1 Chapter Chapter 2 The Whole Numbers

Multiplying Whole Numbers and Area Section 1.6 Multiplying Whole Numbers and Area

Multiplying Whole Numbers Multiplication is repeated addition but with different notation. 6 + 6 + 6 + 6 + 6 = The  is called a multiplication sign. Objective A

Use the Properties of Multiplication. Objective A Use the Properties of Multiplication.

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.

Example Multiply. a. 4 × 1 b. 0(5) c. 1(52) d. (76)(0) = 4 = 0 = 52

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).

Properties Distributive Property Multiplication distributes over addition. For example, 2(3 + 4) = 2  3 + 2  4

Example Rewrite 4(5 + 6) using the distributive property. 4(5 + 6) = 4  5 + 4  6

Multiply Whole Numbers. Objective B Multiply Whole Numbers.

Multiplying Whole Numbers Example: Use the distributive property to multiply 3 and 79. Write 79 in expanded form. Apply the Distributive Property. Objective B Multiply. Add.

Multiplying Whole Numbers Example: Multiply 624 by 3. Objective B Continued

Multiplying Whole Numbers Example: Multiply 91 by 72. Objective B Continued

Multiply by Whole Numbers Ending in Zero(s). Objective C Multiply by Whole Numbers Ending in Zero(s).

Multiplying Whole Numbers Ending in Zero(s) Example: Multiply 3 by 9000. 3  9000 = 3 • 9 • 1000 = (27) • 1000 = 27,000 Objective C

Example Multiply 35 • 3000 35 • 3000 = 105,000 Objective C

Example Multiply 600  600 600 • 600 = 360,000 Objective C

Find the Area of a Rectangle. Objective D Find the Area of a Rectangle.

Finding the Area of a Rectangle Example: Find the area of the following rectangle. 12 inches 4 inches Objective D

Solve Problems by Multiplying Whole Numbers. Objective E Solve Problems by Multiplying Whole Numbers.

Solving Problems by Multiplying Key Words or Phrases Example Symbols Multiply Multiply 3 by 4 3  4 Product The product of 5 and 10 5  10 Times 6 times 4 6  4 Objective E

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 Objective C

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

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