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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:
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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.
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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. 7 2 9 3 =27 (carry the 2, bring down the 7) 1 7 5 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) 3 6 5 4 =20, 20 +3=23 (carry the 2, bring down the 3) 2 3 1 4 =4, 4 +2=6 (bring down the 6) 6 3. Draw a line and add. 6 8 3 7 Answer: 62,694 Your Turn Problem #2 Find the product of 729 and 86.
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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
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