Section 1.9: Operations with Fractions, Decimals and Percent Chapter 1: Introduction to Algebra Properties of real numbers 1) Rewrite using the associative property of addition: (푥 + 2) + 푦 2) Rewrite using the associative property of addition: (푦 + 2) + 푥 Properties of real numbers 3) Rewrite using the associative property of multiplication: 6(푐 × 푑) 4) Rewrite using the associative property of multiplication: 7(푎 × 푏) Properties of real numbers 5) Rewrite using the commutative property of addition: 푥 + 5 6) Rewrite using the commutative property of addition: 푦 + 9 Properties of real numbers 7) Rewrite using the commutative property of multiplication: 푥5 8) Rewrite using the commutative property of multiplication: 푦9 Properties of real numbers 9) Rewrite using the commutative property of multiplication: (푥 – 3)7 10) Rewrite using the commutative property of multiplication: (푥 – 2)5 11) Rewrite using the distributive property, and simplify: 5(2 + 4) 12) Rewrite using the distributive property, and simplify: 7(5 + 3) 13) Rewrite using the distributive property, and simplify: (7 + 3)8 14) Rewrite using the distributive property, and simplify: (5 + 2)9 15) Rewrite using the distributive property, and simplify: 5(10 − 4) 16) Rewrite using the distributive property, and simplify: 7(5 − 3) 17) Rewrite using the distributive property, and simplify: (2 − 3)8 18) Rewrite using the distributive property, and simplify: (1 − 2)9 19) Rewrite using the distributive property: 5(푥 + 푦) 20) Rewrite using the distributive property: 7(푎 + 푏) 21) Rewrite using the distributive property: (푐 + 푑)8 22) Rewrite using the distributive property: (푥 + 푦)9 23) Rewrite using the distributive property, and simplify: 5(푎 − 4) 24) Rewrite using the distributive property, and simplify: 7(푐 − 5) 25) Rewrite using the distributive property, and simplify: (푥 − 2)8 26) Rewrite using the distributive property, and simplify: (푦 − 2)9 #27 – 38: Simplify 27) −5(푥 − 2) 28) −3(푦 – 4) 29) −(3푥 – 2푦) 30) −(5푥 – 4푦) 31) 8(3푥2 + 5푥 – 4) 32) 6(2푦2 + 3푦 – 9) 33) −2(4푥2 + 6푥 – 3) 34) −3(5푦3 – 6푦 + 1) 1 4 9 2 6 15 35) ( 푥 + ) 36) ( 푥 + ) 2 5 2 3 9 8 3 4 6 3 15 7 37) ( 푥 − ) 38) ( 푥 − ) 4 9 5 5 9 6 Section 1.9: Operations with Fractions, Decimals and Percent Chapter 1: Introduction to Algebra. 0 Fractions in the form and division problems of the form 0 ÷ 푥 푥 Every fraction obeys the following rules 풏풖풎풆풓풂풕풐풓 • = 풂풏풔풘풆풓 풅풆풏풐풎풊풏풂풕풐풓 • 풂풏풔풘풆풓 × 풅풆풏풐풎풊풏풂풕풐풓 = 풏풖풎풆풓풂풕풐풓 6 For example: = 3 and 3× 2 = 6 2 0 What does the fraction 푟푒푑푢푐푒 푡표? 6 I know that the above rule must apply to the answer: 0 = 푎푛푠푤푒푟 and 푎푛푠푤푒푟 × 6 = 0 6 0 I claim: = 0 6 I will show you that it does. 0 푤푒 푘푛표푤 푡ℎ푎푡 = 푎푛푠푤푒푟 푎푛푑 푎푛푠푤푒푟 × 6 = 0 6 • 푐ℎ푎푛푔푒 푎푛푠푤푒푟 푡표 0 0 • = 0 Then: 0× 6 = 0 6 • 푠푛푐푒 0 × 6 푑표푒푠 푒푞푢푎푙 0 퐼 푘푛표푤 푚푦 푎푛푠푤푒푟 푠 푐표푟푟푒푐푡 0 Thus = 0 6 Rule for fractions with 0 in the numerator 0 = 0; 푝푟표푣푑푒푑 푥 ≠ 0 푥 and 0 0 ÷ 푥 = 0; 푝푟표푣푑푒푑 푥 ≠ 0 (since = 0 ÷ 푥) 푥 Section 1.9: Operations with Fractions, Decimals and Percent Chapter 1: Introduction to Algebra. 푥 Fractions in the form , (푥 ≠ 0) and division problems in the form 푥 ÷ 0, 푥 ≠ 0 0 12 What does the fraction 푟푒푑푢푐푒 푡표? 0 I know that the above rule must apply to the answer: 12 = 푎푛푠푤푒푟 and 푎푛푠푤푒푟 × 0 = 12 0 This is a problem when we try to figure out how to solve this: 푎푛푠푤푒푟 × 0 = 12 • The left side will always reduce to zero, no matter what number I replace with the word answer. The times 0 on the left side forces the left side to always equal 0. • There is no number to change the word answer to so that the left side will equal 12 12 • There is no way to reduce the fraction 0 12 Thus, we say = 푢푛푑푒푓푛푒푑 0 Rule for fractions with 0 in the denominator: 푥 = 푢푛푑푒푓푛푒푑; 푝푟표푣푑푒푑 푥 ≠ 0 and 0 푥 x ÷ 0 = 푢푛푑푒푓푛푒푑; 푝푟표푣푑푒푑 푥 ≠ 0 (since = x ÷ 0) 0 #39 – 46: Simplify 5 2 39) 40) 0 0 41) 12 ÷ 0 42) 8 ÷ 0 0 0 43) 44) 7 6 45) 0 ÷ 3 46) 0 ÷ 9 .