## Properties of Multiplication

• Why should I bother learning this?
• This is an excellent opportunity to provide examples of how the use of multiplication saves so much time compared to repeated addition. Using rolls of coins can be a motivating factor for many students. For example, bring in 10 rolls of nickels. Explain to the students that each roll contains 40 nickels. If a nickel is worth 5 cents, how many cents is a roll of nickels worth? Have a volunteer add 5 forty times at the board. Have another student multiply 5 x 40. The efficiency of using multiplication to find the total amount in equal groups will be evident.

• Why does zero times another number equal zero?
• To explain multiplication by zero, be sure to reinforce that multiplication involves groups of items (for example, 2 x 5 is two groups of five). The expression 0 x 5 is zero groups of five. If you have zero groups then your product must be zero. Similarly, 5 x 0 is five groups with zero in each group. If there is zero in each group, then the product must be zero.

• Do you always get the same answer in a multiplication problem if you switch the numbers around like 4 x 7 and 7 x 4?
• This is an excellent chance to discuss the commutative property of multiplication. Display a multiplication table in the classroom. Have students use the table to see how the commutative property works for multiplication.

Multi-digit by one-digit:

Properties of Multiplication: