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The Relationship of Multiplication and Division

Videos and solutions to help Grade 6 students build and clarify the relationship of multiplication and division by evaluating identities such as a ÷ b • b = a and a • b ÷ b = a.

New York State Common Core Math Module 4, Grade 6, Lesson 2

Related Topics:
Lesson Plans and Worksheets for Grade 6
Lesson Plans and Worksheets for all Grades
More Lessons for Grade 6
Common Core For Grade 6

Opening Exercise

Draw a pictorial representation of the division and multiplication problems using a tape diagram.
a. 8 ÷ 2
b. 3 × 2


1. Build a tape diagram to represent units.
2. Divide the units into three equal groups.
3. Write an expression to represent the process you modeled with the tape diagram.
4. Evaluate the expression.
5. Use your squares to demonstrate what it would look like to multiply 3 by 3.
6. Alter our original expression 9 ÷ 3 to create an expression that represents what we did with the tape diagram.
7. Evaluate the expression.
8. What do you notice about the expression of the tape diagram?
9. Write a number sentence, using variables, to represent the identities we demonstrated with tape diagrams.
10. Use the variable tiles you were provided to demonstrate this number sentence with a series of tape diagrams.

Exit Ticket
Learn why multiplication and division are inverse operations.

1. Fill in the blank to make each number sentence true.
a. 12 ÷ 3 × ____ = 12
b. f × h ÷ h =
c. 45 × ___ ÷ 15 = 45
d. ___ ÷ r × r = p

Problem Set
1. Fill in each blank to make the equation true.
132 ÷ 3 × 3 =_____
_____ ÷ 25 × 25 = 225
56 × _____ ÷ 8 = 56
452 × 12 ÷ _____= 452

2. How is the relationship of addition and subtraction similar to the relationship of multiplication and division? A review of the relationship between addition and subtraction and the relationship between multiplication and division.

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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