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.
• 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.
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
Try the free Mathway calculator and
problem solver below to practice various 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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