Divide and Conquer: Mastering Mixed Number Division

Mathematics Grades 7th Grade 3:33 Video
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Lesson Description

Learn how to divide mixed numbers by converting them to improper fractions and applying the concept of reciprocals. This lesson will equip you with the skills to confidently tackle division problems involving mixed numbers.

Video Resource

Dividing mixed numbers example

Khan Academy

Duration: 3:33
Watch on YouTube

Key Concepts

  • Mixed Numbers
  • Improper Fractions
  • Reciprocals
  • Dividing Fractions

Learning Objectives

  • Convert mixed numbers to improper fractions.
  • Calculate the reciprocal of a fraction.
  • Divide mixed numbers by converting to improper fractions and multiplying by the reciprocal.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the definitions of mixed numbers and fractions. Briefly discuss why it's difficult to directly divide mixed numbers. Introduce the concept of converting them to improper fractions as a solution.
  • Video Viewing (10 mins)
    Play the Khan Academy video 'Dividing mixed numbers example.' Encourage students to take notes on the steps involved in converting mixed numbers to improper fractions and dividing them.
  • Guided Practice (15 mins)
    Work through a few examples together as a class. Start with simpler mixed numbers and gradually increase the complexity. Emphasize each step: converting to improper fractions, finding the reciprocal, and multiplying.
  • Independent Practice (15 mins)
    Provide students with a set of division problems involving mixed numbers to solve independently. Circulate the room to provide support and answer questions.
  • Wrap-up (5 mins)
    Review the key steps and address any remaining questions. Assign homework for further practice.

Interactive Exercises

  • Mixed Number Conversion Relay
    Divide the class into teams. Each team receives a set of mixed numbers. Team members take turns converting the mixed numbers to improper fractions and passing them to the next member. The first team to correctly convert all their mixed numbers wins.
  • Reciprocal Race
    Present fractions one at a time on the board. Students race to write down the reciprocal of each fraction. Award points for speed and accuracy.

Discussion Questions

  • Why is it necessary to convert mixed numbers to improper fractions before dividing?
  • What is a reciprocal and why is it important when dividing fractions?

Skills Developed

  • Converting Mixed Numbers to Improper Fractions
  • Calculating Reciprocals
  • Dividing Fractions
  • Problem Solving

Multiple Choice Questions

Question 1:

What is the first step in dividing mixed numbers?

Correct Answer: Convert the mixed numbers to improper fractions.

Question 2:

What is the reciprocal of 3/4?

Correct Answer: 4/3

Question 3:

When dividing fractions, you multiply by the what of the second fraction?

Correct Answer: Reciprocal

Question 4:

What is 2 and 1/2 converted to an improper fraction?

Correct Answer: 5/2

Question 5:

Which of the following is the same as 5 divided by 1/2?

Correct Answer: 5 x 2/1

Question 6:

What is the value of 1 divided by 1/4?

Correct Answer: 4

Question 7:

When simplifying an answer, a fraction should always be in _______ form.

Correct Answer: Lowest Terms

Question 8:

What is the result of 3/5 divided by 2/3?

Correct Answer: 9/10

Question 9:

What is 1 and 1/4 divided by 1/2?

Correct Answer: 5/2

Question 10:

Dividing by a fraction is the same as multiplying by its _______.

Correct Answer: Reciprocal

Fill in the Blank Questions

Question 1:

A number with a whole number part and a fraction part is called a _______ number.

Correct Answer: mixed

Question 2:

A fraction where the numerator is greater than the denominator is called an _______ fraction.

Correct Answer: improper

Question 3:

The _______ of a fraction is obtained by swapping the numerator and the denominator.

Correct Answer: reciprocal

Question 4:

To divide fractions, you multiply by the _______ of the divisor.

Correct Answer: reciprocal

Question 5:

The improper fraction for 3 and 1/4 is _______.

Correct Answer: 13/4

Question 6:

Before dividing mixed numbers, they must be converted to _______ fractions.

Correct Answer: improper

Question 7:

The reciprocal of 5 is _______.

Correct Answer: 1/5

Question 8:

The answer to a division problem is called the _______.

Correct Answer: quotient

Question 9:

Simplifying a fraction means reducing it to _______ terms.

Correct Answer: lowest

Question 10:

When dividing mixed numbers, it is important to remember to multiply the first fraction by the _______ of the second fraction after converting to improper fractions.

Correct Answer: reciprocal

Educational Standards

7.N.1:[Standard] Read, write, represent, and compare rational numbers, expressed as integers, fractions, and decimals. Explain and apply the concept of absolute value. 7.N.2:[Standard] Calculate with rational numbers, with and without positive integer exponents, to model and solve mathematical problems.

Teaching Materials

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