Fractions as Division: Unlocking the Connection

Mathematics Grades 7th Grade 6:44 Video
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Lesson Description

Explore the relationship between fractions and division, understanding how they are two sides of the same coin. This lesson uses visual models to make the abstract concept concrete.

Video Resource

Understanding fractions as division | Fractions | 5th grade | Khan Academy

Khan Academy

Duration: 6:44
Watch on YouTube

Key Concepts

  • Fractions represent parts of a whole.
  • Division is the process of splitting a whole into equal groups.
  • The fraction bar acts as a division symbol.

Learning Objectives

  • Students will be able to explain the equivalence between a fraction and division.
  • Students will be able to represent division problems as fractions.
  • Students will be able to solve simple division problems using fractions.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the concepts of multiplication and division as inverse operations. Use simple examples like 2 x 4 = 8 and 8 / 4 = 2 to illustrate the relationship.
  • Video Viewing (10 mins)
    Play the Khan Academy video 'Understanding fractions as division | Fractions | 5th grade | Khan Academy'. Encourage students to take notes on the key points and examples.
  • Guided Practice (15 mins)
    Work through examples of converting fractions to division problems and vice versa. Use visual aids, such as drawing diagrams, to help students understand the concept. For instance, show how 1/3 is the same as 1 divided into 3 equal parts.
  • Independent Practice (15 mins)
    Provide students with practice problems to solve on their own. These problems should include both converting fractions to division problems and solving division problems by expressing them as fractions. Include word problems to increase the difficulty.
  • Wrap-up and Assessment (5 mins)
    Review the key concepts of the lesson. Administer a short quiz or ask questions to assess student understanding.

Interactive Exercises

  • Fraction Division Matching Game
    Create cards with fractions on some cards, and their equivalent division problems on other cards. Have students match the cards to reinforce the concept of equivalence.

Discussion Questions

  • How does understanding fractions as division help us solve real-world problems?
  • Can you think of any situations where it's easier to use a fraction instead of division, or vice versa?
  • Why is it important to understand that a fraction is also a division problem?

Skills Developed

  • Conceptual Understanding of Fractions
  • Problem-Solving
  • Mathematical Reasoning

Multiple Choice Questions

Question 1:

Which of the following is equivalent to 5/8?

Correct Answer: 5 divided by 8

Question 2:

What division problem does the fraction 2/7 represent?

Correct Answer: 2 divided by 7

Question 3:

If a pizza is cut into 6 slices and you eat 2 slices, what fraction represents the portion you ate, and what division problem is that equivalent to?

Correct Answer: 2/6, 2 divided by 6

Question 4:

Which expression represents 4 divided by 9 as a fraction?

Correct Answer: 4/9

Question 5:

What is the result of 1 divided by 5 expressed as a fraction?

Correct Answer: 1/5

Question 6:

If 3 friends share 2 cookies equally, what fraction of a cookie does each friend get? What is the corresponding division problem?

Correct Answer: 2/3, 2 divided by 3

Question 7:

What does the fraction bar in a fraction such as 3/4 represent?

Correct Answer: Division

Question 8:

Which of the following demonstrates the inverse relationship between multiplication and division?

Correct Answer: 2 x 3 = 6 and 6 / 3 = 2

Question 9:

What fraction represents the division problem 7 divided by 9?

Correct Answer: 7/9

Question 10:

If 5 people share 4 apples equally, what fraction represents how much each person gets? What is the equivalent division problem?

Correct Answer: 4/5, 4 divided by 5

Fill in the Blank Questions

Question 1:

The fraction bar in a fraction acts as a ________ symbol.

Correct Answer: division

Question 2:

The fraction 4/9 is equivalent to 4 ________ by 9.

Correct Answer: divided

Question 3:

When you divide a whole into equal parts, you are creating ________.

Correct Answer: fractions

Question 4:

The numerator of a fraction is the number being ________, and the denominator is the number you are dividing by.

Correct Answer: divided

Question 5:

The inverse operation of multiplication is ________.

Correct Answer: division

Question 6:

The expression 6 divided by 11 can be written as the fraction ________.

Correct Answer: 6/11

Question 7:

If you have 1 item and divide it into 4 equal groups, each group has ________ of the item.

Correct Answer: 1/4

Question 8:

Division is the process of splitting a whole into ________ groups.

Correct Answer: equal

Question 9:

The fraction 8/12 means 8 ________ by 12.

Correct Answer: divided

Question 10:

When we say 'one-third' we are dividing one whole into ________ equal parts.

Correct Answer: 3

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.1.2:[Objective] Recognize and generate equivalent representations of rational numbers, including equivalent fractions. 7.A.3:[Standard] Represent mathematical situations using equations and inequalities involving variables and rational numbers.

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