{"id":54,"date":"2025-01-02T23:05:01","date_gmt":"2025-01-02T23:05:01","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/chapter\/rational-and-irrational-numbers-get-stronger-answer-key\/"},"modified":"2025-01-02T23:05:01","modified_gmt":"2025-01-02T23:05:01","slug":"rational-and-irrational-numbers-get-stronger-answer-key","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/chapter\/rational-and-irrational-numbers-get-stronger-answer-key\/","title":{"raw":"Rational and Irrational Numbers: Get Stronger Answer Key","rendered":"Rational and Irrational Numbers: Get Stronger Answer Key"},"content":{"raw":"\n

Rational Numbers<\/h2>\n
    \n\t
  1. Yes, this is a rational number.<\/li>\n\t
  2. No, this is not a rational number.<\/li>\n\t
  3. [latex]\\frac{2}{7}[\/latex]<\/li>\n\t
  4. [latex]\\frac{33}{70}[\/latex]<\/li>\n\t
  5. [latex]4\\frac{1}{6}[\/latex]<\/li>\n\t
  6. [latex]\\frac{19}{8}[\/latex]<\/li>\n\t
  7. [latex]0.\\bar{4}[\/latex]<\/li>\n\t
  8. [latex]0.0432[\/latex]<\/li>\n\t
  9. [latex]\\frac{23}{100}[\/latex]<\/li>\n\t
  10. [latex]\\frac{9}{10}[\/latex]<\/li>\n\t
  11. [latex]\\frac{29}{132} [\/latex]<\/li>\n\t
  12. [latex]\\frac{3}{16}[\/latex]<\/li>\n\t
  13. [latex]\\frac{8}{9} [\/latex]<\/li>\n\t
  14. [latex]\\frac{62}{147}[\/latex]<\/li>\n\t
  15. [latex]\\frac{4987}{37632} [\/latex]<\/li>\n\t
  16. [latex]\\frac{325}{552}[\/latex]<\/li>\n\t
  17. [latex]\\frac{6}{25}[\/latex]<\/li>\n\t
  18. [latex]23\\%[\/latex]<\/li>\n\t
  19. [latex]75[\/latex]<\/li>\n\t
  20. The total number of members in the group is [latex]164[\/latex].<\/li>\n\t
  21. [latex]65\\%[\/latex]<\/li>\n\t
  22.  There are [latex]24 [\/latex] students in Professor Donaldson's history of film class who say their favorite movie genre is comedy.<\/li>\n\t
  23. There are [latex]3,120 [\/latex] people in Tara's town who are food insecure.<\/li>\n\t
  24. Maddie needs [latex]4.8[\/latex] cups of mayonnaise and [latex]3.2[\/latex] cups of apple cider vinegar.<\/li>\n\t
  25. There is [latex]41.8[\/latex] liters of oxygen in [latex]200 [\/latex] liters of air.<\/li>\n\t
  26. The discount on the laptop is [latex]$140.00[\/latex].<\/li>\n\t
  27. [latex]13[\/latex] kilograms is equivalent to [latex]28.660[\/latex] pounds (rounded to three decimal places).<\/li>\n\t
  28. [latex]10[\/latex] miles is equivalent to [latex]633,600[\/latex] inches.<\/li>\n\t
  29. For the markup question regarding Wegmans cereal:
    \n
      \n\t
    1. The markup in dollars is [latex]$0.79[\/latex].<\/li>\n\t
    2. The markup is [latex]52.7%[\/latex] of the original cost (rounded to one decimal place).<\/li>\n<\/ol>\n<\/li>\n\t

    3. \n
        \n\t
      1. After a [latex]50\\%[\/latex] discount on the original price of [latex]$150.00[\/latex], the price of the item becomes [latex]$75.00[\/latex].<\/li>\n\t
      2. [latex]25\\%[\/latex] of the sale price is [latex]$18.75[\/latex].<\/li>\n\t
      3. When an additional [latex]25\\%[\/latex] coupon is applied to the discounted price of [latex]$75.00[\/latex], the new price becomes [latex]$56.25[\/latex].<\/li>\n\t
      4. The total amount saved on the item is [latex]$93.75[\/latex], which is the difference between the original price and the final price paid.<\/li>\n\t
      5.  The effective discount percentage is [latex]62.5\\%[\/latex].<\/li>\n\t
      6.  The effective discount percentage is not equal to [latex]75\\%[\/latex]. This is because the second discount of [latex]25\\%[\/latex] is applied to the already discounted price, not the original price. The discounts compound rather than add directly, leading to a smaller percentage discount than simply adding the two percentages together.<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

