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Chapter 1: Problem 2

Find each sum using a number line. $$7+(-2)$$

Short Answer

Expert verified
The answer is 5.

Step by step solution

01

Identify Starting Point

Start at 7 on the number line. This is because the original number we are adding to is 7.
02

Move to the Left

Move 2 steps to the left. The concept here is that we are adding -2, which is the same as subtracting 2, hence we move 2 steps to the left.
03

Identify the New Position

Your new position on the number line is the answer to the addition problem. After moving 2 steps left from 7, you would land on 5. Therefore, \(7 + (-2) = 5\).

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Key Concepts

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

Negative Numbers
Understanding negative numbers can be likened to thinking about temperatures below zero on a thermometer or levels below ground in a building.
When you hear or see a negative number, like -2, it means you are going in the opposite direction from zero compared to positive numbers.
Some key points about negative numbers:
  • They are numbers less than zero and are represented with a minus sign (-).
  • They appear to the left of zero on a number line.
  • When adding a negative number, it is akin to subtracting its positive equivalent.
Negative numbers can initially seem a bit confusing.
Think of them as stepping backward if zero is your starting point.
Integer Operations
Integer operations involve mathematical functions like addition and subtraction but restrict these operations to whole numbers or integers.
Integers can be positive, negative, or zero.
When adding integers, it is important to consider the signs:
  • If both numbers have the same sign, add their absolute values. The result takes the same sign.
  • If the numbers have opposite signs, subtract the smaller absolute value from the larger. The result takes the sign of the number with the larger absolute value.
For example, in the problem of adding 7 and -2, we identify:
  • 7 is positive
  • -2 is negative
Since they have opposite signs, we subtract 2 from 7, resulting in 5.
This approach ensures calculations with negative numbers are clear and accurate.
Arithmetic Practice
Mastering arithmetic with number lines enhances your ability to visualize math problems.
Number lines can serve as a powerful tool to understand arithmetic, especially when dealing with negative numbers or operations that may initially seem tricky.
Here's how to effectively use a number line:
  • Identify the starting number on the number line.
  • Determine the direction to move 鈥� left for negative numbers, right for positive numbers.
  • Count the number of spaces to move.
  • Observe where you land. This spot represents the result of your arithmetic problem.
Continuous practice with number lines can bolster confidence and comfort with addition, subtraction, and understanding negative values.
It's a hands-on way to grasp the concepts and become proficient in elementary mathematical operations.

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Most popular questions from this chapter

Use a calculator to find a decimal approximation for each irrational number, correct to three decimal places. Between which two integers should you graph each of these numbers on the number line? $$-\sqrt{12}$$

Why is the order of operations agreement needed?

What are additive inverses?

In Exercises \(109-116\), write a numerical expression for each phrase. Then simplify the numerical expression by performing the given operations. The product of \(-6\) and \(-4,\) decreased by \(-5\)

From here on, each exercise set will contain three review exercises. It is essential to review previously covered topics to improve your understanding of the topics and to help maintain your mastery of the material. If you are not certain how to solve a review exercise, turn to the section and the worked example given in parentheses at the end of each exercise. Determine whether 18 is a solution of \(16=2(x-1)-x\) (Section 1.1, Example 4)
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