 # The Relationship of Division and Subtraction

Videos and solutions to help Grade 6 students build and clarify the relationship of division and subtraction by determining that 12 ÷ x = 4 means 12- x - x - x - x = 0

New York State Common Core Math Module 4, Grade 6, Lesson 4

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Common Core For Grade 6

Learn the relationship of division and subtraction.

Lesson 4 Student Outcomes

Students build and clarify the relationship of division and subtraction by determining that means 12 ÷ x = 4 means 12- x - x - x - x = 0 .

Discussion

Try the following:

Build a tape diagram that has 20 squares.
Divide the tape diagram into 4 equal sections.
How many squares are in each of the 4 sections?
Write a number sentence to demonstrate what happened.
Combine your squares again to have a tape diagram with 20 squares.
Now subtract 4 squares from your tape diagram.
Write an expression to demonstrate what happened.
Subtract 4 more squares and alter your expression to represent the new tape diagram.
Subtract 4 more squares and alter your expression to represent the new tape diagram.
Subtract 4 more squares and alter your expression to represent the new tape diagram.
Last time, subtract 4 more squares and alter your expression to represent a number sentence showing the complete transformation of the tape diagram.

Do you recognize a relationship between 20 ÷ 4 = 5 and 20 - 4 - 4 - 4 - 4 -4 = 0 ? If so, what is it?

Exercise 1

Build subtraction expressions using the indicated equations.

Exercise 2

Answer each question using what you have learned about the relationship of division and subtraction.

a. If 12 ÷ x = 3, how many times would x have to be subtracted from 12 in order for the answer to be zero? What is the value of x?

b. 36 - f - f - f -f =0. Write a division sentence for this repeated subtraction sentence. What is the value of f?

c. If 24 ÷ b = 12. c. which number is being subtracted twelve times in order for the answer to be zero?

Closing

In each of the circles, we can place an operation to satisfy the organizer. In the last four lessons, we have discovered that each operation has a relationship with other operations, whether they are inverse operations or they are repeats of another.

What is the inverse operation of addition?
Repeated subtraction can be represented by which operation?
Which operation is the inverse of division?
Is multiplication the repeat operation of addition?

Problem Set Sample Solutions

Build subtraction expressions using the indicated equations.

1. 24 ÷ x = 4
2. 36 ÷ x = 6
3. 28 ÷ y = 7
4. 30 ÷ y = 5
5. 16 ÷ z = 4

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