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Section 1 – 1: The Real Number System Selected Worked Homework Problems 4 1 2 ⎧ , , ⎨ − 8 , − π , − , − .75 , − .333... , 0 , 5 10 3 ⎩ 1a) List all the negative integers.! 1b) List all the negative rational numbers. Negative Counting numbers! ! ! ! { − 8 }! Negative Fractions or negative decimals that terminate or repeat. 4 ⎧ ⎫ ⎨ − 8 , − , − .75 , − .333... ⎬ 5 ⎩ ⎭ ! 1c) List all the negative irrational numbers.! 1d) List all the negative real numbers. ! Negative decimals that! DO NOT terminate or repeat. { − π }! ⎫ 3 , 6 , 81 = 9 ⎬ ⎭ Any negative number. 4 ⎧ ⎫ ⎨ − 8 , − π , − , − .75 , − .333... ⎬ 5 ⎩ ⎭ ! 1e) List all the positive integers. ! 1f) List all the positive rational numbers. Positive Counting numbers! ! ! ! Positive Fractions or decimals that terminate or repeat. ⎧ 1 2 ⎫ , , 6 , 81 = 9 ⎬ ⎨ ⎩ 10 3 ⎭ {6 , 81 = 9 }! ! 1g) List all the positive irrational numbers. ! 1h) List all the positive real numbers. Positive decimals that! DO NOT terminate or repeat. { } 3 ! ! Any positive number ⎧ 1 2 , , ⎨ ⎩ 10 3 ! 1i) List all the integers.! 1j) List all the whole numbers. Positive or Negative Counting ! numbers and zero! {−8 , 0 , 6 , 81 = 9 } ! ⎫ 3 , 6 , 81 = 9 ⎬ ⎭ Counting numbers and zero { 0 , 6 , 81 = 9 } 1k) List all the irrational numbers. ! 1l) List a number that is not positive or negative. { −π , { 0} 3 Math 100 ! } ! ! Section 1 – 1 HW WKD! © 2016 Eitel 3. What is the additive inverse of 7 ?! 4. What is the multiplicative inverse of 7 ? The additive inverse adds to give zero! the multiplicative inverse multiplies to give 1 7−7= 0 so − 7 is the additive inverse of 7 ! 1 =1 7 1 so is the multiplicative inverse of 7 7 7• 2 ?! 3 The additive inverse adds to give zero! 7. What is the additive inverse of 2 2 − =0 3 3 2 2 so − is the additive inverse of ! 3 3 2 3 • =1 3 2 3 2 so is the multiplicative inverse of 2 3 −3 ?! 5 The additive inverse adds to give zero! 9. What is the additive inverse of −3 3 + =0 5 5 3 −3 so + is the additive inverse of ! 5 5 Math 100 ! 2 ? 3 the multiplicative inverse multiplies to give 1 8. What is the multiplicative inverse of −3 ? 5 the multiplicative inverse multiplies to give 1 10. What is the multiplicative inverse of −3 −5 • =1 5 3 −5 −3 so is the multiplicative inverse of 3 5 Section 1 – 1 HW WKD! © 2016 Eitel Select the property the justifies each statement: A: Commutative property of multiplication! B: Distributive property of multiplication C: Identity property of multiplication! D: Identity property of addition E: Commutative property of addition! F: Inverse property of multiplication! 11. 5 + 3 = 3 + 5 ____! ! The order of addition has been changed so! E: Commutative property of addition! 12. 5 •1 = 5 ____ the product of 5 and this number stays 5 D: Identity property of multiplication 1 3 • = 1 ____! 3 1 1 the product of and this number gives 1! 3 F: Inverse property of multiplication! 14. 2 • 6 = 6 • 2 ____ 15. 7 + 0 = 7 ____! 16. 2(x + 4) = 2x + 8 ____ the sum of 7 and this number stays 7! Each term in the brackets are multiplied by 2 D: Identity property of addition! B: Distributive property of multiplication 13. The order of multiplication has been changed A: Commutative property of multiplication 17. Does a ÷ b = b ÷ a for all real numbers?! 18. Does a − b = b − a for all real numbers: Give an example that proves that ! Give an example that proves that division is not commutative for! subtraction is not commutative for all all real numbers?! real numbers? 6 ÷ 2 ≠ 2 ÷ 6! Math 100 ! ! 6−2≠ 2−6 Section 1 – 1 HW WKD! © 2016 Eitel