Ch.3 Algebraic Fraction and Formulas

1. Chapter 3
Algebraic Fraction and
Formulars
組員：蔡敬霈（5）
羅力恆（6）
楊曉泓（8）
羅祖耀（9）
李啟駿（12）
梁啟章（13）

2. Definition
 Both numerator and denominator are polynomials. Denominator
contain variable（未知數）
x + y
x
x + y x
 Note： 不可約
 Because and are not the same.

3. Multiplication of Algebraic Fractions
 In multiplication of fractions, we
multiply the numerators and
denominators separately to get
the product.
 Example:3
5
´
7
4
=
3´7
5´ 4
=
21
20
 The same method can be
applied to the multiplication of
algebraic fractions.
 Example:
a
c
´
c
d
=
a ´ c
b´ d

4. Division of Algebraic Fractions
 The principle of division of algebraic fractions is the same as that of
fractions.
 Example:
a
b
¸
c
d
=
a
b
´
d
c
=
a ´ d
b´ c
=
ad
bc

5. Addition of Algebraic Fractions
 For algebraic fractions, if the denominators are the same, we can
perform the addition directly in the same way.
 However, if the denominators of the algebraic fractions are not the
same, we have to find lowest common multiple (L.C.M.) of the
denominators first.
 Example:
4x
+
7y
x
7y
=
4x + x
7y
=
5x
7y

6. Subtraction of Algebraic Fractions
 For algebraic fractions, if the denominators are the same, we can
perform the subtraction directly in the same way.
 However, if the denominators of the algebraic fractions are not the
same, we have to find lowest common multiple (L.C.M.) of the
denominators first.
 Example:
3a
-
5b
a
5b
=
3a - a
5b
=
2a
5b

7. Formula
h
b
A = BH
If B = 4, H = 6
A = BH
= 4 X 6 = 24
In fact, when the values of two
variables are given, the values of
the remaining variable is fixed and
can be found by substitution.

8. Formula
 Example:
V = IR, I = 2 R = 110 V
 Given a formula if and , find the value of .
Solution
I = 2 R =110 V = IR,
 When and ,
= 2´110
= 220

9. Change of Subject