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Chapter 3: Problem 24

For the following exercises, perform the indicated operations. $$ -6-5 $$

Short Answer

Expert verified
Answer: -11

Step by step solution

01

Rewrite the expression as an addition of the opposite of the second number

Rewrite the subtraction operation as an addition operation by adding the opposite of the second number to the first number: $$ -6 - 5 \Rightarrow -6 + (-5) $$
02

Add the numbers

Now, add the two negative numbers together: $$ -6 + (-5) = -11 $$
03

Write down the answer

The result of the subtraction operation between the two negative numbers is also a negative number: $$ -6 - 5 = -11 $$

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Key Concepts

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

Addition of Integers
In mathematics, adding integers is an essential skill. When you add integers, you combine their values to find the total. A positive integer increases the total, while a negative integer decreases it.
For example, in our exercise, by converting the subtraction into an addition, we see how the expression \(-6 - 5\) becomes \(-6 + (-5)\).
This shows us that instead of subtracting, we are adding the opposite of 5, which is -5. This approach makes it clearer especially when working with negative numbers.
  • Always convert subtraction into addition by using the opposite integer.
  • When both numbers are negative, add their absolute values, and the sum becomes negative.
  • If you add a positive number to a negative number, it's like subtraction. Find the difference and keep the sign of the number with the larger absolute value.
Subtraction of Integers
Subtraction of integers might seem more complicated at first, but once you understand the process, it's quite straightforward. The key idea is to transform subtraction into addition.
In our example, the subtraction \(-6 - 5\) is turned into an addition problem: \(-6 + (-5)\). This not only simplifies the computation but also aligns with how addition works with negative numbers.
  • When subtracting a positive number, think of it as adding a negative. For instance, \(-6 - 5\) equals \(-6 + (-5)\).
  • Subtracting a negative number is like adding its opposite positive number.
  • Always try to rewrite subtraction problems in terms of addition to simplify the process.
Negative Numbers
Understanding negative numbers is pivotal in mastering integer operations. Negative numbers are values less than zero, shown with a minus sign \((-\)).
They behave differently than positive numbers when it comes to addition and subtraction.
  • A negative number plus another negative number results in a more negative value. Like our example, adding \(-6 + (-5)\) gives \(-11\).
  • Negative numbers subtract from positive results, reducing the overall value.
  • When subtracting with negatives, remember to translate the operation into adding opposites. For \(-6 - 5\), we think of it as adding \(-5\) to \(-6\).
      • By mastering the quirks of negative numbers, you can confidently handle any integer operation with ease.

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Most popular questions from this chapter

Find the value of each of the following expressions. \(P=\frac{n(n-2)(n-4)}{2 n} . \quad\) Find \(P\) if \(n=-6\)

Determine the value of \(-[-(-|-5|)]\)

Convert the numbers used in the following problems to scientific notation. The average mass of a newborn American female is about 3360 grams.

Convert the numbers used in the following problems to scientific notation. Cells in the human liver have masses of about 0.000000008 gram.

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