At the end of the lesson, the learner will be able to: divide integers (with non-zero divisor) interpret quotients of rational numbers by describing real-world contexts

1. DIVISION OF
INTEGERS

2. Objectives
At the end of the lesson, you will be
able to:
divide integers (with non-zero divisor)
interpret quotients of rational numbers
by describing real-world contexts

3. Introduction
•Doing division of integers is not that
different from doing simple division of
whole numbers, which you have learned
before. Probably, the only difference in the
method is the signs.
•Fortunately, the sign rules for multiplication
of integers are the same with division.

4. Learn about It!
Division of integers is almost the same as
the division of whole numbers except that
the sign of the quotient needs to be
determined.
In the expression a ÷ b = c,
a is called the “dividend” or “numerator”,
b the “divisor” or “denominator” and
c is called the “quotient”.

5. Three Cases in Dividing Integers
Case 1. If both the dividend and the
divisor are positive, the quotient will be
positive.
Examples
1. (+20) ÷ (+5) = +4 or
+20
+5
= +4
2. (+8) ÷ (+4) = +2 or
+8
+4
= +2

6. Three Cases in Dividing Integers
Case 2. If both the dividend and the
divisor are negative, the quotient will
be positive.
Examples
1. (-20) ÷ (-5) = +4
2. (-8) ÷ (-4) = +2

7. Three Cases in Dividing Integers
Case 3. If only one of the dividend or
the divisor is negative, the quotient will
be negative.
Examples
1. (+20) ÷ (-5) = -4
2. (-8) ÷ (+4) = -2
3. (-30) ÷ (+5) = -6

8. Answer the following in your
activity notebook.
1. 36 ÷ (-4)
2. (-48) ÷ (-6)
3. 64 ÷ 4

9. Solution
1. 36 ÷ (-4) = -9
2. (-48) ÷ (-6) = +8
3. 64 ÷ 4 = 16

10. Tips
1. The divisor should not be equal to
zero because a number divided by
zero is undefined.
2. The quotient of two integers is not
always an integer. It can be a
decimal number.

11. Key Points
1. If the signs of the dividend and the
divisor are the same, then the
quotient will be positive.
2. If the signs are different, then the
quotient will be negative.

12. 1. Identify the dividend, the divisor,
and the quotient of the expression
𝑑
𝑓
= 𝑔.
a. The dividend is g, the divisor is f, and
the quotient is d.
b. The dividend is f, the divisor is d, and
the quotient is g.
c. The dividend is d, the divisor is f, and
the quotient is g.
d. The dividend is g, the divisor is d, and
the quotient is f.

13. 2. Complete the statement: If both
the dividend and the divisor are
negative, the quotient will be ____.
a. Positive
b. Negative

14. 3. What is the sign of the quotient
of -3 ÷ 4?
a. Positive
b. Negative

15. 4. Which of the following statements
is true for the expression
𝑑
𝑓
= 𝑔.
a. If d is negative and g is positive, then
f is positive.
b. If d is negative and g is negative,
then f is negative.
c. If d is negative and g is positive, then
f is negative.
d. If d is positive and g is positive, then
f is negative.

16. 5. Simplify (-6) ÷ (3)
a. -3
b. -2
c. 2
d. 3

17. 6. Simplify (+600) ÷ (-30)
a. -20
b. 2
c. -2
d. 20

18. 7. Simplify (+625) ÷ (-5)
a. -125
b. -25
c. 25
d. 125

19. 8. If
−100
𝑥
= -50, what is the value
of x?
a. 50
b. 2
c. -50
d. -2

20. 9. Which of the following is the
answer when you simplify the
expression 160 ÷ (-20) ÷ (-4)?
a. 8
b. 2
c. -8
d. -2

21. 10. An equation is true when the left-
hand side of the equation is equal to
the right-hand side. Which of the
following equations are true?
a. (-36) ÷ (+4) = 18 ÷ (-2)
b. (-16) ÷ (-4) = (-4) ÷ 1
c. 100 ÷ (-10) = (-50) ÷ 10
d. -24 ÷ (-3) = (-16) ÷ (-2)