Divide a Fraction by a Fraction

Divide a Fraction by a Fraction

Mia’s Method

Opening

Mia's Method

Mia uses the following method to find 23÷14:

“To find 23÷14, I need to find the number of fourths in 23. I can make a model of 23, but I think it would be difficult to figure out the number of fourths in the model.

“I think the problem would be easier if both fractions had the same denominator. I can change the denominator of each fraction to 12 and rewrite the problem as 812÷312.

“Now I can make a model of 812 and then find the number of groups of 3 twelfths in my model.

“In my model there are 2 groups of 3 twelfths, with 23 of a group of 3 twelfths left over.
So, 23÷14=223.”

  • Discuss Mia’s method with your partner and then with the class.

Math Mission

Opening

Explore methods for dividing a fraction by a unit fraction.

Explore Dividing Fractions by Unit Fractions

Work Time

Explore Dividing Fractions by Unit Fractions

  • Use Mia’s method to find 45÷13.
  • Check your answer.

Ask yourself:

  • Did you change 45 and 13 to fractions that have the same denominator?
    • How many five-fifteenths (515) are in 1215?

Carlos’s Method

Work Time

Carlos’s Method

Carlos uses the following method to find 72÷14:

“I can change this problem to a multiplication problem by multiplying by the inverse. The multiplicative inverse, or reciprocal, of 14 is 4.”

Here is Carlos’s solution:

72×4=282 or 14

So, 72÷14 = 14.

  • Use Carlos’s method to find 83÷15.

How can you rewrite the division problem as a multiplication problem using the reciprocal of 15?

Prepare a Presentation

Work Time

Prepare a Presentation

Explain how you divided a fraction by a unit fraction. Use your work to support your explanation.

Challenge Problem

Below are two methods for dividing a fraction by a unit fraction.

Method 1
To divide a fraction by a unit fraction, multiply the numerator of the fraction by the denominator of the unit fraction.

Method 2
To divide a fraction by a unit fraction, rewrite both fractions so they have a common denominator. The answer is the quotient of the numerators.

  • Choose one of the methods. Use the division problem 45÷13 to explain why the method works.

Make Connections

Performance Task

Ways of Thinking: Make Connections

As your classmates present, take notes to clarify your understanding of how to divide a fraction by a unit fraction.

As your classmates present, ask questions such as:

  • Do all of the methods make sense?
  • Which methods did you find easier to use? Why?
  • Which methods did you find more difficult to use? Why?
  • How are the two models you just looked at alike? How are they different?
  • Where do you see the unit fraction in your model?
  • Why can multiplication be used to solve a division problem?
  • Is there a general pattern you can use to divide any fraction by a unit fraction?

Servings of Rice

Work Time

Servings of Rice

A pot contains 213 cups of rice. How many 12-cup servings does the pot contain?

  • Write a division problem to represent this situation.
  • Solve the problem using any method you wish.
  • Check your answer.

Ask yourself:

  • What is the total amount of rice in the pot? You should divide the total amount of rice into equal groups of what size? How many equal-sized groups are there?
  • Did you write 2 1 3 as a fraction? Would rewriting both fractions so they have a common denominator help you find the answer?

Divide a Fraction by a Unit Fraction

Formative Assessment

Summary of the Math: Divide a Fraction by a Unit Fraction

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

Check your summary.

  • Do you describe at least two methods for dividing a fraction by a unit 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 way I can figure out how to solve a division problem when I am dividing by a unit fraction is...