Class 6 Maths Algebra Introduction

Introduction

Algebra is a branch of mathematics that uses letters. Letters allow us to write formulas, rules as well as define unknown quantities. Thus, these letters can represent variables. A variable means something that can vary and can change. The value of a variable that can satisfy an equation is called solution of the equation. For example: If two matchsticks are required to form the letter ‘L’, then we get the following rule:

(Letter ‘L’. As shown, 2 matchsticks are used to make one ‘L’)

Number of matchsticks required = 2n.

Here n is the number of Ls required to be made. So if one L uses two matchsticks, then 2 Ls will use 4 matchsticks. This is obtained by the following rule:

2n = 2(2) = 4.

Here n is a variable and we can put a number depending how many Ls we are required to make.

The use of variable can be further understood by solving some questions.

 

 

Problem : Find the rule which gives the number of matchsticks required to make the following matchsticks patterns. Use a variable to write the rule.  A pattern of letter as 

 

(Letter ‘U’)

Solution:

Number of matchsticks used to make one U = 3

Number of matchsticks required = 3n

Where n is the number of Us required to be made.

 

Problem : Leela is Radha's younger sister. Leela is 4 years younger than Radha. Can you write Leela's age in terms of Radha's age? Take Radha's age to be x years.  Leela and Radha

Solution:

Radha’s age =   x years

Leel is 4 years younger than Radha. Hence we can obtain Leela’s age by deducting 4 years from te age of Radha. So, we get :

Leela’s age = (x – 4) years

 

Problem: Oranges are to be transferred from larger boxes into smaller boxes. When a large box is emptied, the oranges from it fill two smaller boxes and still 10 oranges remain outside. If the number of oranges in a small box are taken to be x, what is the number of oranges in the larger box?

Solution:

Number of oranges in 1 small box = x

Number of oranges in 2 small boxes = 2x

Number of oranges still left = 10

Hence, number of oranges in the larger box = 2x + 10

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