1.5 Multiplication 1 The multiplication of two numbers a and b can be expressed by the equation a  b = c where a and b are factors and c is called the product (a and b are also called multiplicands). Phrases for Multiplication product times Multiplied by Twice (2  __ ) Example: The product of 5 and 9. Translates to: 5  9 = 45 Notice that the order for multiplication does not matter. 4  10 is the same as 10  4. This is called the Commutative Property for Multiplication. a  b = b  a where a and b are numbers. Example: 5  7 = 7  5 35 = 35 Commutative Property for Multiplication The number 1 is the identity element of multiplication because for any number a, a  1 = a and 1  a = a. The number 1 is the identity element of multiplication because when 1 is multiplied by any number, the resulting product is the original number Multiplicative Identity Element Example: 5  1 =5 4  3 12 Factors (or multiplicands) product Example:

1.5 Multiplication 2 Since the order does not matter; i.e., 5  (2  3) = (5  2)  3 (both equal 30), this gives another property. This is called the Associative Property for Multiplication. a  (b  c) = (a  b)  c where a, b and c are numbers. Associative Property for Multiplication Example: 4  (9  5) = (4  9)  5 The numbers are in the same order, the parentheses are in different positions. Your Turn Problem #1 State the indicated Property: a)12  1 =12 b)3  7 = 7  3 c)3  (5  8) = (3  5)  8 a)Multiplicative Additive Identity b)Commutative Property of Multiplication c)Associative Property of Multiplication Answers Recall: Parentheses Parentheses is a mathematical expression which indicates: do inside first. Example: 5  (2  3) Since there are parentheses, we will do that first. 5  6 30 Notice: We would get the same answer if we multiplied the 5 and 2 first, i.e. (5  2 =10, then 10  3 =30). The order does not matter because the order in which the multiplication is performed will not matter.

1.5 Multiplication 3 Note: Many students have a hard time with multiplying (getting the correct answer) because of one problem, they haven’t memorized the multiplication facts. Without knowing these, it is impossible to do these problems correctly. 7 times 9 equals what number? Of course it is sixty-three. So memorize those facts, if you need help making a chart or flash cards, ask a math tutor for assistance. 1. Multiply the top factor by the ones digit in the bottom factor, carrying as you go  3 =27 (carry the 2, bring down the 7)  3 =15, 15 +2=17 (carry the 1, bring down the 7) 4 1  3 =3, 3 +1=4 (bring down the 4) 2. Multiply the top factor by the tens digit in the bottom factor, carrying as you go. A zero will be written first. 0 9  4 =36 (carry the 3, bring down the 6)  4 =20, 20 +3=23 (carry the 2, bring down the 3)  4 =4, 4 +2=6 (bring down the 6) 6 3. Draw a line and add Answer: 62,694 Your Turn Problem #2 Find the product of 729 and 86.

1.5 Multiplication 4 Example: Mark agreed to buy a car paying $400 per month for 6 years. How much will he have paid after the 6 years? Solution: 6 years equals 72 months Multiply 400 by 72 Answer: $28,800 A Honda holds 17 gallons of gas. If the Honda gets 28 miles per gallon, how far can the Honda go on a full tank of gas? Your Turn Problem #3 Answer: 476 miles The End