Select even or odd numbers

Learning Objectives Define even and odd numbers using algebraic expressions (2k and 2k+1). Determine the parity (evenness or oddness) of polynomial expressions for any integer input. Apply the rules of operations (addition, subtraction, multiplication) to predict the parity of outcomes. Select even or odd numbers from sets defined by algebraic rules, including quadratic and simple radical expressions. Construct simple algebraic proofs for properties of even and odd numbers. Analyze and solve problems by separating them into cases based on the parity of a variable. If you pick any integer, square it, and add the original integer back, will you always get an even number? 🤔 Let's use algebra to find out! This tutorial moves beyond simply identifying even and odd numbers....

TermDefinitionExample Even NumberAn integer that is exactly divisible by 2. Any even number can be expressed in the form 2k, where k is an integer.14 is an even number because 14 = 2 * 7. Here, k = 7. Odd NumberAn integer that is not exactly divisible by 2, leaving a remainder of 1. Any odd number can be expressed in the form 2k + 1, where k is an integer.-9 is an odd number because -9 = 2 * (-5) + 1. Here, k = -5. ParityThe property of an integer of being either even or odd. Two integers have the same parity if they are both even or both odd.7 and 11 have the same parity (both are odd). 4 and 6 have the same parity (both are even). 3 and 8 have different parity. Integer (ℤ)The set of whole numbers and their opposites. Parity is a property that applies only to integers.{... -3, -2, -1, 0,...

Parity of Sums and Differences Let E be an even number and O be an odd number. 1. E ± E = E 2. O ± O = E 3. E ± O = O Use these rules to quickly determine the parity of an addition or subtraction without calculating the exact result. For example, the sum of two odd numbers (like 3+5=8) is always even. Parity of Products Let E be an even number and O be an odd number. 1. E × E = E 2. E × O = E 3. O × O = O The product is even if at least one of the factors is even. The product is odd only if all factors are odd. Parity of Powers Let E be an even number, O be an odd number, and n be a positive integer. 1. E^n = E 2. O^n = O Raising an even or odd number to a positive integer power does not change its parity. For example, 7^3 is odd because 7 is odd.