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Chapter 1: Problem 13

Add using the number line. \(-3+(-5)\)

Short Answer

Expert verified
-8

Step by step solution

01

Identify the starting point

Begin at the number -3 on the number line.
02

Understand the operation

Since we are adding a negative number -5, this means we will move to the left on the number line.
03

Make the moves

Start at -3. Move 5 units to the left: -4, -5, -6, -7, -8.
04

Determine the result

After moving 5 units to the left, you land on -8.

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Key Concepts

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

number line
The number line is a visual tool that helps us understand numbers and their relationships. Picture a horizontal line with numbers placed at equal intervals. Zero is at the center, positive numbers extend to the right, and negative numbers stretch to the left.

When adding numbers, we use the number line to show our movement. Each step to the right represents adding a positive number, and each step to the left signifies adding a negative number.
For example, if we need to add -3 and -5, we start at -3 on the number line. Then, we move 5 steps to the left because we are adding a negative number (-5). We land on -8.
integers
Integers are the set of whole numbers and their negative counterparts. This includes {..., -3, -2, -1, 0, 1, 2, 3, ...}. They do not have fractions or decimals, making them easy to locate on a number line.

When working with integers, it鈥檚 important to understand their properties and how they behave in operations like addition.
  • Negative integers are less than zero and found to the left of zero on the number line.
  • Positive integers are greater than zero and appear to the right of zero.
  • Zero is neutral, not positive nor negative.
Using these properties, we can perform operations such as addition by visualizing movements on the number line.
addition
Addition is the process of combining two or more numbers to get a total. When adding integers, the number line can be extremely helpful.

Here are some steps to help you add integers:
  • Identify the starting point: Begin at the first number on the number line.
  • Understand the operation: Determine if you are adding a positive or negative number. This informs your direction on the number line.
  • Make the moves: Move the number of steps corresponding to the integer being added. Right for positive, left for negative.
  • Determine the result: The point where you land is your answer.
Following these steps can make adding integers, even negative ones, straightforward and intuitive.

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Most popular questions from this chapter

Translate to an inequality. When Helga's calculator gives a decimal value for \(\sqrt{2}\) and that value is promptly squared, the result is \(2 .\) Yet when that same decimal approximation is entered by hand and then squared, the result is not exactly \(2 .\) Why do you suppose this is?

Translate to an inequality. Is the following statement true? Why or why not? \(\sqrt{a^{2}}=|a|\) for any real number \(a\).

Write an equivalent expression without using grouping symbols. $$ -[5-6 x] $$

Simplify using a calculator. Round your answer to the nearest thousandth. $$ \frac{46-(3-8)^{3}}{2\left[35-(18-26)^{2}\right]} $$

If \(n\) is positive and \(m\) is negative, what is the sign of \(n+(-m) ?\) Why?
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