3.7.2: Key Concepts

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    From LibreTexts, under CC BY 4.0, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    Key Concepts

    3.1 Introduction to Integers

    • Opposite Notation
      • means the opposite of the number
      • The notation is read the opposite of
    • Absolute Value Notation
      • The absolute value of a number is written as .
      • for all numbers.

    3.2 Add Integers

    • Addition of Positive and Negative Integers
      both positive, sum positive both negative, sum negative
      When the signs are the same, the counters would be all the same color, so add them.
      different signs, more negatives different signs, more positives
      Sum negative sum positive
      When the signs are different, some counters would make neutral pairs; subtract to see how many are left.

    3.3 Subtract Integers

    • Subtraction of Integers
      2 positives 2 negatives
      When there would be enough counters of the color to take away, subtract.
      5 negatives, want to subtract 3 positives 5 positives, want to subtract 3 negatives
      need neutral pairs need neutral pairs
      When there would not be enough of the counters to take away, add neutral pairs.
      Table 3.13
    • Subtraction Property
    • Solve Application Problems
      • Step 1. Identify what you are asked to find.
      • Step 2. Write a phrase that gives the information to find it.
      • Step 3. Translate the phrase to an expression.
      • Step 4. Simplify the expression.
      • Step 5. Answer the question with a complete sentence.

    3.4 Multiply and Divide Integers

    • Multiplication of Signed Numbers
      • To determine the sign of the product of two signed numbers:
        Same Signs Product
        Two positives
        Two negatives        		 Positive
        Positive
        Different Signs Product
        Positive • negative
        Negative • positive        		 Negative
        Negative
    • Division of Signed Numbers
      • To determine the sign of the quotient of two signed numbers:
        Same Signs Quotient
        Two positives
        Two negatives        		 Positive
        Positive
        Different Signs Quotient
        Positive • negative
        Negative • Positive        		 Negative
        Negative
    • Multiplication by
      • Multiplying a number by gives its opposite:
    • Division by
      • Dividing a number by gives its opposite:

    3.5 Solve Equations Using Integers; The Division Property of Equality

    • How to determine whether a number is a solution to an equation.
      • Step 1. Substitute the number for the variable in the equation.
      • Step 2. Simplify the expressions on both sides of the equation.
      • Step 3. Determine whether the resulting equation is true.
        • If it is true, the number is a solution.
        • If it is not true, the number is not a solution.
    • Properties of Equalities
      Subtraction Property of Equality Addition Property of Equality


    • Division Property of Equality
      • For any numbers and
        If , then .

    3.7.2: Key Concepts is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by LibreTexts.