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Chapter 2: Problem 5

Subtract. $$ 3-8 $$

Short Answer

Expert verified
The result of subtracting 8 from 3 is -5.

Step by step solution

01

Convert to Addition

To simplify subtraction, convert the expression to an addition problem. Subtracting 8 from 3 is equivalent to adding negative 8 to 3. So, we rewrite the expression as: \[ 3 + (-8) \]
02

Calculate the Sum

Add \[ 3 + (-8) \]Start by considering where these two numbers are on the number line. Begin at 3 and move left 8 units (because -8 is negative). The result is:\[ -5 \]
03

Result

Thus, after adding, we find:\[ 3 - 8 = -5 \]

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Key Concepts

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

Number Line
When thinking about integer subtraction, a number line can be extremely helpful. The number line is a visual representation of real numbers laid out in a sequence. Integers appear as equally spaced points along this line. We use it to understand both the direction and value of numbers when performing operations like addition or subtraction.

To use a number line:
  • Locate the first number on the line. In our case, this is 3.
  • Determine the direction to move based on the operation. Subtraction means moving left on the number line.
  • The amount you move correlates with the second number in the operation. Here, you move 8 units left to reach our result.
Using the number line in this way visually demonstrates that when we start at 3 and move 8 units to the left, we land at -5, showing that 3 minus 8 is indeed -5.
Negative Numbers
Negative numbers can be a bit tricky at first, but they simply represent numbers less than zero. They appear on the number line to the left of zero and are integral to understanding subtraction. Negative numbers have unique properties:
  • They express amounts below zero, like debts or losses.
  • Adding a negative is the same as subtracting its positive counterpart.
  • If you're subtracting a large positive number from a smaller positive number, you get a negative result.
In our problem, when transforming 3-8 into 3+(-8), we realize we're adding a negative. This is equivalent to subtracting the positive 8, which brings us to the left on our number line, landing at -5.
Addition and Subtraction of Integers
Understanding the addition and subtraction of integers is crucial because these operations form the foundation of arithmetic with whole numbers. Here鈥檚 how it works:
  • Addition: When you add two numbers, you find a result by moving to the right on the number line. The positive sum moves further to the right.
  • Subtraction: When you subtract one integer from another, determine how far to move to the left on the number line, essentially the same as adding the corresponding negative number.
  • Adding a Negative: This operation effectively decreases the value. Adding negative numbers is the equivalent of moving left on the number line.
For example, the subtraction 3 - 8 was transformed into the addition operation 3 + (-8). This change lets us think about subtraction as adding an inverse or opposite, resulting in a step to the left on the number line, ending at -5.

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Most popular questions from this chapter

Insert \(<\) or \(>\) between each pair of integers to make a true statement. $$ \begin{array}{ll} -7 & -5 \end{array} $$

Choose all numbers for \(x\) from each given list that make each statement true. \(|x|>4\) a. 0 b. -4 c. 5 d. -100

Insert \(<,>,\) or \(=\) between each pair of numbers to make a true statement. $$ -|-8| \quad-|-4| $$

Graph each integer in the list on the same number line. $$ 7,5,2,0 $$

Simplify. $$ |7| $$
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