5.2 Fractions as Quotients and Fraction Multiplication

Unit Goals

  • Students develop an understanding of fractions as the division of the numerator by the denominator, that is $a \div b = \frac{a}{b}$, and solve problems that involve the multiplication of a whole number and a fraction, including fractions greater than 1.

Section A Goals

  • Represent and explain the relationship between division and fractions.
  • Solve problems involving division of whole numbers leading to answers that are fractions.

Section B Goals

  • Connect division to multiplication of a whole number by a non-unit fraction.
  • Connect division to multiplication of a whole number by a unit fraction.
  • Explore the relationship between multiplication and division.

Section C Goals

  • Find the area of a rectangle when one side length is a whole number and the other side length is a fraction or mixed number.
  • Represent and solve problems involving the multiplication of a whole number by a fraction or mixed number.
  • Write, interpret and evaluate numerical expressions that represent multiplication of a whole number by a fraction or mixed number.
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Glossary Entries

  • area

    The number of square units that cover a flat figure without gaps or overlaps.


  • cubic unit
    A unit cube with side lengths that are standard measurement units that is used to measure volume.

  • rectangular prism
    A solid figure which has six faces that are rectangles.

  • unit cube
    A cube whose sides are 1 unit long, used to measure volume.

  • volume
    The number of unit cubes that fill a solid figure without gaps or overlap.