Abbreviations in algebra

Introduction:

 Abbreviations in algebra are used to represent the shortcut terms in mathematics.Algebra is one of the most important branches in mathematics. An algebraic expression is a collection of algebra termssuch as variables; constants. Algebra performs operations such as polynomial equations, addition, multiplication, subtraction, functions, solving factorization and linear equations. Unknown numbers are represented by using letters (alphabets).


Basic abbreviations in algebra:



Examples for abbreviations in algebra:


Example1:

What number plus 5ml makes 17ml?

Solution:

  x + 5 = 17

      = 17 - 5

  x = 12ml


Example 2:

To add two algebraic expression (x2 + 3x +7) & (3x3 + 5x + 17) 

Solution:

(x2 + 3x +7) + (3x3 + 5x2 +17x + 23)

= 3x3 + (x2+5x2) + (3x+17x) + (7+23)

= 3x3 + 6x2 + 20x+30

The Answer is 3x3 + 6x2 + 20x+30


Example3:

How many liters in 12kiloliters?

Solution:

Given 12 kiloliters

1 kiloliter="1000liters

  =12*1000

  =12000liter


Example4:

Ina jug contains 40l of milk, in these 4l of water to be replaced insteadof 4l of milk in a jug. If the process repeatedly occur in two times then how much milk in jug?

Solution:

 x = 40 lit, y="4lit," n="3

= x (1-(y/x)) n

= 40(1-(4/40)) 3

= 40(36/40) 3

= 40*(36/40)*(36/40)*(36/40)

= 29.16 liter

40l mixture has 29.16 liter milk


Example5:

In a bucket contains 20 lit of honey, among these 5 lit of milk to be replaced instead of 5 lit of honey in ajug. If the process repeatedly occurs in four times then how much literhoney in jug?

Solution:

 x = 20 lit, y="5lit," n="5

= x (1-(y/x)) n

= 20(1-(5/20)) 5

= 20(15/20) 5

= 20*(15/20)*(15/20)*(15/20)*(15/20)*(15/20)

= 4.764 liter

20l mixture has 4.764 liter honey


Practice problems for abbreviations in algebra:


1)In a jug contains 10l of milk, in these 4l of water to be replaced instead of 4l of milk in a jug. If the process repeatedly occurs in one time then how much milk in jug?

Answer: 3.6 lit


2) How many liters in 2.25kiloliters?

Answer: 2250 lit