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Chapter 1: Problem 80

Simplify each expression. $$[3+(-1)]+[-2+(-3)]$$

Short Answer

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Step by step solution

01

Remove Parenthesis

First, remove the parenthesis from the expression. This doesn't involve any computation, but merely rewriting the expression. It becomes: \(3 + -1 + -2 + -3\).
02

Add Like Terms

Next, add the positive and negative numbers separately. This gives: \(3 + -1 + -2 + -3 = 3 + (-1 + -2 + -3)\).
03

Calculate Final Result

Solve for each group separately. This results in: \(2 + -6 = -4\).

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Key Concepts

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

Parentheses Removal
When we simplify algebraic expressions, removing parentheses is often the first step. Think of parentheses as a way to group numbers together, almost like a wrapping that needs to be peeled away before handling the contents inside.
  • Removing parentheses doesn't mean changing the numbers, but just rewriting the expression without them.
  • Be mindful of signs while doing this; the numbers should keep their signs as they were inside the parentheses.
  • In expressions like "+(-)" or "-(-)", ensure you pay attention to how the signs interact.
For example, in the expression \[[3+(-1)]+[-2+(-3)]\],just rewrite it as \[3 + -1 + -2 + -3\], which keeps the expression the same but eliminates the parentheses to prepare for further simplification.
Like Terms Addition
After removing parentheses, the next step in simplifying algebraic expressions is to combine like terms. Like terms are terms that have the same variable parts raised to the same power or are constant numbers.
  • In this example, we only have constant numbers, so all the numbers are considered like terms.
  • Combine the numbers by adding or subtracting them according to their signs.
  • Start by grouping positive numbers together and negative numbers together to simplify calculation.
For instance, in the expression \[3 + -1 + -2 + -3\],we need to add \[-1, -2, -3\],which are all negative, into a single number.This becomes \[-6\].Then we add the positive number \[3\]resulting in the simplified expression \[3 - 6 = -3\].
Algebraic Expressions
Algebraic expressions can seem complex, but they are simply mathematical phrases that can include numbers, variables, and operations. Simplifying them involves getting the expression into its most basic form.
  • Focus on understanding the role of each part of the expression.
  • In our example, we're working solely with numbers, which makes it a numerical expression rather than a true algebraic expression with variables.
  • The process taught here applies to more complex expressions too, just with additional steps involving variables.
To simplify an algebraic expression:
  • First, remove any parentheses.
  • Second, combine like terms (numeric or variable).
  • Lastly, compute any simple arithmetic to reach the most simplified form.
The skills you gain here provide a foundation for handling all sorts of algebraic expressions, setting the stage for more advanced math.

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Most popular questions from this chapter

Use the given property to rewrite the expression in a different form. SEE EXAMPLE \(6 .\) (OBJECTIVE 5 ) \((x+y) z ;\) commutative property of addition.

Write each inequality as an equivalent inequality in which the inequality symbol points in the opposite direction. $$3 \leq 7$$

Write each sentence as a mathematical expression. The sum of adding three and four is equal to seven.

Use the given property to rewrite the expression in a different form. SEE EXAMPLE \(6 .\) (OBJECTIVE 5 ) \(1 x ;\) multiplicative identity property.

How does the product of one proper and one improper fraction compare with the two factors?
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