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Chapter 1: Problem 7

Use a number line to represent each sum or difference. $$-2+(-7)$$

Short Answer

Expert verified
Using a number line, locate the starting point at -2. To add -7, move 7 units to the left of -2. The ending point will be at -9. Thus, \(-2 + (-7) = -9\).

Step by step solution

01

Draw the number line

Draw a horizontal number line that includes both -2 and -7, with an appropriate scale. Make sure the line is clear and properly labeled to show negative numbers.
02

Identify the starting point

Locate the first integer, -2, on the number line. This will be our starting point. Place an arrow or a marker on -2 to indicate the starting position.
03

Moving along the number line

From the starting point, we need to add a negative number, which means moving to the left along the number line. Starting from -2, move left by 7 units (as the second number is -7).
04

Identify the ending point

After moving 7 units to the left from the starting point (-2), you will reach the ending point, which is the sum of the two integers. The ending point on the number line should be -9.
05

Write down the sum

Now that you've reached the ending point, it's time to write down the result of the given sum: \(-2 + (-7) = -9\).

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Key Concepts

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

Integer Operations
Integer operations involve performing basic arithmetic calculations with whole numbers. These operations include addition, subtraction, multiplication, and division. When dealing with integers, it's crucial to understand that they can be both positive and negative.

  • Addition: When adding integers, the overall sign will depend on the numbers involved. Positive numbers tend to increase in value, while adding negative numbers decreases the value.
  • Subtraction: Subtracting an integer is the same as adding its opposite. For example, subtracting (-3) is the same as adding (3).
  • Multiplication and Division: Multiplying or dividing two integers with the same sign gives a positive result, while different signs give a negative result.
Understanding these basic rules helps to navigate any math problem involving integers. With practice, you can easily determine the result of any integer operation.
Negative Numbers
Negative numbers are integers that are less than zero. These numbers are often represented on a number line extending to the left of zero. When we talk about negative numbers, it's important to understand a few key points:

  • Negative numbers have a distinct position on the number line compared to positive numbers.
  • They are used in real-world contexts, like indicating a loss or temperature below freezing.
  • When visualizing, the more you move to the left, the smaller or more negative the number becomes.
Using negative numbers often involves reversing our typical understanding of addition and subtraction. For instance, adding a negative number often means moving to the left on the number line, which actually makes the sum smaller.
Adding Integers
Adding integers is all about determining the sum of two or more whole numbers, which can be positive or negative. The number line is a powerful tool to make this concept more visual and understandable.

To add integers effectively, follow these simple steps:
  • Identify the starting point: Find the position of the first integer on the number line.
  • Determine the direction: If you're adding a positive integer, move to the right. If it's negative, move to the left.
  • Count the steps: Move along the number line the number of units that correspond to the absolute value of the integer you are adding.
For example, adding -2 and -7, as shown in the exercise, requires starting at -2 and moving 7 spaces to the left. This lands us at -9, giving us the final sum: (-2) + (-7) = -9. Practicing on a number line helps solidify these concepts.

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Most popular questions from this chapter

Add or subtract as indicated. $$7.3-11.2$$

Divide. $$-108 \div 9$$

Add or subtract as indicated. $$380+(-192)$$

Divide. $$-42 \div(-6)$$

Write a mathematical expression for each and simplify. 8 more than the quotient of 54 and \(-6\)
See all solutions

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