Download DESCRIBING MATHEMATICAL SYSTEM

DESCRIBING MATHEMATICAL
SYSTEM
PROVE THAT IF A=B, AND C=D, THEN A+C = B+D.
COMPLETE THE TABLE BELOW
PROVE THAT IF a=b, and c=d, then a+c = b+d. Complete the table below
STATEMENT
REASON
1. a=b
Given
2. a + c = b + c
Add both side by c
3. c =d
Given
4. c + b = d + b
Add both side by b
5. a + c = b + d
Addition Property of Equality
GIVEN: X, Y AND Z ARE REAL NUMBERS AND X>Y
PROVE: X + Z > Y + Z
Given: x, y and z are real numbers and x>y
Prove: x + z > y + z
STATEMENT
1. x > y
REASON
Given
2. x + z > y + z Addition axiom
GIVEN: -4 = M
PROVE: M = -4
Given: -4 = m
Prove: m = -4
STATEMENT
1.-4 = m
2. -4 + 4 = m + 4
3. 0 = m + 4
4. 0 – m = m + 4 -m
5. –m = 0 + 4
6. –m = 4
7. (-1)(-m) = (-1)(4)
8. m = -4
REASON
Given
Addition Axiom
Existence of additive inverse
Addition axiom
Existence of additive inverse
Additive identity
Multiply both side by -1
Multiplication axiom
GIVEN: 4(2X-3) + 16 = 5X + 37
PROVE: X = 11
Given: 4(2x-3) + 16 = 5x + 37
Prove: x = 11
STATEMENT
REASON
1. 4(2x-3) + 16 = 5x + 37
Given
2. 8x – 12 + 16 = 5x + 37
Distributive Property
3. 8x + 4 = 5x + 37
Combined like terms
4. 8x + 4 – 4 = 5x + 37 - 4
Addition axiom
5. 8x = 5x + 33
Existence of additive inverse
6. 8x -5x = 5x + 33 – 5x
Addition axiom
7. 3x = 33
Existence of additive inverse
8. 1/3 (3x) = (33)1/3
Existence of multiplicative inverse
9. x = 11
Simplify
GIVEN: 7B – 25 = 2B
PROVE: B = 5
Given: 7b – 25 = 2b
Prove: b = 5
STATEMENT
REASON
1. 7b – 25 = 2b
Given
2. 7b – 25 + 25 = 2b + 25
Addition axiom
3. 7b = 2b + 25
Existence of additive inverse
4. 7b – 2b = 2b + 25 -2b
Addition axiom
5. 7b – 2b = 25
Existence of additive inverse
6. 5b = 25
Combine like terms
7. 1/5(5b) = 1/5 (25)
Existence of multiplicative
inverse
Simplify
8. b = 5
FIGURE IT OUT
2 (-a + 5) = (2)(-a) + (2)(5)
2/5 . 1 = 2/5
(X + 5)+2 = X+(5+2)
¼(4X) = X
( x + y) + z = z + (x+ y)
FIGURE IT OUT
2 (-a + 5) = (2)(-a) + (2)(5)
DISTRIBUTIVE PROPERTY
2/5 . 1 = 2/5
EXISTENCE OF MULTIPLICATIVE IDENTITY AXIOM
(X + 5)+2 = X+(5+2)
ASSOCIATIVE AXIOM
¼(4X) = X
EXISTENCE OF MULTIPLICATIVE INVERSE
( x + y) + z = z + (x+ y)
COMMUTATIVE AXIOM
1. _______________ ARE TERMS THAT DO NOT HAVE CONCRETE DEFINITION
BUT CAN BE DESCRIBED. ON THE OTHER HAND, 2. ______________ REQUIRE
DEFINITION. THERE ARE STATEMENTS ASSUMED TO BE TRUE EVEN WITHOUT
PROOF WHICH WE CALLED AS AXIOMS OR POSTULATES. HOWEVER, THE
TWO HAS DISTINCTION IN SUCH A WAY THAT 3.____________ ARE OFTEN
USED IN GEOMETRY WHILE THE 4. ___________ ARE USED IN ALL AREAS OF
MATHEMATICS. WHEN THE STATEMENT SHOWS EVIDENCES OR PROVEN TO
BE TRUE, WE CALL IT AS 5. _________________.
UNDEFINED TERMS
DEFINED TERMS
AXIOMS
POSTULATES
THEOREMS