Problem 15 Add. Do not use the number line ... [FREE SOLUTION]

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Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 10: Problem 15

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 what needs to be solved. The problem requires adding two negative integers: $ -17 + (-25) $.

- Add the Absolute Values

When adding two negative numbers, add their absolute values together. Find the absolute values of -17 and -25. The absolute value of -17 is 17, and the absolute value of -25 is 25. Calculate: $ 17 + 25 = 42 $.

- Apply the Sign

Since both numbers were negative, the result will also be negative. Thus, affix the negative sign to the sum of the absolute values:$ -42 $.

- Verification

Use a number line as a check (optional). Starting at -17, if you move 25 units to the left, you will land at -42.

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Key Concepts

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

absolute value

Absolute value represents the distance of a number from zero on the number line, regardless of direction. For instance, the absolute value of -17 is 17, and the absolute value of -25 is 25. It makes no difference that these numbers are negative 鈥� we only care about how far each is from zero. Understanding absolute value is crucial when adding negative numbers because we first treat them as positive values for the addition.

integer operations

Integer operations include addition, subtraction, multiplication, and division involving whole numbers (both positive and negative). When performing addition with negative integers, we sum their absolute values and then affix the appropriate sign. For example, to solve $ -17 + (-25) $, we first add the absolute values (17 and 25) to get 42. Since the original integers were both negative, the result is -42.

negative numbers

Negative numbers are numbers less than zero, denoted with a minus sign (-). They exist on the left side of zero on the number line. When you add two negative numbers, you end up with a more negative result. For instance, adding -17 and -25 yields -42. Practicing with negative numbers helps build confidence in performing operations with them.

number line verification

Using a number line can help verify the results of adding integers. Though not necessary for every calculation, it is a valuable visual aid. To check $ -17 + (-25) $ on a number line: Start at -17 and move 25 units left (since we're adding a negative number). You will land at -42, confirming that \ -17 + (-25) = -42 \ is indeed correct. This reinforces our result and builds intuition for working with negative numbers.

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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

- Add the Absolute Values

- Apply the Sign

- Verification

Key Concepts

absolute value

integer operations

negative numbers

number line verification

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