The document discusses the properties of arithmetic operations including: identity, additive inverse, multiplicative inverse, associative, commutative, distributive, and zero divisor properties. Examples are provided to illustrate each property. An evaluation section includes practice problems for students to apply the properties by completing tables or rewriting expressions. The document aims to help students understand and relate the different properties of arithmetic operations in real-life situations.

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. IDENTITYPROPERTY: 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
• ¼x1=¼
PROPERTIES OF ARITHMETIC OPERATIONS

4. B. ADDITIVEINVERSEPROPERTY: For every α there is a
unique number -α such that the sum of α and -α is 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. MULTIPLICATIVEINVERSE(Real&RationalNumbersonly):
For every nonzero real or rational number α there
is a unique number 1/α such that the product of α
and 1/α is 1.
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 α x
1
α
= 1 =
1
α
x α
TOPIC:
PROPERTIES OF ARITHMETIC OPERATIONS

6. D. ASSOCIATIVE PROPERTY: When three or more numbers
are added together, changing the grouping of the numbers
being added does not change the value of the results. The
same goes for three or more numbers multiplied together.
(Note that in arithmetic expressions, the "grouping" of
numbers is indicated by parenthesis).
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. COMMUTATIVEPROPERTY: Whentwonumbersareadded
together,thetwonumberscanbechangedwithout
changingthevalueoftheresult.Thesamethingistruefor
twonumbersbeingmultipliedtogether.
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. ZERODIVISORPROPERTY: 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.
Aseron Angelo D. Armas Catherine 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
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14. REFERENCES:
• Math Words by Bruce Simmons
Websites: mathwords.com
• Math Warehouse
Website: mathwarehouse.com
• Study Website: study.com
• Coolmat Website: coolmath.com
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