LESSON PLAN IN MATHEMATICS 7

1. PROPERTIES
OF THE
OPERATIONS
IN THE SET OF
INTEGERS

2. OBJECTIVES
. Identify the Six Properties in the
Operation of Integers
. Demonstrate and apply the Six
Properties in the Operation of
Integers

3. DRILL
Look for the missing numbers
15 + 20 = 20 + _____
5 X 2 = 2 X _____
125 = 5 X _____

4. REVIEW
Answer the following operations
25 + 5 =_____
-21 + (-13) =_____
14 + (-7) =_____

5. Kuwentong Pangkabuhayan
Mang Arturo have five carabaos, 4
ducklings and 6 chickens in his
backyard. Counting the number of
legs, Who among of you can give
the mathematical sentence using
only plus (+) and equal (=) symbols
of the problem?

6. Exactly!
Fill the blanks with the correct
number that will make it exact.
(8 + ___ ) + 1 = ___ + ( 5 + 1 )
What are the numbers in the blanks
5 8
What property is illustrated?

7. THE SIX PROPERTIES
OF THE OPERATIONS
ON THE SET OF
INTEGERS

8. 1. CLOSURE PROPERTY
Two integers that are added and multiplied remain as
integers. The set of integers is closed under addition and
multiplication.
The Closure Property for real numbers states that if a and
b are real numbers, then a + b is a unique real number.
Example 1: Adding two real numbers produces another real
number.
15
+ 16_
21
The number "21" is a real number

9. : Multiplying two real numbers produces another real
number
The number "312" is a real number.

10. 2. COMMUTATIVE PROPERTY
Changing the order of two numbers that are either
being added or multiplied does not change the value.
a+b = b+a
ab = ba
Examples:
2 + 3 = 3 + 2, since 2 + 3 = 5 and also 3 + 2 = 5.
(-16) +( -5) = (-5) + (-16)
100 + 99 = 99 + 100
(2) (3) = (3) (2), since (2)(3) = 6 and also (3)(2) = 6.
(-4) (-15) = (-15) (-4)
Note: Subtraction and Division are not commutative.

11. 3. ASSOCIATIVE PROPERTY
Changing the grouping of numbers that are
either being added or multiplied does not
change its value.
(a + b) + c = a + (b + c)
(ab) c = a (bc)
Examples:
(10 + 25) + 5 = 10 + (25 + 5)
2(6 X 4) = (2 X 6)4

12. 4. DISTRIBUTIVE PROPERTY
When two numbers have been added/subtracted and then multiplied by
a factor, the result will be the same when each number is multiplied by
the factor and the products are then added / subtracted.
a ( b + c) = ab + ac
a ( b – c) = ab – ac
Examples:
2( 8 + 9 ) = 2X8 + 2X9
Checking 2 X 17 = 16 + 18
34 = 34
2( 8 – 9) = 2X8 - 2X9
2X (-1) = 16 – 18
-2 = -2

13. 5. IDENTITY PROPERTY
5a. Additive Identity - states that the sum of
any number and 0 is the given number. Zero is
the additive identity.
a + 0 = a
Examples:
4 + 0 = 4
-10 + 0 = -10
99 + 0 = 99

14. 5. IDENTITY PROPERTY
5b. Multiplicative Identity - states that the
product of any number and 1 is the given number,
a • 1 = a. One is the multiplicative identity.
a X 1 = a
Examples:
12 x 1 = 12
-32 x 1 = -32
99 x 1 = 99

15. 6. INVERSE PROPERTY
6a. Additive Inverse - states that the sum of any
number and its additive inverse is zero. The
additive inverse of a positive number is the
negative of that number, that is
a + ( -a) = 0
Example:
10 + (-10) = 0
-19 + 19 = 0

16. 6. INVERSE PROPERTY
6b. Multiplicative Inverse Property states that
the product of any number and its multiplicative
inverse or reciprocal is 1. The multiplicative
inverse of the number a is
Examples:

17. ABSTRACTION
We already finished discussing the six properties on the operation of integers;
1. What is Closure Property?
2. What is Commutative Property?
3. What is Associative Property?
4. What is a Distributive Property?
5. What is Identity?
a. Identity Property of Addition?
b. Identity Property of Multiplication?
6. What is Inverse Property?
a. Inverse Property of Addition?
b. Inverse Property of Multiplication?

18. Kuwentong Pangkabuhayan
Mang Arturo have five carabaos, 4 ducklings
and 6 chickens in his backyard. Counting the
number of legs, Who among of you can give
the mathematical sentence using only plus (+)
and equal (=) symbols of the problem?