        Irrational Numbers<\/h2>\n
          \n\t
        1. [latex]\\sqrt{70}[\/latex], [latex]5 + 9\\pi[\/latex]<\/li>\n\t
        2. [latex]2\\sqrt{3}[\/latex]<\/li>\n\t
        3. [latex]11\\sqrt{5}[\/latex]<\/li>\n\t
        4. [latex]4\\sqrt{7}[\/latex]<\/li>\n\t
        5. [latex]14\\sqrt{15}[\/latex]<\/li>\n\t
        6. [latex]18\\sqrt{10}[\/latex]<\/li>\n\t
        7. [latex]6\\sqrt{3}[\/latex]<\/li>\n\t
        8. [latex]-7\\sqrt{7}[\/latex]<\/li>\n\t
        9. This expression involves [latex]\\pi[\/latex] and the square root of [latex]2[\/latex], which are both irrational numbers. Without a calculator, we can't get a numerical value for this expression. It is as simplified as it can be without numeric approximation.<\/li>\n\t
        10. [latex]15.8\\pi[\/latex]<\/li>\n\t
        11. Since these do not have the same irrational part, the calculation can not be done.<\/li>\n\t
        12. [latex]6\\sqrt{60}[\/latex]<\/li>\n\t
        13. [latex]\\frac{ 3\\sqrt{2}}{2}[\/latex]<\/li>\n<\/ol>\n

          Real Numbers<\/h2>\n
            \n\t
          1. Rational Number, Real Number<\/li>\n\t
          2. Irrational number, Real Number<\/li>\n\t
          3. Irrational number, Real Number<\/li>\n\t
          4. Natural number, Integer, Rational Number, Real Number<\/li>\n\t
          5. Commutative Property of Addition<\/li>\n\t
          6. Commutative Property of Multiplication<\/li>\n\t
          7. Associative Property of Addition<\/li>\n\t
          8. Associative Property of Multiplication<\/li>\n\t
          9. Distributive Property<\/li>\n\t
          10. Multiplicative Inverse Property<\/li>\n\t
          11. Additive identity property<\/li>\n\t
          12. Additive identity property<\/li>\n\t
          13. Commutative Property of Addition<\/li>\n\t
          14. [latex]122[\/latex]<\/li>\n\t
          15. [latex]260[\/latex]<\/li>\n\t
          16. [latex]273[\/latex]<\/li>\n\t
          17. [latex]1,300[\/latex]<\/li>\n\t
          18. [latex]1,287[\/latex]<\/li>\n\t
          19. [latex]4,343[\/latex]<\/li>\n<\/ol>\n","rendered":"

            Rational Numbers<\/h2>\n
              \n
            1. Yes, this is a rational number.<\/li>\n
            2. No, this is not a rational number.<\/li>\n
            3. [latex]\\frac{2}{7}[\/latex]<\/li>\n
            4. [latex]\\frac{33}{70}[\/latex]<\/li>\n
            5. [latex]4\\frac{1}{6}[\/latex]<\/li>\n
            6. [latex]\\frac{19}{8}[\/latex]<\/li>\n
            7. [latex]0.\\bar{4}[\/latex]<\/li>\n
            8. [latex]0.0432[\/latex]<\/li>\n
            9. [latex]\\frac{23}{100}[\/latex]<\/li>\n
            10. [latex]\\frac{9}{10}[\/latex]<\/li>\n
            11. [latex]\\frac{29}{132}[\/latex]<\/li>\n
            12. [latex]\\frac{3}{16}[\/latex]<\/li>\n
            13. [latex]\\frac{8}{9}[\/latex]<\/li>\n
            14. [latex]\\frac{62}{147}[\/latex]<\/li>\n
            15. [latex]\\frac{4987}{37632}[\/latex]<\/li>\n
            16. [latex]\\frac{325}{552}[\/latex]<\/li>\n
            17. [latex]\\frac{6}{25}[\/latex]<\/li>\n
            18. [latex]23\\%[\/latex]<\/li>\n
            19. [latex]75[\/latex]<\/li>\n
            20. The total number of members in the group is [latex]164[\/latex].<\/li>\n
            21. [latex]65\\%[\/latex]<\/li>\n
            22.  There are [latex]24[\/latex] students in Professor Donaldson’s history of film class who say their favorite movie genre is comedy.<\/li>\n
            23. There are [latex]3,120[\/latex] people in Tara’s town who are food insecure.<\/li>\n
            24. Maddie needs [latex]4.8[\/latex] cups of mayonnaise and [latex]3.2[\/latex] cups of apple cider vinegar.<\/li>\n
            25. There is [latex]41.8[\/latex] liters of oxygen in [latex]200[\/latex] liters of air.<\/li>\n
            26. The discount on the laptop is [latex]$140.00[\/latex].<\/li>\n
            27. [latex]13[\/latex] kilograms is equivalent to [latex]28.660[\/latex] pounds (rounded to three decimal places).<\/li>\n
            28. [latex]10[\/latex] miles is equivalent to [latex]633,600[\/latex] inches.<\/li>\n
            29. For the markup question regarding Wegmans cereal:\n
                \n
              1. The markup in dollars is [latex]$0.79[\/latex].<\/li>\n
              2. The markup is [latex]52.7%[\/latex] of the original cost (rounded to one decimal place).<\/li>\n<\/ol>\n<\/li>\n
              3. \n
                  \n
                1. After a [latex]50\\%[\/latex] discount on the original price of [latex]$150.00[\/latex], the price of the item becomes [latex]$75.00[\/latex].<\/li>\n
                2. [latex]25\\%[\/latex] of the sale price is [latex]$18.75[\/latex].<\/li>\n
                3. When an additional [latex]25\\%[\/latex] coupon is applied to the discounted price of [latex]$75.00[\/latex], the new price becomes [latex]$56.25[\/latex].<\/li>\n
                4. The total amount saved on the item is [latex]$93.75[\/latex], which is the difference between the original price and the final price paid.<\/li>\n
                5.  The effective discount percentage is [latex]62.5\\%[\/latex].<\/li>\n
                6.  The effective discount percentage is not equal to [latex]75\\%[\/latex]. This is because the second discount of [latex]25\\%[\/latex] is applied to the already discounted price, not the original price. The discounts compound rather than add directly, leading to a smaller percentage discount than simply adding the two percentages together.<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

