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Chapter 3: Problem 81

In the following exercises, simplify each expression. $$ 135+(-110)+83 $$

Short Answer

Expert verified
108

Step by step solution

01

Identify and group terms

Identify the terms in the expression: 135, -110, and 83.
02

Simplify the sum of positive numbers

Add the positive numbers first: 135 + 83. So, 135 + 83 = 218.
03

Add the negative term

Add the result from step 2 to the negative term: 218 + (-110). 218 - 110 = 108.
04

State the simplified expression

The simplified expression is 108.

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Key Concepts

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

Addition of Integers
When we talk about adding integers, we are referring to combining both positive and negative whole numbers. Knowing how to add integers correctly is fundamental in simplifying expressions.

Here are some important tips:
  • Same Sign Integers: When adding two positive integers or two negative integers, simply add their absolute values and keep the common sign.
  • Different Sign Integers: When adding a positive integer and a negative integer, subtract the smaller absolute value from the larger absolute value. The result takes the sign of the number with the larger absolute value.
In the exercise, we see the integers 135, -110, and 83. We start by adding the positive integers together, then include the negative number at the end.
Grouping Terms
Grouping terms is a crucial step in simplifying expressions. It helps to simplify calculations and avoids confusion. When dealing with multiple integers in an expression, always:

  • Identify all the terms
  • Group same-sign terms together initially, if possible
  • Simplify in manageable parts to reduce errors
In the exercise, we first identified all terms: 135, -110, and 83. By grouping the positive numbers (135 and 83) together, we simplify the calculation to 135 + 83 = 218. Then, we handle the negative term by adding 218 and -110. Grouping terms effectively makes complex expressions much easier to manage and solve.
Negative Numbers
Understanding negative numbers is key in algebra and real-life math applications. Negative numbers are less than zero, usually represented with a minus sign (-). When simplifying expressions involving negatives:

  • Subtracting a negative is the same as adding its positive counterpart: a - (-b) becomes a + b
  • Adding a negative is the same as subtracting its positive counterpart: a + (-b) becomes a - b
  • Negative numbers follow the same arithmetic rules as positive numbers
In our exercise, adding -110 to a positive number is essential. By recognizing that 218 + (-110) is equivalent to 218 - 110, we get a simplified result of 108. Grasp these principles, and working with negatives will become second nature.

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