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Section 0.2P: Practice

  • Page ID
    192780
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    Practice Makes Progress

    In the following exercises, simplify.

    Exercise

    \(−\dfrac{108}{63}\)

    Exercise

    \(\dfrac{120}{252}\)

    Exercise

    \(\dfrac{14x^2}{21y}\)

    Exercise

    \(−\dfrac{210a^2}{110b^2}\)

    In the following exercises, perform the indicated operation and simplify.

    Exercise

    \(−\dfrac{3}{4}\left(−\dfrac{4}{9}\right)\)

    Exercise

    \(\left(−\dfrac{14}{15}\right)\left(\dfrac{9}{20}\right)\)

    Exercise

    \(\dfrac{3}{7}⋅21n\)

    Exercise

    \(\dfrac{5}{18}÷\left(−\dfrac{15}{24}\right)\)

    Exercise

    \(−\dfrac{\dfrac{8}{21} }{\dfrac{12}{35}}\)

    Exercise

    \(\dfrac{\dfrac{m}{3}}{\dfrac{n}{2}}\)

    Exercise

    \(\dfrac{7}{12}+\dfrac{5}{8}\)

    Exercise

    \(\dfrac{7}{12}−\dfrac{9}{16}\)

    Exercise

    \(−\dfrac{2}{3}−\left(−\dfrac{3}{4}\right)\)

    Exercise

    \(\dfrac{x}{3}+\dfrac{1}{4}\)

    Exercise

    \(−\dfrac{5a}{3}+\left(−\dfrac{10}{6}\right)\)

    Exercise

    \(−\dfrac{5a}{3}÷\left(−\dfrac{10}{6}\right)\)

    Exercise

    \(\dfrac{5⋅6−3⋅4}{4⋅5−2⋅3}\)

    Exercise

    \(\dfrac{7⋅4−2(8−5)}{9⋅3−3⋅5}\)

    Exercise

    \(\dfrac{2}{\dfrac{1}{3}+\dfrac{1}{5}}\)

    Exercise

    \(\dfrac{\dfrac{7}{8}−\dfrac{2}{3}}{\dfrac{1}{2}+\dfrac{3}{8}}\)

    Exercise

    \(−\dfrac{3}{8}÷\left(−\dfrac{3}{10}\right)\)

    Exercise

    \(−\dfrac{3}{8}+\dfrac{5}{12}\)

    Exercise

    \(\dfrac{11}{12a}⋅\dfrac{9a}{16}\)

    Exercise

    \(\dfrac{1}{2}+\dfrac{2}{3}⋅\dfrac{5}{12}\)

    Exercise

    \(1−\dfrac{3}{5}÷\dfrac{1}{10}\)

    Exercise

    \(12\left(\dfrac{9}{20}−\dfrac{4}{15}\right)\)

    Exercise

    \(\dfrac{\dfrac{5}{8}+\dfrac{1}{6}}{\dfrac{19}{24}}\)

    Exercise

    \(\left(\dfrac{5}{9}+\dfrac{1}{6}\right)÷\left(\dfrac{2}{3}−\dfrac{1}{2}\right)\)

    Writing Exercises

    Exercise

    Why do you need a common denominator to add or subtract fractions? Explain.

    Exercise

    Explain how you find the reciprocal of a fraction.

    Self Check

    Use this checklist to evaluate your mastery of the objectives of this section.

    This table has 4 columns, 5 rows and a header row. The header row labels each column I can, confidently, with some help and no, I don’t get it. The first column has the following statements: simplify fractions, multiply and divide fractions, add and subtract fractions, use the order of operations to simplify fractions, evaluate variable expressions with fractions. The remaining columns are blank.

    If most of your checks were:

    …confidently. Congratulations! You have achieved the objectives in this section. Reflect on the study skills you used so that you can continue to use them.

    …with some help. This must be addressed quickly because topics you do not master become potholes in your road to success. In math, every topic builds upon previous work. It is crucial to establish a strong foundation before proceeding. Who can you ask for help? Your classmates, tutors, and class instructor are good resources.

    …no - I don’t get it! This is a warning sign, and you must not ignore it. You should get help right away, or you will quickly be overwhelmed. Meet with your instructor during their drop-in hours as soon as you can to discuss your situation. Together, you can devise a plan to get the help you need.


    This page titled Section 0.2P: Practice is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Math Department.

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