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Chapter 1: Problem 104

Simplify. $$ 39+(-88)-29-(-83) $$

Short Answer

Expert verified
The simplified result is 5.

Step by step solution

01

Combine positive and negative signs

Rewrite the expression by combining the positive and negative signs: 39 + (-88) - 29 - (-83) simplifies to: 39 - 88 - 29 + 83
02

Perform the addition and subtraction from left to right

Start by calculating from left to right: 39 - 88 = -49Then continue with: -49 - 29 = -78Finally, add 83: -78 + 83 = 5

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Key Concepts

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

Addition and Subtraction of Integers
Understanding how to add and subtract integers is crucial in algebra. Integers are whole numbers and their opposites. They include negative numbers, zero, and positive numbers. When adding or subtracting integers, keep a few rules in mind:
  • If both integers have the same sign, add their absolute values and keep the sign.
  • If the integers have different signs, subtract the smaller absolute value from the larger absolute value and take the sign of the number with the larger absolute value.
For example, in our exercise, we have: 39 + (-88) - 29 - (-83). We need to handle the negative signs carefully. Combining these, we get: 39 - 88 - 29 + 83. Here, subtraction is the same as adding the opposite:
  • 39 - 88: different signs, so subtract and take the sign of the larger absolute value, resulting in -49.
  • -49 - 29: same sign, so add their absolute values and keep the sign, resulting in -78.
  • -78 + 83: different signs, so subtract and take the sign of the larger absolute value, resulting in 5.
Learning these rules makes it easier to manage calculations involving integers.
Combining Like Terms
Combining like terms is a method used to simplify algebraic expressions by merging terms that have the same variables to a common power. In our exercise, while the terms don鈥檛 involve variables, the principle still applies when dealing with constants (numbers without variables).

The terms 39, -88, -29, and 83 are all constants. To combine, or simplify, these terms:
  • Group the positive and negative (subtracted) terms separately to keep the math clearer.
  • First combine the 39 and 83 (the positive numbers)
  • Next, combine -88 and -29 (the negative numbers).
  • Then add the results of these combinations for the final simplified form.
This grouping method helps to ensure that terms are not mistakenly added or subtracted and adds clarity to your calculations.
Order of Operations
Order of operations is a set of rules that determines the correct sequence to evaluate a math expression. The commonly remembered acronym PEMDAS stands for: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).

In our given exercise, 39 + (-88) - 29 - (-83), we follow these steps:
  • Addressing the negative signs by rewriting to: 39 - 88 - 29 + 83.
  • Then, solve from left to right because there are no parentheses or exponents, and addition/subtraction have equal priority here.
Step-by-step, it goes:
  • First, compute 39 - 88 to get -49.
  • Second, calculate -49 - 29 to get -78.
  • Finally, add -78 + 83 to get 5.
By following the order of operations, you ensure that you simplify expressions correctly and avoid common errors.

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