{"id":893,"date":"2017-11-10T21:12:10","date_gmt":"2017-11-10T21:12:10","guid":{"rendered":"http:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/?post_type=chapter&p=893"},"modified":"2018-04-10T18:19:50","modified_gmt":"2018-04-10T18:19:50","slug":"problem-bank-4","status":"publish","type":"chapter","link":"https:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/chapter\/problem-bank-4\/","title":{"raw":"Problem Bank","rendered":"Problem Bank"},"content":{"raw":"[latexpage]\r\n
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Problem 6<\/h3>\r\n

Harriet is part of a group of five children who share four pies. Jeff is part of a group of seven children who share four pies. Jean is part of a group of seven children who share six pies.<\/p>\r\n\r\n

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  1. Who gets more pie, Harriet or Jeff? Justify your answer!<\/li>\r\n \t
  2. Who gets more pie, Jeff or Jean? Justify your answer!<\/li>\r\n \t
  3. Who gets more pie, Harriet or Jean? Justify your answer!<\/li>\r\n<\/ol>\r\n<\/div>\r\n \r\n
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    Problem 7<\/h3>\r\n

    Yesterday was Zoe\u2019s birthday, and she had a big rectangular cake. Today,\u00a0 $\\frac 2 5$\u00a0of the cake is left. The leftover cake<\/strong> is shown here.<\/p>\r\n

    \"\"<\/p>\r\n

    Draw a picture of the original (whole) cake and explain your work.<\/p>\r\n\r\n<\/div>\r\n \r\n

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    Problem 8<\/h3>\r\n

    Use benchmarks and intuitive methods to arrange the fractions below in ascending order. Explain how you decided. (The point of this problem is to think more and compute less!):<\/p>\r\n\\[ \\frac25, \\qquad \\frac13, \\qquad \\frac58, \\qquad \\frac14, \\qquad \\frac23, \\qquad \\frac34, \\qquad \\frac47.\\]\r\n\r\n<\/div>\r\n \r\n

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    Problem 9<\/h3>\r\n

    Which of these fractions has the larger value? Justify your choice.<\/p>\r\n\\[\\frac{10001}{10002} \\quad\\text{ or } \\quad\\frac{10000001}{10000002}.\\]\r\n\r\n<\/div>\r\n \r\n

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    Problem 10<\/h3>\r\n

    Solve each division problem. Look for a shortcut, and explain your work.<\/p>\r\n\\[\\frac{251+251+251+251}{4} \\]\r\n\r\n\\[\\frac{377+377+377+377+377}{5} \\]\r\n\r\n\\[ \\frac{123123+123123+123123+123123+123123+123123}{3}\\]\r\n\r\n<\/div>\r\n \r\n

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    Problem 11<\/h3>\r\n

    Yoko says<\/p>\r\n

    \\[\\frac{16}{64} = \\frac14\\]<\/p>\r\n

    because she cancels the sixes:<\/p>\r\n

    \\[ \\frac{1\\cancel{6}}{\\cancel{6}4} = \\frac14.\\]<\/p>\r\n

    But note:<\/p>\r\n

    \\[\\frac{16}{64} = \\frac{1\\cdot 16}{4 \\cdot 16} = \\frac{1 \\cdot \\cancel{16}}{4 \\cdot \\cancel{16}} = \\frac14.\\]<\/p>\r\n

    So is Yoko right? Does her cancelation rule always work? If it does not always work, can you find any other example where it works? Can you find every example where it works?<\/p>\r\n\r\n<\/div>\r\n \r\n

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    Problem 12<\/h3>\r\n

    Jimmy says that a fraction does not change in value if you add the same amount to the numerator and the denominator. Is he right? If you were Jimmy\u2019s teacher, how would you respond?<\/p>\r\n\r\n<\/div>\r\n \r\n

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    Problem 13<\/h3>\r\n
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    1. Shelly says that if\u00a0$ab < cd$\u00a0then $\\frac{a}b \\ <\\ \\frac{c}d$. Is Shelly\u2019s claim always true, sometimes true, or never true? If you were Shelly\u2019s teacher, what would you say to her?<\/li>\r\n \t
    2. Rob says that if\u00a0$ad < bc$\u00a0then $\\frac{a}b \\ <\\ \\frac{c}d$. Is Rob\u2019s claim always true, sometimes true, or never true? If you were Rob\u2019s teacher, what would you say to him?<\/li>\r\n<\/ol>\r\n<\/div>\r\n \r\n
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      Problem 14<\/h3>\r\n

      Jill, her brother, and another partner own a pizza restaurant. If Jill owns\u00a0$\\frac 1 3$\u00a0of the restaurant and her brother owns\u00a0$\\frac 1 4$\u00a0of the restaurant, what fraction\u00a0does the third partner own?<\/p>\r\n\r\n<\/div>\r\n \r\n

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      Problem 15<\/h3>\r\n

      John spent a quarter of his life as a boy growing up, one-sixth of his life in college, and one-half of his life as a teacher. He spent his last six years in retirement. How old was he when he died?<\/p>\r\n\r\n<\/div>\r\n \r\n

