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Factorization Class 8 ICSE

  Factorization :   The process of writing an algebraic expression as the product of two or more expressions is called factorization or the resolution of the given expression into its factors. Factorisation Of An Expression By Taking Out The Common Factor : Factorize : 1 . 6xy - 4xz = 2x(3y - 2z) 2. 9b x² + 15 b²x = 3bx(3x + 5b) 3. 4 a²b - 6a b² + 8ab = 2ab(2a - 3b + 4) 4. 5 x² + 15 x 3  - 20x = 5x (x + 3 x² - 4) 5. 2 x 3  +   x² - 4x = x (2 x² + x - 4) 6.  a 3 b -  a² b² -  b 3   = b( a 3 -  a² b  -  b² ) 7. 28 a² b²c - 42 a b² c² = 14a b² c(2a - 3c) 8.  15x ²y  - 6xy ²  + 9y 3  = 3y( 5 x² - 2 xy + 3y ²) 9. 10x ²y +  15xy ² - 25x ²y ² = 5xy(2x + 3y - 5xy) 10. 18 x ²y - 24xyz = 6xy(3x - 4z) 11. 27 a 3 b 3  - 45 a 4 b 2  =  9 a 3 b 2 (3b -5 a ) 12. 4(a + b) - 6(a + b) 2  = 2(a + b) (2 - 3(a + b)) = 2(a + b) ( 2 - 3a - 3b) 13. 2a(3x + 5y) - 5b(3x  + 5y) = (2a - 5b) (3x + 5y) 14. 2x (p ² + q ²) + 4y  (p ² + q ²) = (2x + 4y)  (p ² + q ²)                                                   = 
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Division Of Rational Numbers Class 8

 Properties Of Division of Rational Numbers

 Property 1 : Closure Property : If a/b and c/d are any two rational numbers such that c/d ≠0, then(a/b ÷ c/d)  is also a rational number.

Example : Consider the rational numbers -3/40 and 11/24. 

-3/40 ÷ 11/24 = -3/40 * 24/11 = -72/440 = -18/110, which is also rational.

Property 2 : For any rational number a/b, we have :

                     (a/b ÷ 1) = a/b.

Example : 5/7 ÷ 1 = 5/7 ÷ 1/1 = 5/7 *1/1 = 5/7

Property 3 : For any non-zero rational number a/b, we have :

                      (a/b ÷ a/b ) = 1

Examples : 5/6 ÷ 5/6 = 5/6 *6/5 = 30/30 = 1


1. Find the quotient :

i) 17/8 ÷ 51/4

ii) -16/35 ÷ 15/14

iii) -12/7 ÷ (-16)

iv) -9 ÷ (-5/18)


2. Divide the sum of 13/5 and -12/5 by the product of -31/7 and 1/-2.



3, Divide the sum of 65/12 and 8/3 by their difference.


4. The area of room is 651/4   sq. metres. If its breadth is  51/16 metres, what is its length?




12





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Class 8 Rational Numbers

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Multiplication of Rational Numbers Class 8

  Multiplication of Rational Numbers Class 8 Properties of Multiplication of Rational numbers Property 1 : Closure Property : The product of two rational numbers is always a rational number                       Example : -2/9 and 15/4 are rational numbers.                                          -2/9 * 15/4 = -30/36 = -5/6                                                                                which is also rational number. Property 2 : Commutative Law : If a/b and c/d are any two rational numbers,                                                          then (a/b)*(c/d) = (c/d)*(a/b)                       Example : -36/25 * -15/28 = -15/28 * -36/25 Property 3 : Associative Law : If a/b, c/d, and e/f are three rational numbers,                                                       then  (a/b * c/d)*e/f = a/b * (c/d * e/f)                      Example : 2/5, -5/12 and -7/15 are three rational numbers                                        (2/5 * -5/12) * -7/15 = 2/5 * (-5/12
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Factorization Class 8 ICSE

  Factorization :   The process of writing an algebraic expression as the product of two or more expressions is called factorization or the resolution of the given expression into its factors. Factorisation Of An Expression By Taking Out The Common Factor : Factorize : 1 . 6xy - 4xz = 2x(3y - 2z) 2. 9b x² + 15 b²x = 3bx(3x + 5b) 3. 4 a²b - 6a b² + 8ab = 2ab(2a - 3b + 4) 4. 5 x² + 15 x 3  - 20x = 5x (x + 3 x² - 4) 5. 2 x 3  +   x² - 4x = x (2 x² + x - 4) 6.  a 3 b -  a² b² -  b 3   = b( a 3 -  a² b  -  b² ) 7. 28 a² b²c - 42 a b² c² = 14a b² c(2a - 3c) 8.  15x ²y  - 6xy ²  + 9y 3  = 3y( 5 x² - 2 xy + 3y ²) 9. 10x ²y +  15xy ² - 25x ²y ² = 5xy(2x + 3y - 5xy) 10. 18 x ²y - 24xyz = 6xy(3x - 4z) 11. 27 a 3 b 3  - 45 a 4 b 2  =  9 a 3 b 2 (3b -5 a ) 12. 4(a + b) - 6(a + b) 2  = 2(a + b) (2 - 3(a + b)) = 2(a + b) ( 2 - 3a - 3b) 13. 2a(3x + 5y) - 5b(3x  + 5y) = (2a - 5b) (3x + 5y) 14. 2x (p ² + q ²) + 4y  (p ² + q ²) = (2x + 4y)  (p ² + q ²)                                                   = 
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