Problem 22 Add. Do not use the number line ... [FREE SOLUTION]

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Chapter 1: Problem 22

Add. Do not use the number line except as a check. \(-17+(-25)\)

Short Answer

Expert verified

-42

Step by step solution

Understand the Problem

Identify the numbers involved in the addition. In this case, we need to add -17 and -25.

Identify the Sign of Each Number

Notice that both numbers are negative (-17 and -25). When adding two negative numbers, the results will always be a negative number.

Add the Absolute Values

Add the absolute values of the two numbers. The absolute value of -17 is 17, and the absolute value of -25 is 25. Therefore, we calculate 17 + 25.

Combine the Results

Calculate 17 + 25: 17 + 25 = 42. Since both original numbers were negative, the result will also be negative. Therefore, -17 + -25 = -42.

Verify Your Answer Using the Number Line

To check your work, visualize placing -17 on the number line and then moving 25 units further left. You should end up at -42.

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Key Concepts

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

absolute values

When adding negative numbers, understanding the concept of absolute values is crucial. The absolute value of a number is its distance from 0 on the number line, regardless of direction. Essentially, it turns negative numbers into positive ones. For instance, the absolute value of -17 is 17. Applying this to the problem, we disregard the negative signs and first add the absolute values: 17 + 25. This simplifies the addition process before reintroducing the signs.

number line

A number line is an excellent visual tool for understanding addition and subtraction, especially with negative numbers. Imagine a line with 0 in the center, positive numbers to the right, and negative numbers to the left. For the exercise -17 + (-25), start at -17 on the number line. Moving 25 units to the left means counting from -17, down past -18, -19, and so on, until you reach -42. Visualizing this helps verify our calculated result.

negative number addition

Adding negative numbers might seem tricky at first, but it's straightforward with some practice. When you add two negative numbers, think about adding their absolute values first. You then place a negative sign in front of the result. In our example, adding -17 and -25, we ignored the negative signs at first and added 17 and 25 to get 42. Since we're adding two negative numbers, the sum is also negative. Thus, -17 + (-25) equals -42. Remembering this rule makes handling negative addition much easier.

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91影视

Add. Do not use the number line except as a check. \(-17+(-25)\)

Short Answer

Step by step solution

Understand the Problem

Identify the Sign of Each Number

Add the Absolute Values

Combine the Results

Verify Your Answer Using the Number Line

Key Concepts

absolute values

number line

negative number addition

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