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Chapter Chapter1 2 The Whole Numbers Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 1 Section 1.6 Multiplying Whole Numbers and Area Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 2 Multiplying Whole Numbers Multiplication is repeated addition but with different notation. 6 30 6+6+6+6+6= 5 factor factor product The is called a multiplication sign. Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 3 Properties Multiplication Property of 0 The product of 0 and any number is 0. For example, 5 0 = 0 and 0 8 = 0. Multiplication Property of 1 The product of 1 and any number is that same number. For example, 1 9 = 9 and 7 1 = 7. Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 4 Example Multiply. a. 4 × 1 = 4 b. 0(5) = 0 c. 1(52) = 52 d. (76)(0) = 0 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 5 Properties Commutative Property of Multiplication Changing the order of two factors does not change their product. For example, 4 3 = 12 and 3 4 = 12. Associative Property of Multiplication Changing the grouping of factors does not change their product. For example, (2 3) 4 = 2 (3 4). Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 6 Properties Distributive Property Multiplication distributes over addition. For example, 2(3 + 4) = 2 3 + 2 4 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 7 Example Rewrite 4(5 + 6) using the distributive property. 4(5 + 6) = 4 5 + 4 6 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 8 Multiplying Whole Numbers Example: Use the distributive property to multiply 3 and 79. 3(79) 3(70 9) 3 70 3 9 210 27 237 Write 79 in expanded form. Apply the Distributive Property. Multiply. Add. Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 9 Multiplying Whole Numbers Example: Multiply 624 by 3. 1 624 3 1872 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 10 Multiplying Whole Numbers Example: Multiply 91 by 72. 91 72 182 6370 6552 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 11 Multiplying Whole Numbers Ending in Zero(s) Example: Multiply 3 by 9000. 3 9000 = 3 9 1000 = (27) 1000 = 27,000 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 12 Finding the Area of a Rectangle Example: Find the area of the following rectangle. 12 inches 4 inches 12 4 48 square inches Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 13 Solving Problems by Multiplying Key Words or Phrases Example Symbols Multiply Multiply 3 by 4 34 Product The product of 5 and 10 5 10 Times 6 times 4 64 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 14 Example A particular color printer can print 21 pages per minute. How many pages can it print in 25 minutes? Pages per minute Number of minutes = 21 25 21 25 105 420 525 pages Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 15 Example A professor of history purchased DVDs and CDs through a club. Each DVD was priced at $11 and each CD cost $9. He bought eight DVDs and five CDs. Find the total cost of the order. Price of 8 DVDs = (11)(8) = $88 Price of 5 CDs = 5(9) = $45 Total = $88 + $45 = $133 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 16 Example If an average page in a book contains 163 words, estimate, rounding each number to the nearest hundred, the total number of words contained on 391 pages. 163 rounds to 200 391 rounds to 400 200(400) = 80,000 words Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 17