Skip to main content
Mathematics LibreTexts

1.3.2.1: Exercises

  1. Last updated
  2. Save as PDF
  • Page ID
    82830

    • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    Section 1.3.2.1 Exercises

    1. Which is larger:  \(\dfrac{2}{3} \) or \( \dfrac{5}{8} \)?  Which one would be on the right if they were graphed on a number line?
    2. Write the fractions in order from smallest to largest.
    3.   \(\dfrac{3}{4}, \dfrac{5}{8}, \dfrac{2}{3}, \dfrac{7}{6}, \dfrac{2}{5}\)
    4. Simplify each fraction by putting it in lowest terms.
      1. \(\dfrac{15}{35}
      2. \(\dfrac{56}{21}
      3. \(\dfrac{9}{20}
    5. You survey students in your class and find that 8 students are left-handed and 28 are not.  Write the ratio of left-handed students to all students as a fraction in simplest form.
    6. Evaluate:
      1. \(\dfrac{4}{9} +\dfrac{1}{3}\)  
      2. \(\dfrac{3}{10} +\dfrac{5}{12}+\dfrac{1}{6}\)  
      3. \(\dfrac{7}{12} -\dfrac{9}{16}\)  
      4. \(8 -\dfrac{5}{7}\)  
      5. \(\dfrac{7}{8} -\dfrac{3}{4}+\dfrac{5}{4}-\dfrac{1}{2}\)  
      6. Evaluate:
      7. \(\left(\dfrac{3}{6}\right)\cdot \left( 4\dfrac{5}{8}\right) \cdot \left(\dfrac{2}{15}\right)\)  
      8. \( \left( \dfrac{5}{6}\right)^2\)
      9. \(6 \cdot 4\dfrac{2}{3} \)
      10. \( \left(12\cdot \dfrac{3}{4}\right) +\left( 15\cdot \dfrac{1}{5}\right)\)
      11. \( \left(\dfrac{1}{2} \right)^2\cdot \left( \dfrac{5}{3}\right)^2 \)
      12. \( \dfrac{1}{3}\div \dfrac{1}{2}\)
      13. \( \dfrac{13}{28}\div \dfrac{39}{14}\)
      14. \( \dfrac{4}{3}\div 6\)
      15. \( 4+\dfrac{3}{8}\div\dfrac{3}{16}\)
    7. Rewrite as rational numbers in fraction form.
      1. \(2 \dfrac{3}{8}\)
      2. \( 1\dfrac{1}{5}\)
      3. \(-4 \dfrac{2}{7}\)
      4. \( 5\dfrac{47}{100}\)
    8. Write each rational number as a mixed number.
      1. \( \dfrac{5}{3}\)
      2. \( -\dfrac{8}{5}\)
      3. \( \dfrac{43}{10}\)
      4. \( \dfrac{16}{3}\)
      5. \( \dfrac{38}{6}\)
    9. True or False.
      1. \(\sqrt{9}+\sqrt{16}=\sqrt{9+16} \)
      2. \(\sqrt{9\cdot 16}=\sqrt{9}\sqrt{6} \)
      3. \( \sqrt{\left( \dfrac{9}{16}\right)}=\dfrac{\sqrt{9}}{\sqrt{16}}\)
    10. Simplify each expression.  Leave irrational numbers in exact form; do not approximate them.
      1. \(6\sqrt{3}+4\sqrt{3} \)
      2. \(2(6\sqrt{3}+4\sqrt{3}) \)
      3. \( \dfrac{6\sqrt{3}+4\sqrt{3}}{2\sqrt{3}}\)
      4. \( 2\sqrt{3}\cdot\sqrt{3}\)
      5. \( 2\sqrt{3} (6\sqrt{3}+4\sqrt{3}) \)
      6. \(  4\sqrt{3}^2\)
      7. \( (4\sqrt{3})^2\)
      8. \( 5\pi+4\pi\)
      9. \( \dfrac{12\pi}{4\pi} \)
      10. \(2(5\pi+4\pi) \)
      11. \( 2\cdot 5\pi^2\)
      12. \(2\cdot(5\pi)^2 \)
      13. \( (2\cdot 5\pi)^2 \)
      14. \( 2\pi \cdot 5^2\)
    11. Compare the two numbers in each pair using the correct inequality symbol.
      1. -6 ____ -2
      2. -5 ____ -9
      3. -7 ____ 2
      4. -3/5 ____ -4/7
      5. -2.56 ____ - 3.4
      6. Evaluate these expressions
      7. -5/7 + 2/7
      8. 4.79 – 8.39
      9. -64 – 25.5
      10. 23 1/3 - 52 2/3
      11. 6/5 ÷ 3/8
      12. 4 2/5 - 2 7/8
      13. 3 1/2 • 4 1/3
    12. How many quarter-pound burgers can you make from 7 ½ pounds of hamburger meat?
    13. In a recent election on campus, 760 students voted.  The winning candidate received 4/7 of the votes cast.  How many students voted for this candidate?
    14. Evaluate 48 – 2.8x for x = 10
    15. Evaluate 1/2 h(b + B) for h = 3/2 , b = 4 ½ , B = 6
    16. Write these rational numbers as decimal numbers.
      1. \( \dfrac{2}{5} \)
      2. \( \dfrac{3}{5} \)
      3. \( \dfrac{7}{20} \)
      4. \( \dfrac{7}{8} \)
      5. \( \dfrac{17}{100} \)
      6. \( \dfrac{5}{10} \)
      7. \( \dfrac{13}{400} \)
      8. \(  \dfrac{1}{3} \)
      9. \( \dfrac{5}{6} \)
      10. \(  \dfrac{4}{7} \)
      11. \(  \dfrac{8}{5} \)
      12. \( \dfrac{5}{4} \)
      13. 5
      14. \( \dfrac{8}{3} \)
    17. Rewrite these decimal numbers as rational numbers in lowest terms.
      1. 0.6
      2. 0.48
      3. 0.028
      4. 0.89
      5. \(0.\bar{6}\)
      6. 2.5
      7. 12.25

    This page titled 1.3.2.1: Exercises is shared under a not declared license and was authored, remixed, and/or curated by Leah Griffith, Veronica Holbrook, Johnny Johnson & Nancy Garcia.