PROPERTIES OF ARITHMETIC OPERATIONS

PREPARED BY:
Mary Joy M. Toquero
Mary Grace M. Toquero
Herman R. Pilapil

1. PROPERTIES OF
ARITHMETIC OPERATIONS
PREPARED BY:
Mary Joy M. Toquero
Mary Grace M. Toquero
Herman R. Pilapil

2. OBJECTIVES:
A.I can state and illustrate the different properties of
arithmetic operations.
B.I can relate the properties of arithmetic operations in
real-life situations.
C.I can rewrite the given expressions according to the
given property.

3. TOPIC:
A.IDENTITY PROPERTY: Addition by 0 or multiplication by
1 result in no change of original number.
Examples: Identity Property for Addition
•7 + 0 = 7
•a + 0 = a
•5 + 0 =5
Identity Property for Multiplication
•100,000,000,000 * 1 = 100,000,000,000
•¼ x 1 = ¼
PROPERTIES OF ARITHMETIC OPERATIONS

4. B.ADDITIVE INVERSE PROPERTY: For every αthere is a
unique number -αsuch that the sum of αand -αis 0.
Note that we write α+ (-b) as α-b.
Examples:
•9 + (-9) = 0
•a + (-a) = 0
•6 + -6 = 0
TOPIC:
PROPERTIES OF ARITHMETIC OPERATIONS

5. C.MULTIPLICATIVE INVERSE (Real & Rational Numbers only) :
Foreverynonzerorealorrationalnumberαthere
isauniquenumber1/αsuchthattheproductofα
and1/αis1.
Examples:
3
5
x
5
3
=1
9 (
1
9
)=1
2
5
x
5
2
=
10
10
=1
3
5
x
5
3
=1 αx
1
α
=1=
1
α
xα
TOPIC:
PROPERTIES OF ARITHMETIC OPERATIONS

6. D.ASSOCIATIVEPROPERTY:Whenthreeormorenumbers
areaddedtogether,changingthegroupingofthenumbers
beingaddeddoesnotchangethevalueoftheresults.The
samegoesforthreeormorenumbersmultipliedtogether.
(Notethatinarithmeticexpressions,the"grouping"of
numbersisindicatedbyparenthesis).
4 + (5+3) = (4+5) +3 (3 x 4) x 2 = 3 x (4 x 2)
4+ (8) = (9) + 3 (12) x 2 = 3 x (8)
12 = 12 24 = 24
Examples:
TOPIC:
PROPERTIES OF ARITHMETIC OPERATIONS

7. E.COMMUTATIVE PROPERTY: When two numbers are added
together, the two numbers can be changed without
changing the value of the result. The same thing is true for
two numbers being multiplied together.
Examples:
4 + 5 = 5 + 4
9 = 9
4 x 7 = 7 x 4
TOPIC:
PROPERTIES OF ARITHMETIC OPERATIONS

8. F.DISTRIBUTIVEPROPERTY:Multiplyinganumberbyasum
givesthesameresultastakingthesumoftheproducts.
Examples: 2 (3 + 5) = 2 (3) + 2 (5)
2 (8) = 6 + 10
16 = 16
TOPIC:
PROPERTIES OF ARITHMETIC OPERATIONS

9. G.ZERO DIVISOR PROPERTY : If the product of two
numbers is zero, then one or the other number
must be zero.
Example: 10 x 0 = 0
0 =0
TOPIC:
PROPERTIES OF ARITHMETIC OPERATIONS

10. EVALUATION:
Test I
Directions: Complete the table. Which property of real
numbers justify each statement?
GIVEN PROPERTY
1.0 + (–3) = –3
2.2 (3 –5) = 2 (3) –2 (5)
3.(–6) + (–7) = (–7) + (–6)
4.1 x (–9) = –9
5.–4 x –¼ = 1
1

11. EVALUATION:
Test I
Directions: Complete the table. Which property of real
numbers justify each statement?
GIVEN PROPERTY
6.2 x (3 x 7) = (2 x 3) x 7
7.10 + (–10) = 0
8.2(5) = 5(2)
9.1 x (–¼) = –¼
10.(–3) (4 + 9) = (–3) (4) + (–3) (9)
2

12. EVALUATION:
Test II
Directions: Rewrite the following expressions using the given
property.
1.12a –5a Distributive Property
2.(7a) b Associative Property
3.8 + 5 Commutative Property
4.–4 (1) Identity Property
5.25 + (-25) Inverse Property

13. REFERENCES:
•Mathematics -Grade 7 Learner's Material Elizabeth R.
AseronAngelo D. ArmasCatherine P. Vistro-Yu, PhD
pp. 33-40
•Yale-New Haven Teachers Institute -Using Basic
Properties to Solve Problems in Math
by Carolyn N. Kinder
Website: teachersinstitute.yale.edu
•Math Words by Bruce Simmons
Website: www.mathwords.com
Carolyn N. Kinder
1

14. REFERENCES:
•Math Words by Bruce Simmons
Websites: mathwords.com
•Math Warehouse
Website: mathwarehouse.com
•Study Website: study.com
•CoolmatWebsite: coolmath.com
Carolyn N. Kinder
2