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      Problem 16<\/h3>\r\n

      Nana was planning to make a red, white, and blue quilt. One-third was to be red and two-fifths was to be white. If the area of the quilt was to be 30 square feet, how many square feet would be blue?[footnote]Image used under Creative Commons CC0 1.0 Universal Public Domain Dedication. [\/footnote]<\/p>\r\n\r\n\r\n[caption id=\"attachment_1323\" align=\"aligncenter\" width=\"300\"]\"\" Ku'u Hae Aloha (My Beloved Flag), Hawaiian cotton quilt from Waimea, before 1918, Honolulu Academy of Arts.[\/caption]\r\n\r\n \r\n\r\n<\/div>\r\n

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      Problem 17<\/h3>\r\n

      Rafael ate one-fourth of a pizza and Rocco ate one-third of it. What fraction of the pizza did they eat?<\/p>\r\n\r\n<\/div>\r\n \r\n

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      Problem 18<\/h3>\r\n

      Problem 18<\/b> (Tangrams). Tangrams[footnote]Tangram image from Wikimedia Commons, public domain.[\/footnote] are a seven-piece puzzle, and the seven pieces can be assembled into a big square.<\/p>\r\n

      \"\"<\/p>\r\n\r\n

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      1. \u00a0If the large square shown above is one whole, assign a fraction value to each of the seven tangram pieces. Justify your answers.<\/li>\r\n \t
      2. The tangram puzzle contains a small square. If the small square (the single tangram piece) is one whole, assign a fraction value to each of the seven tangram pieces. Justify your answers.<\/li>\r\n \t
      3. \u00a0The tangram set contains two large triangles. If a large triangle (the single tangram piece) is one whole, assign a fraction value to each of the seven tangram pieces. Justify your answers.<\/li>\r\n \t
      4. \u00a0The tangram set contains one medium triangle. If the medium triangle (the single tangram piece) is one whole, assign a fraction value to each of the seven tangram pieces. Justify your answers.<\/li>\r\n \t
      5. \u00a0The tangram set contains two small triangles. If a small triangle (the single tangram piece) is one whole, assign a fraction value to each of the seven tangram pieces. Justify your answers<\/li>\r\n<\/ol>\r\n<\/div>\r\n \r\n
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        Problem 19<\/h3>\r\n

        Mikiko said her family made two square pizzas at home. One of the pizzas was 8 inches on each side, and the other was 12 inches on each side. Mikiko ate\u00a0$\\frac 1 4$\u00a0of the small pizza and\u00a0$\\frac 1 {12}$\u00a0of the large pizza. So she said that she ate<\/p>\r\n\\[\\frac14 + \\frac1{12}\r\n\\\u00a0 = \\\r\n\\frac3{12} + \\frac1{12}\r\n\\\u00a0 = \\\u00a0 \\frac4{12}\r\n\\\u00a0 = \\\r\n\\frac13\\]\r\n

        of a pizza. Do you agree with Mikiko\u2019s calculation? Did she eat\u00a0$\\frac 1 3$\u00a0of a whole pizza? Carefully justify your answer. (This question is tricky. It's probably a good idea to draw a picture!)<\/p>\r\n\r\n<\/div>\r\n \r\n

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        Problem 20<\/h3>\r\n

        Look at the triangle of numbers. There are lots of patterns here! Find as many as you can. In particular, try to answer these questions:<\/p>\r\n\r\n

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        1. What pattern describes the first number in each row?<\/li>\r\n \t
        2. How is each fraction related to the two fractions below it?<\/li>\r\n \t
        3. Can you write down the next two rows of the triangle?<\/li>\r\n<\/ol>\r\n

          \"\"<\/p>\r\n\r\n<\/div>\r\n \r\n

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          Problem 21<\/h3>\r\n

          Marie made a sheet cake at home, but she saved some to bring to work and share with her co-workers the next day. Answer these questions about Marie\u2019s cake. (Draw a picture!)<\/p>\r\n\r\n

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          1. Suppose Marie saved\u00a0$\\frac 1 2$\u00a0of the cake for her co-workers and the co-workers ate\u00a0$\\frac 3 4$\u00a0of this. What fraction of the entire cake did they eat?<\/li>\r\n \t
          2. What if Marie saved\u00a0$\\frac 1 6$\u00a0instead, and they ate\u00a0$\\frac 2 3$\u00a0of this?<\/li>\r\n \t
          3. What if she saved\u00a0$\\frac 5 7 $\u00a0of the cake and they ate\u00a0$\\frac 1 2$\u00a0of this?<\/li>\r\n<\/ol>\r\n<\/div>\r\n \r\n
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            Problem 22<\/h3>\r\n

            An elementary school held a \u201cFamily Math Night\u201d event, and 405 students showed up. Two-thirds of the students who showed up won a door prize. How many students won prizes?<\/p>\r\n\r\n<\/div>\r\n \r\n

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            Problem 23<\/h3>\r\n

            For each picture shown:<\/p>\r\n\r\n