Fractions and Division in Word Problems

Reciprocals and Dividing by Fractions

Formative Assessment

Summary of the Math: Reciprocals and Dividing by Fractions

Read and Discuss

  • The fractions ab and ba, with numerators and denominators inverted, are called reciprocals of each other.
  • The key property of reciprocals is that their product is always 1.

    ab×ba=a×bb×a=1
  • Reciprocals are also called multiplicative inverses. This name refers to the fact that if you multiply a fraction by a number, and then multiply the result by the reciprocal of the fraction, the result is “undone.” For example:

    34×5=154
    154×43=153=5
  • You can use the properties of reciprocals to help you divide by fractions. The general rule is: To divide by a fraction, multiply by the reciprocal of the fraction. Algebraically, the rule looks like this: ab÷cd=ab×dc=adbc

Can you:

  • Solve a problem that involves dividing a fraction by a fraction?
  • Determine which operation is needed to solve a word problem?
  • Explain what reciprocals are and how to use them to help you solve division problems involving fractions?