Even or odd: arithmetic rules

Learning Objectives Define even and odd numbers based on their properties. Identify whether a given whole number is even or odd by examining its ones digit. Determine the parity (even or odd) of a sum of two numbers without performing the full addition. Determine the parity of a difference of two numbers without performing the full subtraction. Determine the parity of a product of two numbers without performing the full multiplication. Apply even/odd arithmetic rules to solve simple number sense problems. Explain the reasoning behind the arithmetic rules for even and odd numbers. Have you ever wondered why some numbers can be split perfectly into two equal groups, while others always leave one left over? 🤔 Let's explore the secret lives of numbers! In this lesson, y...

TermDefinitionExample Even NumberA whole number that can be divided by 2 with no remainder. Even numbers always end in 0, 2, 4, 6, or 8.14 is an even number because 14 ÷ 2 = 7. Its ones digit is 4. Odd NumberA whole number that, when divided by 2, leaves a remainder of 1. Odd numbers always end in 1, 3, 5, 7, or 9.23 is an odd number because 23 ÷ 2 = 11 with a remainder of 1. Its ones digit is 3. ParityThe property of a whole number being either even or odd. It tells us whether a number can be divided by 2 evenly.The parity of 100 is even. The parity of 57 is odd. SumThe result obtained when two or more numbers are added together.The sum of 6 and 7 is 13. DifferenceThe result obtained when one number is subtracted from another.The difference between 15 and 8 is 7. ProductThe result obtain...

Addition Parity Rules $$ \text{Even} + \text{Even} = \text{Even} \quad (E + E = E) $$ $$ \text{Odd} + \text{Odd} = \text{Even} \quad (O + O = E) $$ $$ \text{Even} + \text{Odd} = \text{Odd} \quad (E + O = O) $$ These rules help predict if the sum of two numbers will be even or odd. Notice that if both numbers have the same parity (both even or both odd), their sum is even. If they have different parities, their sum is odd. Subtraction Parity Rules $$ \text{Even} - \text{Even} = \text{Even} \quad (E - E = E) $$ $$ \text{Odd} - \text{Odd} = \text{Even} \quad (O - O = E) $$ $$ \text{Even} - \text{Odd} = \text{Odd} \quad (E - O = O) $$ $$ \text{Odd} - \text{Even} = \text{Odd} \quad (O - E = O) $$ These rules help predict if the difference between two numbers will be even or odd....