Two Methods for Dividing Fractions by Fractions

Two Methods for Dividing Fractions by Fractions

Emma Makes Soup

Opening

Emma Makes Soup

Emma made 134 quarts of soup. She is serving the soup in bowls that hold 38 quart each.

How many bowls can she fill?

  • Write a division expression to represent this situation, but do not solve the problem yet.

Math Mission

Opening

Explore methods for dividing a fraction by a fraction.

Emma’s Soup Problem

Work Time

Emma’s Soup Problem

Emma made 134 quarts of soup. She is serving the soup in bowls that hold 38 quart each.

How many bowls can she fill?

  • Solve this problem using any method you wish. Use the division expression you wrote in the Opening.
  • Check your answer.

Did you rewrite 134 as a fraction? Would rewriting both fractions so they have a common denominator help you find the answer?

Common Denominators

Work Time

Common Denominators

One method for dividing two fractions is to first write them with a common denominator. The answer will be the quotient of the numerators.

  • Use this method to solve 56÷25.
  • Check your answer.
  • Explain why this method works.

To explain why this method works, think about what happens to the common denominators when you change the division problem into a multiplication problem using the reciprocal.

Fraction Problem

Work Time

Fraction Problem

  • Solve the problem 23÷35 using any method.
  • Check your answer.

Can you use multiplication to find the answer?

Prepare a Presentation

Work Time

Prepare a Presentation

Explain the method you used to divide a fraction by a fraction. Use your work to support your explanation.

Challenge Problem

Look at the two problems below:

57÷12

57÷14

  • Explain how you can tell which answer will be greater without actually solving the problems.

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about your classmates’ methods for dividing a fraction by a fraction.

As your classmates present, ask questions such as:

  • What does dividing a fraction by a fraction mean?
  • What happens when the fractions are written with a common denominator?
  • How is dividing a fraction by a fraction similar to dividing a fraction by a unit fraction? How is it different?

Methods for Dividing a Fraction by a Fraction

Formative Assessment

Summary of the Math: Methods for Dividing a Fraction by a Fraction

Write a summary about how to divide a fraction by a fraction.

Check your summary.

  • Do you describe at least two methods for dividing a fraction by a fraction?

Reflect On Your Work

Work Time

Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

One thing that still confuses me about dividing with fractions is …