1) Even Integers: an integer that is divisible by two (ex. 6, 8, 10, 12, 14)
2) Odd Integers: an integer that is not divisible by two (ex. 7, 9, 11, 13, 15)
3) Consecutive Even Integers: even integers that increase in units of 2 (ex. 2, 4, 6)
4) Consecutive Odd Integers: odd integers that increase in units of 2 (ex. 3, 5, 7, 9)
5) Algebraic Representation of Consecutive Even/Odd Integers: x, x + 2, x + 4…

MATH RULES FOR EVEN / ODD INTEGERS

            Addition                                  Subtraction                             Multiplication

    Even + Even = Even                  Even – Even = Even                 Even × Even = Even
    Even + Odd = Odd                    Even – Odd = Odd                    Even × Odd = Even
    Odd + Odd = Even                    Odd – Odd = Even                     Odd × Odd = Odd

Also remember that, if the problem does not specifically refer to positive or negative integers, then zero must be included as an integer.

SAMPLE PRACTICE QUESTION FOR EVEN / ODD INTEGERS

If q is an even integer, which of the expressions results in an even integer?
(A) q(12) – 7      (B) 5 + 7q      (C) 5q – 3q      (D) 2q + 3      (E) 4q + 1

     Solution 1: Using Even / Odd Rules
     (A) even(even) – odd = even – odd = odd
     (B) odd + odd(even) = odd + even = odd
     (C) odd(even) – odd(even) = even – even = even
     (D) even(even) + odd = even + odd = odd
     (E) even(even) + odd = even + odd = odd

     Solution 2: Using Plug-In (using q = 2)
     (A) 2(12) – 7 = 17 = odd
     (B) 5 + (7)(2) = 5 + 14 = 19 = odd
     (C) (5)(2) – (3)(2) = 10 – 6 = 4 = even
     (D) (2)(2) + 3 = 4 + 3 = 7 = odd
     (E) (4)(2) + 1 = 8 + 1 = 9 = odd

Math: Even / Odd Integer Practice

Lesson Includes:

—Math Terms for Even / Odd Integers

—Rules for Even Odd Integers

—Sample Practice Questions

—Practice Questions

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EVEN & ODD INTEGERS REVIEW QUIZ

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