Problem 26 Fill in the blank with the appro... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

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Chapter 3: Problem 26

Fill in the blank with the appropriate number. $$1+(-1)= _____ $$

Short Answer

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Step by step solution

Understand the problem

We need to find the result of adding 1 and -1 to fill in the blank.

Identify the numbers involved

The numbers involved in this problem are 1 and -1.

Perform the addition

Add the numbers: 1 + (-1). When adding a positive number to its corresponding negative number, the result is 0.

Fill in the blank

Since 1 + (-1) equals 0, fill in the blank with the number 0.

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Key Concepts

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

Understanding Negative Numbers

Negative numbers are numbers less than zero, represented with a minus sign (-). They are opposites of positive numbers. For example, -3 is the opposite of 3. Negative numbers are used to show values below zero, such as temperatures below freezing or depths below sea level.
In math, they follow some different rules compared to positive numbers. For instance, when adding a negative number to a positive number, you are essentially subtracting that value. This helps us understand why 1 + (-1) equals 0, because we are taking away 1 from 1.

Steps in Addition

Addition is one of the basic operations in arithmetic. It combines two or more numbers to make a new total. Here are important points:

When adding positive numbers, you simply move to the right on the number line.
When adding negative numbers, you move to the left.
When adding a positive and a negative number, you determine which number has a larger absolute value (ignore the sign), then move in the direction of the number with the larger absolute value.

Understanding the addition of negative numbers helps to solve problems like 1 + (-1). Since their absolute values are the same but opposite in sign, they cancel each other out, resulting in 0.

Basic Arithmetic Principles

Basic arithmetic includes the simple operations of addition, subtraction, multiplication, and division. To master arithmetic, it is important to understand:

Commutative Property: In addition, numbers can be added in any order (e.g., 2 + 3 = 3 + 2).
Associative Property: Grouping does not change the sum (e.g., (1 + 2) + 3 = 1 + (2 + 3)).
Identity Property: Adding 0 to a number does not change its value (e.g., 5 + 0 = 5).

In the exercise given, applying these principles to 1 + (-1) demonstrates the identity property, where the sum of a number and its opposite is always zero. This showcases the neutralizing effect of negative numbers in basic arithmetic.

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91影视

Fill in the blank with the appropriate number. $$1+(-1)= _____ $$

Short Answer

Step by step solution

Understand the problem

Identify the numbers involved

Perform the addition

Fill in the blank

Key Concepts

Understanding Negative Numbers

Steps in Addition

Basic Arithmetic Principles

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