Math for Grade 7 - Amethyst

1. PROPERTIES OF
REAL NUMBERSPrepared by: Ms. Jenny Tuazon

2. CLOSURE PROPERTY
OF ADDITION
The sum of any two real
number is a real number.
Where a + b is a real number

3. EXAMPLE:
2 is a real number and
3.5 is a real number so 2
+ 3.5 or 5.5 is a real
number

4. CLOSURE PROPERTY
OF MULTIPLICATION
The product of any two real
numbers is a real number.
Where ab is a real number.

5. EXAMPLE:
12 is a real number and
1
3
is a real number, so 12 ∙
1
3
or 4 is a real number.

6. COMMUTATIVE
PROPERTY OF
ADDITION
Two real numbers can be
added in any order.
Where 𝒂 + 𝒃 = 𝒃 + 𝒂

7. EXAMPLE:

8. ASSOCIATIVE PROPERTY
OF ADDITION
If three real numbers are added,
it makes no difference which two
are added first.
Where 𝒂 + 𝒃 + 𝒄 = 𝒂 + (𝒃 + 𝒄)

9. EXAMPLE:

10. ASSOCIATIVE PROPERTY
OF MULTIPLICATION
If three real numbers are multiplied,
it makes no difference which two are
multiplied first.
Where 𝒂 ∙ 𝒃 𝒄 = 𝒂(𝒃 ∙ 𝒄)

11. EXAMPLE:

12. DISTRIBUTIVE PROPERTY OF
MULTIPLICATION OVER
ADDITION/SUBTRACTION
Multiplication distributes over
addition/subtraction
Where 𝒂 𝒃 + 𝒄 = 𝒂𝒃 + (𝒂𝒄)

13. EXAMPLE:

14. IDENTITY PROPERTY OF ADDITION
Any number added to the identity
element 0 will remain unchanged. 0 is the
identity element of addition.
𝒂 + 𝟎 = 𝟎 + 𝒂
𝒂 = 𝒂

15. IDENTITY PROPERTY OF
MULTIPLICATION
Any number multiplied to the identity
element 1 will remain unchanged. 1 is the
identity element of multiplication.
𝒂 𝟏 = 𝟏(𝒂)
𝒂 = 𝒂

16. INVERSE PROPERTY OF ADDITION
The sum of a number and its additive
inverse (opposite) is the identity element 0.
a and –a are additive inverses.
𝒂 + −𝒂 = −𝒂 + 𝒂
𝟎 = 𝟎

17. INVERSE PROPERTY OF
MULTIPLICATION
The product of a number and its multiplicative
inverse (reciprocal) is the identity element 1. 𝒂 and
𝟏
𝒂
are multiplicative inverses.
𝒂
𝟏
𝒂
=
𝟏
𝒂
𝟏
𝟏 = 𝟏
Where 𝐚 ≠ 𝟎

18. SEATWORK # 2

19. Identify the axiom or real number property that
justifies each statement. Write your answer
before the number.
1. 31+ x = x + 31
2. 5(x – 4) = 5x – 20
3. 4(xy) = 4x(y)
4. 9+(-9) = 0
5. 𝒙 𝟐
∙ 𝟖 = 𝟖 ∙ 𝒙 𝟐
6. 𝟎 +
𝟕
𝟖
=
𝟕
𝟖
7. 1,001 (1) = 1,001
8. 𝟏𝟏 ∙
𝟏
𝟏𝟏
= 𝟏
9. ax + x = x(a+1)
10. (1)(10)=1