4.3 Extending Operations to Fractions

Unit Goals

  • Students learn that a fraction $\frac{a}{b}$ is a product of a whole number $a$ and a unit fraction $\frac{1}{b}$, or $\frac{a}{b} = a \times \frac{1}{b}$, and that $n \times \frac{a}{b} = \frac{(n \space \times \space a)}{b}$. Students learn to add and subtract fractions with like denominators, and to add and subtract tenths and hundredths.

Section A Goals

  • Recognize that $n \times \frac{a}{b} = \frac{(n \space \times \space a)}{b}$.
  • Represent and explain that a fraction $\frac{a}{b}$ is a multiple of $\frac{1}{b}$, namely $a \times \frac{1}{b}$.
  • Represent and solve problems involving multiplication of a fraction by a whole number.

Section B Goals

  • Create and analyze line plots that display measurement data in fractions of a unit ($\frac18, \frac14, \frac12$).
  • Represent and solve problems that involve the addition and subtraction of fractions and mixed numbers, including measurements presented in line plots.
  • Use various strategies to add and subtract fractions and mixed numbers with like denominators.

Section C Goals

  • Reason about equivalence to add tenths and hundredths.
  • Reason about equivalence to solve problems involving addition and subtraction of fractions and mixed numbers.
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Glossary Entries

  • common denominator
    The same denominator in two or more fractions. For instance, \(\frac{1}{4}\) and \(\frac{5}{4}\) have a common denominator.

  • composite number
    A whole number with more than 1 factor pair.

  • denominator
    The bottom part of a fraction that tells how many equal parts the whole was partitioned into.

  • equivalent fractions
    Fractions that have the same size and describe the same point on the number line. For example, \(\frac{1}{2}\) and \(\frac{2}{4}\) are equivalent fractions.

  • factor pair of a whole number
    A pair of whole numbers that multiply to result in that number. For example, 5 and 4 are a factor pair of 20.

  • mixed number
    A number expressed as a whole number and a fraction less than 1. 

  • multiple of a number
    The result of multiplying that number by a whole number. For example, 18 is a multiple of 3, because it is a result of multiplying 3 by 6.

  • numerator

    The top part of a fraction that tells how many of the equal parts are being described.


  • prime number
    A whole number that is greater than 1 and has exactly one factor pair: the number itself and 1.