Division of Integers

Examples, videos, and solutions to help Grade 7 students recognize that division is the reverse process of multiplication, and that integers can be divided provided the divisor is not zero.

New York State Common Core Math Grade 7, Module 2, Lesson 12

Worksheets for Grade 7

Lesson 12 Student Outcomes

• Students recognize that division is the reverse process of multiplication, and that integers can be divided provided the divisor is not zero.
• Students understand that every quotient of integers (with a non-zero divisor) is a rational number and divide signed numbers by dividing their absolute values to get the absolute value of the quotient. The quotient is positive if the divisor and dividend have the same signs and negative if they have opposite signs.

Lesson 12 Summary

• The rules for dividing integers are similar to the rules for multiplying integers (when the divisor is not zero). The quotient is positive if the divisor and dividend have the same signs, and negative if they have opposite signs.
  The quotient of any 2 integers (with a non-zero divisor) will be a rational number.

NYS Math Module 2 Grade 7 Lesson 12 Classwork

Exercise 1: Recalling the Relationship Between Multiplication and Division
a. List examples of division problems that produced a quotient that is a negative number.
b. If the quotient is a negative number, what must be true about the signs of the dividend and divisor?
c. List your examples of division problems that produced a quotient that is a positive number.
d. If the quotient is a positive number, what must be true about the signs of the dividend and divisor?

Rules for Dividing Two Integers:

• A quotient is negative if the divisor and the dividend have _____ signs.
• A quotient is positive if the divisor and the dividend have ____ signs.

Exercise 2: Is the Quotient of Two Integers Always an Integer
Is the quotient of two integers always an integer? Use the work space below to create quotients of integers. Answer the question and use examples or a counterexample to support your claim.
Conclusion: Every quotient of two integers is always a rational number, but not always an integer.

Exercise 3: Different Representation of the Same Quotient
Are the answers to the three quotients below the same or different? Why or why not?
a) -14 ÷ 7
b) 14 ÷ -7
c) -(14 ÷ 7)

Exercise 4: Fact Fluency—Integer Division

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Lesson 12 Problem Set

1. Find the missing values in each column:

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