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Chapter 1: Problem 48

Evaluate each expression. $$ -33-8+10 $$

Short Answer

Expert verified
The value of the expression is -31.

Step by step solution

01

Evaluate the First Two Numbers

Start by evaluating the expression from left to right. First, subtract 8 from -33. This can be thought of as adding -8 to -33. The calculation is: \[-33 - 8 = -41\]
02

Add the Last Number

Now, add 10 to the result of the first step. The calculation is: \[-41 + 10 = -31\]

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Key Concepts

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

Evaluation of Expressions
Evaluating expressions involves processing mathematical expressions according to a hierarchy of operations. When working with expressions, it is essential to go step by step according to the order of operations. In our exercise, we are asked to evaluate the expression \[-33 - 8 + 10\].
A systematic approach is key. We compute from left to right, involving subtraction and addition in our case. Here, we start by evaluating the first part of the expression:
  • Subtract 8 from -33, which gives us -41.
  • Then, take the result of -41 and add 10 to it, resulting in -31.
Breaking down expressions into simple steps is essential to reaching the correct answer.
Negative Numbers
Negative numbers can initially seem tricky, but they follow consistent rules within arithmetic. Understanding these is crucial when performing operations like subtraction and addition in algebra.
In our exercise, we see negative numbers like -33, -8, and standard rules apply:
  • Remember that subtracting a number is the same as adding its negative counterpart. For instance, \(-33-8\) is the same as \(-33+(-8)\).
  • Adding to a negative often results in a less negative or even a positive number, depending on the size of the number added.
  • Negative results occur when a greater negative is added to a lesser positive.
Being familiar with these concepts helps simplify the problems, reducing the fear of negative numbers.
Addition and Subtraction in Algebra
Addition and subtraction are the foundational operations in algebra, where understanding their interactions is crucial. They dictate the steps we take when solving or simplifying expressions. In algebra, we follow basic arithmetic rules with an added focus on variables. However, this exercise sticks to numbers alone to illustrate the steps.
Key points to remember while solving the expression \(-33-8+10\):
  • Bear in mind, subtraction is effectively adding a negative number.
  • The operation order is critical: evaluate from left to right in simple expressions like this one.
  • Practice makes perfect; repetition of such problems helps build confidence and proficiency in handling more complex algebraic expressions in the future.
It's about developing a comfort level with arithmetic operations as a foundation for future algebraic work.

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