Problem 2 Explain, in your own words, how ... [FREE SOLUTION]

Chapter 1: Problem 2

Explain, in your own words, how to add a positive and a negative number.

Short Answer

Expert verified

To add a positive and a negative number, first, understand the number line where positive numbers are to the right of 0, and negative numbers are to the left of 0. Follow these rules for adding the numbers: 1) If signs are the same, add the absolute values and keep the sign; 2) If signs are different, subtract the absolute values and keep the sign of the larger number. For example, when adding +10 and -5 since the signs are different, subtract the absolute values: 10 - 5 = 5, and keep the sign of the larger number (10), resulting in a positive number. So, the final answer is +5 or simply 5.

Step by step solution

Understand the number line

A number line is a straight line that represents the set of real numbers, with a point (usually labeled with a tick mark) for each integer. The positive numbers are to the right of 0, and the negative numbers are to the left of 0.

Determine the rules for adding positive and negative numbers

There are a few rules to keep in mind when adding a positive number to a negative number: 1. When the signs are the same, add the absolute values (i.e., the actual value of the numbers without the signs) and keep the sign 2. When the signs are different, subtract the absolute values and keep the sign of the larger number.

Example

Let's say we need to add 10 to -5. Step 1: Determine the signs of the two numbers. - Since 10 is a positive number, its sign is +. - Since -5 is a negative number, its sign is -. - We have a positive number and a negative number, so the signs are different. Step 2: Apply the rule for adding numbers with different signs. - The absolute value of 10 is 10, and the absolute value of -5 is 5. - Subtract the absolute values of the two numbers (10 - 5), which gives us 5. Step 3: Keep the sign of the larger number. - The larger number in this case is 10 which is positive. - So the result will be a positive number. Step 4: Combine the number with the sign. - As we obtained 5 in Step 2 and a positive sign in Step 3, the result of adding 10 and -5 is +5 or simply 5.

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Key Concepts

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

Number Line

A number line is a powerful visual tool that helps us understand numbers, their relationships, and operations like addition and subtraction. It is a horizontal line where each point corresponds to a real number. Typically, it has zero in the center:

Positive numbers are placed to the right of zero, extending infinitely.
Negative numbers are placed to the left, also extending without end.

The number line is useful for visualizing the addition of positive and negative numbers. For example, when adding a positive number, you move right on the number line; when adding a negative number, you move left. This simple movement on the number line can make understanding addition more intuitive.

Absolute Value

Absolute value is a concept that refers to the non-negative value of a number without considering its sign. When we talk about absolute value, we mean how far a number is from zero on the number line, regardless of direction.

The absolute value of a positive number is itself, because it's already non-negative.
The absolute value of a negative number is the positive version of that number.

It is denoted by two vertical bars, for example, the absolute value of -5 is written as \(|-5| = 5\). In problems involving addition of positive and negative numbers, knowing the absolute values helps in comparing numbers and deciding the direction in which to move on the number line.

Integer Addition

Integer addition involves adding whole numbers, both positive and negative. When adding integers, we can rely on simple rules:

When numbers have the same sign, add their absolute values and use the common sign for the result.
When numbers have different signs, subtract the smaller absolute value from the larger one and keep the sign of the number with the larger absolute value.

For example, when adding 10 to -5, the differening signs rule applies. We find the absolute values: 10 and 5. Then, we subtract 5 from 10, resulting in 5. Since 10 is the larger number and is positive, the result is positive: +5 or just 5. These rules make integer addition straightforward and systematic, easing the calculations.

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91影视

Explain, in your own words, how to add a positive and a negative number.

Short Answer

Step by step solution

Understand the number line

Determine the rules for adding positive and negative numbers

Example

Key Concepts

Number Line

Absolute Value

Integer Addition

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