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Chapter 2: Problem 17

Subtract. $$15-18$$

Short Answer

Expert verified
The result of 15 - 18 is -3.

Step by step solution

01

Identify the Problem Type

We are given the subtraction problem \(15 - 18\). The problem involves subtracting a larger number from a smaller number, which will result in a negative number.
02

Rewrite the Subtraction

Change the subtraction operation into a negative addition: \(15 - 18\) can be rewritten as \(15 + (-18)\). This shows that we're adding a negative number to a positive number.
03

Perform the Addition

Now add \(15\) and \(-18\) together. The result will be negative because \(-18\) has a larger absolute value than \(15\). Calculate: \(15 + (-18) = -3\).
04

Check Your Work

Verify the solution by considering the number line. Starting at 15, moving left 18 places brings you to -3. Thus, the solution is correct.

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Key Concepts

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

Negative Numbers
Negative numbers are numbers less than zero. They are commonly represented with a minus sign, such as -1, -2, -3, and so on. When you subtract a larger number from a smaller one, you get a negative result.

In the example given, subtracting 18 from 15 leads us to a negative number. If you're not used to working with negative numbers, keep these key points in mind:
  • A negative number is always less than zero.
  • Negative numbers are the mirror of positive numbers on the number line.
  • Think of them as debts or temperatures below freezing.
Imagine you have 15, but owe 18. This gives you a remaining balance of -3. Negative numbers are essential in real-world contexts like temperature and finance.
Number Line
A number line is a visual representation of numbers. It helps in understanding both positive and negative numbers in relation to each other.

A number line has zeros in the center, positive numbers to the right, and negative numbers to the left. It's a powerful tool:
  • For visualizing subtraction and addition.
  • To see how negative and positive numbers are arranged.
  • To easily track changes in values step by step.
Take the exercise, for example: starting at 15 on the number line, move 18 steps to the left. You end up at -3. This movement illustrates how subtraction can create a negative result.
Absolute Value
Absolute value measures the distance of a number from zero on the number line, ignoring direction. It is always a positive number or zero.

The absolute value is crucial in subtraction involving negative numbers:
  • It helps determine which number has a greater influence when added or subtracted.
  • Helps in understanding the size of numbers independent of their sign.
  • Is denoted by vertical bars, for example, \(|-18| = 18\).
In the subtraction problem, 18 has a greater absolute value than 15, hence the negative result, -3. Understanding absolute value gives you clearer insight into why the result is negative.

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Most popular questions from this chapter

In Chapter 1 we defined an arithmetic sequence as a sequence of numbers in which each number, after the first number, is obtained from the previous number by adding the same amount each time. Find the next two numbers in each arithmetic sequence below. $$10,5,0, \dots$$

Tracking Inventory By definition, inventory is the total amount of goods contained in a store or warehouse at any given time. It is helpful for store owners to know the number of items they have available for sale in order to accommodate customer demand. This table shows the beginning inventory on May 1 st and tracks the number of items bought and sold for one month. Determine the number of items in inventory at the end of the month. $$\begin{array}{|llll|} \hline \text { Dife } & \text { Uranstation } & \begin{array}{c} \text { What whires of } \\ \text { Thite sysiblity } \end{array} & \begin{array}{l} \text { Which of } \\ \text { thits sold } \end{array} \\ \hline \text { May 1 } & \text { Beginning Inventory } & 400 & \\\ \text { May 3 } & \text { Purchase } & 100 & \\ \text { May 8 } & \text { Sale } & & 700 \\ \text { May 15 } & \text { Purchase } & 600 & \\ \text { May 19 } & \text { Purchase } & 200 & \\ \text { May 25 } & \text { Sale } & &400 \\ \text { May 27 } & \text { Sale } && 300 \\ \text { May 31 } & \text { Ending Inventory } & & \\ \hline \end{array}$$

Subtract. $$-50-60$$

Add or subtract. $$17+3+152+1,200$$

At 10: 00 in the morning in White Bear Lake, Minnesota, Zach notices the temperature is 5 degrees below zero Fahrenheit. Write this temperature as a negative number. By noon the temperature has dropped another 10 degrees. What is the temperature at noon?
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