                  Irrational Numbers<\/h2>\n
                    \n
                  1. [latex]\\sqrt{70}[\/latex], [latex]5 + 9\\pi[\/latex]<\/li>\n
                  2. [latex]2\\sqrt{3}[\/latex]<\/li>\n
                  3. [latex]11\\sqrt{5}[\/latex]<\/li>\n
                  4. [latex]4\\sqrt{7}[\/latex]<\/li>\n
                  5. [latex]14\\sqrt{15}[\/latex]<\/li>\n
                  6. [latex]18\\sqrt{10}[\/latex]<\/li>\n
                  7. [latex]6\\sqrt{3}[\/latex]<\/li>\n
                  8. [latex]-7\\sqrt{7}[\/latex]<\/li>\n
                  9. This expression involves [latex]\\pi[\/latex] and the square root of [latex]2[\/latex], which are both irrational numbers. Without a calculator, we can’t get a numerical value for this expression. It is as simplified as it can be without numeric approximation.<\/li>\n
                  10. [latex]15.8\\pi[\/latex]<\/li>\n
                  11. Since these do not have the same irrational part, the calculation can not be done.<\/li>\n
                  12. [latex]6\\sqrt{60}[\/latex]<\/li>\n
                  13. [latex]\\frac{ 3\\sqrt{2}}{2}[\/latex]<\/li>\n<\/ol>\n

                    Real Numbers<\/h2>\n
                      \n
                    1. Rational Number, Real Number<\/li>\n
                    2. Irrational number, Real Number<\/li>\n
                    3. Irrational number, Real Number<\/li>\n
                    4. Natural number, Integer, Rational Number, Real Number<\/li>\n
                    5. Commutative Property of Addition<\/li>\n
                    6. Commutative Property of Multiplication<\/li>\n
                    7. Associative Property of Addition<\/li>\n
                    8. Associative Property of Multiplication<\/li>\n
                    9. Distributive Property<\/li>\n
                    10. Multiplicative Inverse Property<\/li>\n
                    11. Additive identity property<\/li>\n
                    12. Additive identity property<\/li>\n
                    13. Commutative Property of Addition<\/li>\n
                    14. [latex]122[\/latex]<\/li>\n
                    15. [latex]260[\/latex]<\/li>\n
                    16. [latex]273[\/latex]<\/li>\n
                    17. [latex]1,300[\/latex]<\/li>\n
                    18. [latex]1,287[\/latex]<\/li>\n
                    19. [latex]4,343[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":6,"menu_order":16,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":3,"module-header":"","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/54"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/users\/6"}],"version-history":[{"count":0,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/54\/revisions"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/54\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/media?parent=54"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapter-type?post=54"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/contributor?post=54"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/license?post=54"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}