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Chapter 1: Problem 1

Subtract. See Examples 1 through 5 $$ -6-4 $$

Short Answer

Expert verified
-10

Step by step solution

01

Understand the Problem

We are asked to subtract 4 from -6. This means we need to calculate \(-6 - 4\).
02

Interpret the Operation

Subtracting 4 from -6 is equivalent to adding the negative of 4 to -6. Therefore, we rewrite the expression as \(-6 + (-4)\).
03

Perform the Calculation

Now we perform the addition of two negative numbers: \(-6 + (-4) = -10\).
04

Write the Final Answer

The result of \(-6 - 4\) is \(-10\).

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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 represented with a minus sign, and they appear to the left of zero on a number line. Understanding negative numbers is crucial to solving problems like integer subtraction. Here鈥檚 a simple way to think about them:
  • A negative number can represent a loss or a decrease in quantity.
  • Negative numbers are smaller than zero, and the larger the absolute value, the smaller the value in terms of normal quantity.
For example, -6 represents a level of six units below zero, like owing six dollars. When you subtract using negative numbers, it鈥檚 like navigating further left on the number line.
Subtraction Concept
Subtraction is a basic arithmetic operation used to find the difference between numbers. Learning the concept of subtraction involves understanding what it means to take one quantity away from another. Here's a breakdown of this concept:
  • Subtraction can be viewed as finding how much more one number is than another.
  • In mathematical terms, subtraction is not always about 'taking away', but can also involve 'adding a negative'.
For the expression \(-6 - 4\), this can be seen as adding the opposite, resulting in \(-6 + (-4)\). Instead of removing 4, you add -4 which moves further into negative territory on the number line. This is useful because it simplifies mental calculations by using addition instead.
Integer Operations
Operations involving integers follow specific rules, especially when it comes to adding and subtracting them. Here are some tips for handling integer operations effectively:
  • When dealing with two positive integers, simply add them as usual.
  • When subtracting, transform the operation to add the opposite: \(a - b\) becomes \(a + (-b)\).
  • Two negatives add up and move further into the negative direction: \(-a + (-b)\) equals \(-(a + b)\).
In our example, \(-6 + (-4)\) results in \(-10\) because you're combining the absolute values of the two negative numbers and keeping the negative sign. This approach will help you better understand calculations involving any integer values you encounter.

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Most popular questions from this chapter

In your own words, explain how to multiply two fractions

If \(a\) is a positive number and \(b\) is a negative number, determine whether each statement is true or false. \(b-a\) is always a negative number.

Write each sentence as an equation or inequality. Use \(x\) to represent any unknown number. Twice a number is 17.

In \(2006,\) Gap Inc operated a total of 3054 stores worldwide. The following chart shows the store breakdown by brand. $$ \begin{array}{|l|l|} \hline \text { Brand } & {\text { Number of Stores }} \\ \hline \text { Gap(\mathrm{ Domestic) } } & {1335} \\ \hline \text { Gap (International) } & {256} \\ \hline \text { Banana Republic } & {498} \\ \hline \text { Old Navy } & {960} \\ \hline \text { Forth \& Towne } & {5} \\ \hline \text { Total } & {3054} \\ \hline \end{array} $$ What fraction of Gap-brand stores were Old Navy stores? Simplify this fraction.

Write each sentence as an equation or inequality. Use \(x\) to represent any unknown number. The sum of 8 and twice a number is 42
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