Fractions and Mixed Numbers

Multiplying Fractions

  • Steps for multiplying fractions are not explicitly provided in the transcript, but the examples demonstrate the process of multiplying the numerators and the denominators.

  • Examples:

    • 43⋅25=4⋅23⋅5=815\frac{4}{3} \cdot \frac{2}{5} = \frac{4 \cdot 2}{3 \cdot 5} = \frac{8}{15}
    • 16⋅711=1⋅76⋅11=766\frac{1}{6} \cdot \frac{7}{11} = \frac{1 \cdot 7}{6 \cdot 11} = \frac{7}{66}
    • 23⋅59=2⋅53⋅9=1027\frac{2}{3} \cdot \frac{5}{9} = \frac{2 \cdot 5}{3 \cdot 9} = \frac{10}{27}
    • 85⋅17=8⋅15⋅7=835\frac{8}{5} \cdot \frac{1}{7} = \frac{8 \cdot 1}{5 \cdot 7} = \frac{8}{35}
    • 1721⋅315=17⋅321⋅15=51315=17105\frac{17}{21} \cdot \frac{3}{15} = \frac{17 \cdot 3}{21 \cdot 15} = \frac{51}{315} = \frac{17}{105}
    • 910⋅67=9⋅610⋅7=5470=2735\frac{9}{10} \cdot \frac{6}{7} = \frac{9 \cdot 6}{10 \cdot 7} = \frac{54}{70} = \frac{27}{35}
    • 15⋅27=1⋅25⋅7=235\frac{1}{5} \cdot \frac{2}{7} = \frac{1 \cdot 2}{5 \cdot 7} = \frac{2}{35}

Evaluate Exponential Expressions with Fractional Bases

  • Example:
    • (12)3=1323=18(\frac{1}{2})^3 = \frac{1^3}{2^3} = \frac{1}{8}

Word Problem

  • Samantha made $325 this week at her job.
  • She spent 25\frac{2}{5} of her pay on food.
  • How much did she spend on food?
    • Amount spent on food = 25⋅325=2⋅3255=6505=130\frac{2}{5} \cdot 325 = \frac{2 \cdot 325}{5} = \frac{650}{5} = 130
    • Samantha spent $130 on food.