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Lesson 11

Lesson 11. Multiplying and dividing real numbers. Properties of real numbers. 1. multiplication property of -1 For every real number a, a x -1 = -1 x a = -a 2. multiplication property of 0 For every real number a, a x 0 = 0

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Lesson 11

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  1. Lesson 11 Multiplying and dividing real numbers

  2. Properties of real numbers • 1.multiplication property of -1 • For every real number a, • a x -1 = -1 x a = -a • 2. multiplication property of 0 • For every real number a, • a x 0 = 0 • 3. Inverse property of multiplication • For every real number a, where a is not equal to 0, • a x 1/a = 1/a x a = 1

  3. Multiplying signed numbers • The product of 2 numbers with the same sign is a positive number • The sign of 2 numbers with different signs is a negative number

  4. Raising a number to a power • (-3)4 = (-3)(-3)(-3)(-3)= 81 • (-3)3 = (-3)(-3)(-3)= - 27 • -34= - 3 3 3 3= - 81 • -53 = - 5 5 5 = -125 • (-5)3 = (-5)(-5)(-5)= -125

  5. Dividing signed numbers • 1. The quotient of 2 numbers with the same sign is positive. • 2. the quotient of 2 numbers with different signs is negative

  6. simplify • -72/ -24 • 12.1/ -11 • -5/6 • -2/9

  7. Lesson 12using the properties of real numbers to simplify expressions • The properties of real numbers are used to simplify expressions and write equivalent expressions.

  8. Properties of addition and multiplication • IDENTITY PROPERTY OF ADDITION • For every real number a, • a + 0 = a • IDENTITY PROPERTY F MULTIPLICATION • For every real number a, • a x 1 = a • COMMUTATIVE PROPERTY OF ADDITION • For every real number a and b, • a + b = b + a • COMMUTATIVE PROPERTY OF MULTIPLICATION • For every real number a and b, • a x b = b x a

  9. Properties cont. • ASSOCIATIVE PROPERTY OF ADDITION • For every real number a, b, and c, • (a + b) + c = a + ( b+ c) • a + b + c = a + b + c • ASSOCIATIVE PROPERT OF MULTIPLICATION • For every real number a, b and c, • (a b) c= a (b c) • a b c= a b c

  10. Identifying properties • 1. 1 x 8 = 8 • 2. 6 + 9 = 9 + 6 • 3. (2 x 5) x 4 = 2 x ( 5 x 4) • 4. (7 + 1) + 3 = (1 + 7) + 3 • 5. 0 + 10 = 10 • 6. 17 x 1 = 17

  11. True or false • d x 0 = d • (e r )b= (r e )b • x (y + z) = (x +y )z • d + ( e + f) = ( d + e) + f • How can you be sure???

  12. Lesson 15distributive property • For all real numbers a, b, and c • a (b + c) = a b + ac • And a (b - c) = a b - ac

  13. Distributing positive and negative numbers • Simplify: • 6(4+8)= 6(4) + 6(8) • = 24 + 48 = 72 • 6(2-7) = 6(2) + 6(-7)= 6(2) -6(7) • =12 + -42 = 12 -42 = -30 • -(9+ 4)= -1(9) + -1 ( 4) • = -9 + -4 = -13 • -20(12+8)= -20(12) + -20(8) • = -240 + -160= -400

  14. Simplifying algebraic expressions • m n( m x + n y+ 2p)= mnmx+mnny+mn2p • = m2nx + mn2y +2mnp • (m x +2ny +z) m n= m n m x + mn2ny +m n z • = m2nx + 2mn2y + m n z • (y3-zx3)(-yz) = (-yz)y3 +(-yz)(-zx3) • = -y4z + x3yz2

  15. Check for understanding • 1. Give an example of an expression that can be simplified using the distributive property. • 2.How do properties help you to simplify expressions? • 3. Explain the difference in finding the solution to (-2)2 and -22.

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