Algebraic Fractions (Addition and Subtraction)

 

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In today’s Mathematics class, We will be discussing  Algebraic Fractions. We hope you enjoy the class!

 

Content

  • Equivalent Fractions
  • Addition and Subtraction of algebraic fraction
  • Fractions with brackets

 

Equivalent fractions classnotes.ng 

Equivalent Fraction

Equivalent fractions can be made by multiplying or dividing the numerator and denominator of a fraction by the same quantity.

For Example:

Multiplication

3d = 3 × 2bd × 2b = 6b2bd

Division.

4x6y = 4x ÷ 26y ÷ 2 = 2x3y

 

Complete the following :

(a) 

3a2 = 10

   (b)

5ab12a = 12

Solution:

(a) 3a2 = 10Compare the two denomination2 × 5 = 10 The denominator of the first  has been multiplied by 5The numerator can also be multiplied by 5 3a2 = 3a × 52 × 5 = 15a10

 

(b) 5ab12a = 12The denominator of the first has been divided by aHence, divide the numerator by a.   5ab12a = 5ab ÷ a12a ÷ a = 5b12

 

Evaluation: 

  1. 8b5 = 15
  2. 9ah6ak = 3h
  3. 8yz = 3x8y

 

 

Addition and Subtraction of algebraic fractions

Algebraic fractions must have common denominators before they can be added or subtracted.

Example: 

(a) 52a+72a   (b)  4a + b(c) 1u + 1v    (d) 54c  43d

 

Solution:

(a) 52a + 72a = 5+72a = 12 ÷ 22a ÷ 2 = 6a

 

(b) 4a + b = 4a + b1The L.C.M of a and 1 is a 4a + b1 = 4a + aba= 4 + aba

 

(c) 1u+1vThe L.C.M of u and v is uvHence, 1u+1v = 1×v + 1×uuv = 1×vuv + 1×uuv= v uv+ uuv = v+uuv

 

(d) 54c  43dThe L.C.M of 4c and 3d is 12cd54c  43d = 5×3d12cd  4×4c12cd= 15d12cd  16c12cd= 15d  16c12cd

 

Evaluation

Simplify the following:

(a) 

43a 13a

(b) 

54a  23b

(c) 

2b + 34

 

Fractions with brackets

Examples

Simplify:

(a) 

x+35 + 4x  25

(b) 

7a  36  3a + 54

 

Solution:

(a) x+35 + 4x  25 = x + 3 + 4x  25= x+3 + 4x 2 5= 5x + 15

 

(b) 7a  36  3a + 54The L.C.M of 6 and 4 is 127a  36  3a + 54 = 27a32×6  33a +53×4= 2(7a  3)12  3(3a+5)12= 14a  6  9a  1512collecting like terms = 14a  9a 61512  = 5a2112

 

 

 

 

 

 

Evaluation

Simplify the following

(a)

2a  32 + a+42

(b) 

3x  2d10 + 2c  3d15

(c) 

2a + 3ba + a4b6

 

Weekend Assignment

  1. if 312a = ?4a find ?  (A) 0    (B) 1   (C) 3
  2. Simplify 
    1x1y    (A) x+yxy (B) yxxy (C) xyxy (D) y+xxy
  3. if 2ca = 6c2?  find ?    (A) 3c   (B) 3ac   (C) 3a   (D) 2c
  4. Simplify 4xa + 8xa  (A) 32xa   (B) 4x3  (C) 12x18 (D) 4xa
  5. 78y + 98y   (A) y2  (B) 8y3  (C) y8  (D) 2y

 

THEORY

  1. Simplify 54a  23b
  2. Simplify 2a + 3b7 + 9  4b6

 

 

 

We have come to the end of this class. We do hope you enjoyed the class?

Should you have any further question, feel free to ask in the comment section below and trust us to respond as soon as possible.

In our next class, we will be talking about Simple Algebraic Equations. We are very much eager to meet you there.

 

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