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Chapter 1: Problem 100

Subtracting Integers State the rule for subtracting integers.

Short Answer

Expert verified
The rule for subtracting integers is that subtracting an integer is the same as adding its inverse. For example, \(A - B = A + (-B)\).

Step by step solution

01

State the rule of integer subtraction

The rule for subtracting integers is as follows: \('A - B' = A + (-B)' \). This means that subtracting an integer is the same thing as adding its additive inverse.
02

Explain the rule with an example

For example, consider \(7 - 4\). This is the same as \(7 + (-4) = 3\). Here, -4 is the additive inverse of 4, so subtracting 4 is the same as adding -4.
03

Demonstration of the rule with a negative integer

Here is another example involving a negative integer such as \(7 - -4\). It's the same as \(7 + 4 = 11\). In this case, the additive inverse of -4 is 4.

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Key Concepts

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

additive inverse
The concept of an additive inverse is all about finding a number that, when added to a given number, results in zero. This might sound a little abstract at first, but it is as simple as flipping the sign of a number.
Let's break it down:
  • The additive inverse of a positive number is negative. For example, the additive inverse of +4 is -4.
  • Conversely, the additive inverse of a negative number is positive. For instance, the additive inverse of -4 is +4.
So, why is it important? Subtracting a number is the same as adding its additive inverse. This means instead of subtracting, say 5, you are actually adding -5. This helps in simplifying the operation and eliminating potential errors, especially when dealing with complex computations.
integer operations
Integer operations include addition, subtraction, multiplication, and division, but each operation has its own set of rules which help in handling both positive and negative integers effectively. Today, we're focusing on subtraction.
Subtraction of integers can be tricky because it involves thinking about the direction of the number on the number line:
  • When subtracting a positive integer from another integer, think of it as moving left on the number line.
  • When subtracting a negative integer, which means you are adding a positive, move right on the number line.
It's crucial to apply the rules of integer operations correctly to avoid mistakes. For instance, subtracting -3 from 5 is the same as adding +3 to 5, resulting in 8. This clarity in understanding helps ensure that integer operations are handled accurately.
negative integers
Negative integers are simply those numbers less than zero, represented with a minus sign (-). They work a bit differently than positive integers, especially when it comes to operations.
Here's what you should know about negative integers:
  • When adding negative integers, the result is more negative. For instance, -3 + (-2) = -5.
  • When subtracting a negative integer, you effectively add its positive counterpart, which increases the value.
Real-world scenarios often involve negative integers, such as calculating losses or debts. Understanding how to work with them is critical in making correct calculations in both math problems and real-life situations.

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Most popular questions from this chapter

\(\frac{5}{6}-\frac{1}{3}\)

\([360-(8+12)] \div 5\)

Picture Frame A picture frame is 36 inches wide and its height is 9 inches less than its width. (a) Write an expression for the area of the picture frame. (b) Use the Distributive Property to rewrite the expression. (c) Find the area of the picture frame.

Error Analysis Describe and correct the error. $$ \begin{aligned} -9+\frac{9+20}{3(5)}-(-3) &=-9+\frac{9}{3}+\frac{20}{5}-(-3) \\ &=-9+3+4-(-3) \\ &=1 \end{aligned} $$

\(35 \div 7\)
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