Page 175 - Maths Class 06
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17. From the figure, find the value of a
4a + 3 cm
D C
2a + 1 cm
A B
Perimeter = 10a + 12 cm
At a Glance
l Algebra is a branch of Mathematics in which letters (characters of the English alphabet) are used to
represent a number. Any letter can represent an unknown quantity which can take different values.
Since letters stand for numbers, the four fundamental operations, i e. ., +, –, × and ÷ can be performed
on them as on numbers.
l A statement of equality which involves one or more variables is called an equation.
l An equation involving only one variable with its highest power 1 is called a linear equation in one
variable.
l While solving an equation we can:
add the same number to both sides of the equation;
subtract the same number from both sides of the equation;
multiply both sides of the equation by the same non-zero number; and
divide both sides of the equation by the same non-zero number.
l In an equation, we can drop a term from one side and put it on the other side with the opposite sign.
This process is known as transposition.
l When + ve term transfer to other side it becomes –ve term and when –ve term transfer to other side it
becomes + ve term.
l In trial and error method, we often make a guess of the solution of the equation.
l If letters are used to denote numbers, they are called literals. Literals are usually variables as they can
take different values. Literals obey all the rules of fundamental operations.
l The quantities with fixed numerical values are called constants.
l Variables are quantities that can take any value.
l If a letter is repeated ‘n’ times in a pattern, then we can obtain an algebraic expression in ‘n’ giving us
the number of matchsticks or line segments required to make it.
l Variables allow us to express various rules and properties in a general way. Variables also help us to
solve practical problems.
l An algebraic expression is a combination of variables and constants using all or some of the
fundamental operations.
l An equation is a condition on a variable which is satisfied by a definite value of a variable. The value of
the variable which satisfies the given equation is its solution.
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