer addition is the process of combining whole numbers. Understanding integer addition is essential because it forms the basis for more complex arithmetic and algebra. In our exercise, we have the integers 2, -3, 7, and 10.
Here, the positive integers are 2, 7, and 10, while -3 is a negative integer. To simplify the expression, first group and add the positive integers:
  • Step 2: Add the Positive Numbers
    2 + 7 + 10 = 19
Now, we need to combine this sum with the negative integer:
  • Step 3: Add the Negative Number
    19 + (-3) = 16
By following these steps, we find the simplified result of this expression to be 16. This systematic approach helps in dealing with multiple integers effectively.
Positive and Negative Numbers
Positive and negative numbers are crucial concepts in mathematics. They help describe quantities with direction or value below zero. In our problem, positive numbers are added first:
  • 2, 7, and 10 are positive numbers
  • -3 is the only negative number
Adding positive numbers is straightforward since you are combining quantities that move in the same direction. After summing positive numbers: We get 19 by adding 2, 7, and 10. Next is incorporating the negative number, -3:
  • Adding a negative number is similar to subtracting its positive counterpart.
  • So, 19 + (-3) is the same as 19 - 3.
This results in 16. Understanding how to handle positive and negative integers allows for accurate and efficient calculation.
Step-by-Step Problem Solving
Step-by-step problem solving is a strategy to break down complex problems into simpler, manageable parts. This method ensures clarity and accuracy. For our example, we simplified the expression 2 + (-3) + 7 + 10 using these steps:
  • Step 1: Identify the Numbers
    Identify all numbers in the expression: 2, -3, 7, and 10.
  • Step 2: Add the Positive Numbers
    Combine the positive integers:2 + 7 + 10 = 19.
  • Step 3: Add the Negative Number
    Add the negative integer to the sum from Step 2: 19 + (-3) = 16.
This methodical approach helps in avoiding mistakes and ensures a clear understanding of the problem. By practicing step-by-step problem solving, students can develop strong problem-solving skills that are beneficial for advanced math topics.

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