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Understanding Properties of Numbers: Commutative, Associative, and Distributive

Explore the fundamental properties of numbers including the Commutative, Associative, and Identity properties for addition and multiplication. Learn how these properties simplify expressions and solve problems through practice exercises. By mastering these essential concepts, you'll enhance your ability to manipulate and compute mathematical expressions effectively. Watch instructional videos and apply what you've learned in real-world situations and word problems. Get ready to boost your math skills!

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Understanding Properties of Numbers: Commutative, Associative, and Distributive

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  1. Chapter 1 1-5 Properties of Numbers

  2. Commutative: a + b = b + a • Associative: (a + b) + c = a + (b + c) • Identity Property of Zero: a + 0 = a Addition Properties

  3. Commutative: a * b = b * a • Associative: (a * b) * c = a (b * c) • Identity Property of 1: a * 1 = a Multiplication Properties

  4. http://my.hrw.com/math06_07/nsmedia/lesson_videos/msm2/player.html?contentSrc=6100/6100.xmlhttp://my.hrw.com/math06_07/nsmedia/lesson_videos/msm2/player.html?contentSrc=6100/6100.xml Let’s Practice!

  5. Tell which property is represented. • 1 + (6 + 7) = (1 + 6) + 7 • 1 x 10 = 10 • 3 x 5 = 5 x 3 • 6 + 0 = 6 • 4 x (4 x 2) = (4 x 4) x 2 • x + y = y + x Examples

  6. http://my.hrw.com/math06_07/nsmedia/lesson_videos/msm2/player.html?contentSrc=6674/6674.xmlhttp://my.hrw.com/math06_07/nsmedia/lesson_videos/msm2/player.html?contentSrc=6674/6674.xml Video 2

  7. Simplify each expression. Justify each step. • 8 + 23 + 2 • 2 x (17 x 5) • (25 x 11) x 4 • 17 + 29 + 3 • 16 + (17 + 14) • 5 x 19 x 20 Examples

  8. http://my.hrw.com/math06_07/nsmedia/lesson_videos/msm2/player.html?contentSrc=6675/6675.xmlhttp://my.hrw.com/math06_07/nsmedia/lesson_videos/msm2/player.html?contentSrc=6675/6675.xml Video 3

  9. Use the Distributive Property to find each product. • 2(19) • 5(31) • (22)2 • (13)6 • 8(26) • (34)6 Examples

  10. To find the area of a loft, the architect multiplies the length and the width: (14 + 8) x 10. Use the Distributive Property to find the area of the loft. • A student simplified the expression 6 x (9 + 12) as shown. What is the student’s error. 6 x (9 + 12) = 6 x 9 + 12 = 54 + 12 = 66 Word Problems

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