Problem 96 Add or subtract and reduce to lo... [FREE SOLUTION]

91影视

Elementary Algebra

John Redden

$Math Studyset 91影视 Explanations$ Math

2011 Edition

Chapter 1: Problem 96

Add or subtract and reduce to lowest terms. $$ 23-412+316 $$

Short Answer

Expert verified

-73 is the sum in lowest terms.

Step by step solution

- Understand the Problem

We're asked to find the sum of the integers 23, -412, and 316. This involves a basic addition and subtraction operation.

- Perform Addition and Subtraction

Compute the sum of the integers. The equation is: \[ 23 - 412 + 316 \]Calculate it step by step:1. Subtract 412 from 23 to begin with: \[ 23 - 412 = -389 \]2. Add 316 to the result from step 1: \[ -389 + 316 = -73 \]

- Reduce to Lowest Terms

The result from Step 2 is -73. Since -73 is already an integer, it's in the lowest terms and reduction is not necessary.

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Key Concepts

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

Understanding Integers

Integers are whole numbers that can be either positive, negative, or zero. They do not include fractions or decimals.
These numbers are fundamental in mathematics, especially when we deal with basic operations such as addition and subtraction. Consider these points about integers:

Positive integers are numbers like 1, 2, 3, and so on.
Negative integers are their opposites, like -1, -2, -3, etc.
Zero is also considered an integer, acting as a neutral point between positive and negative numbers.

When solving problems involving integers, it is crucial to pay attention to their signs. Positive and negative signs tell us whether to move forward or backward on the number line. This is key when performing basic operations with integers.

Mastering Basic Operations

Basic operations are the foundational skills of arithmetic, involving addition, subtraction, multiplication, and division. In the case of the exercise we've been discussing, we focus on addition and subtraction.### Addition and SubtractionThese two operations often go hand in hand when working with integers:

Addition involves combining numbers together to form a larger total.
Subtraction is about finding the difference between numbers, like 'taking away.'

If you see an equation like $ 23 - 412 + 316 $, it's about moving in opposite directions on the number line. First, we subtract 412 from 23, resulting in -389. Then, we add 316 to -389, getting -73 as our final result.When working with these operations, always deal with any negative signs first while ensuring each step follows the correct mathematical order.

Reducing to Lowest Terms

Reducing to lowest terms usually applies when dealing with fractions, but it鈥檚 worth understanding in the broader sense.
It means simplifying a number or expression to its simplest form. For integers like -73, simplifying is usually unnecessary because they are already in the simplest form. An integer doesn't have smaller parts like fractions do. However, this concept is an important part of mathematics:

For fractions, it involves dividing the numerator and denominator by their greatest common factor.
In algebra, simplifying can involve combining like terms or reducing expressions.

Remember, understanding the idea behind 'lowest terms' can help clarify when you need to simplify an expression or when it's naturally in its simplest form, like our integer result of -73.

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91影视

Add or subtract and reduce to lowest terms. $$ 23-412+316 $$

Short Answer

Step by step solution

- Understand the Problem

- Perform Addition and Subtraction

- Reduce to Lowest Terms

Key Concepts

Understanding Integers

Mastering Basic Operations

Reducing to Lowest Terms

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