Integers: Addition and Subtraction Fundamentals
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Questions and Answers

If $m = -9$ and $n = +4$, what is the result of $m - n$?

  • $5$
  • $13$
  • $-5$
  • $-13$ (correct)
  • What is the sum of $(-7) + (-5)$?

  • $-2$
  • $12$
  • $-12$ (correct)
  • $2$
  • What is the sum of $(-12) + (+17)$?

  • $-29$
  • $5$ (correct)
  • $29$
  • $-5$
  • If $p = -14$ and $q = -6$, what is $p - q$?

    <p>$-8$</p> Signup and view all the answers

    What is the result of $(-15) + (-10)$?

    <p>$-25$</p> Signup and view all the answers

    Given $r = +20$ and $s = -7$, what is $r - s$?

    <p>$13$</p> Signup and view all the answers

    Calculate $(+8) + (-3)$.

    <p>$11$</p> Signup and view all the answers

    Determine the value of $(+13) - (+9)$.

    <p>$4$</p> Signup and view all the answers

    What is the sum of $(+16) + (+22)$?

    <p>$38$</p> Signup and view all the answers

    If $t = -11$ and $u = -8$, what does $t - u$ equal?

    <p>$-3$</p> Signup and view all the answers

    Study Notes

    Integers: Exploring Addition and Subtraction

    Integers—the set of whole numbers, both positive and negative—are fundamental building blocks of arithmetic operations like addition and subtraction. Let's delve into these core mathematical concepts involving integers so you can better understand this essential part of math education.

    Adding Integers

    To illustrate adding two integers, let's say we have (x = -6) and (y = +3.) To find their sum ((x+ y),) follow these rules:

    1. If both numbers share the same sign, keep it. [(-6)+(+3)=-(6+3)\text{ is }-\mathbf{9}.]

    2. If different signs, switch them and change the answer's sign. [(-6)+(-3) = (-6\underset{\uparrow}{\neg})+(+\underbrace{3}_{\uparrow})\text{ is } -\mathbf{3}.]

    This second rule may seem counterintuitive; however, performing integer addition by toggling signs helps avoid confusion when dealing with large values or complex equations containing more terms in calculations.

    Subtracting Integers

    Subtraction of integers can be approached through three primary methods:

    1. Direct subtraction using the difference between absolute values and considering the signs:

      Suppose (z=-8,) and (w=+4.) Then, [(z-w) = (-8)-(+4)=-(8-4)\text{, which equals }-\mathbf{4}.]

    2. Alternatively, one might choose to rewrite the problem utilizing properties of addition:

    [ (z - w) = z + (-w), \ (-8) + (+4) = -\mathbf{4} . ]

    1. Lastly, some students prefer flipping a number and changing its sign before adding:

    [ (-8 - 4) = (-8 + (-4)),\ -\mathbf{12} \text { since } (-4) = -|4|. ]

    All these techniques converge towards producing identical results, so feel free to select whichever approach suits your learning style best.

    The study of integers lays foundational knowledge required to tackle higher-order mathematics such as algebraic expressions, systems of linear equations, etc., making understanding these simple yet powerful ideas indispensable.

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    Description

    Explore the core concepts of adding and subtracting integers to enhance your understanding of basic arithmetic operations. Dive into rules and methods like direct subtraction, rewriting problems using addition properties, and flipping numbers to change signs.

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