CLASS 6 MATHEMATICS CHAPTER 9(PART-2)
TERMINOLOGY ASSOCIATED WITH ALGEBRA Constants and variables In algebra, we use two types of symbols-constants and variables. Constants-A symbol which has a fixed value is called a constant.
Thus, each of 7, -3, 0, etc. , is a constant.
Variable A symbol (or letter) which can be given various numerical values is called a variable. Thus, a variable is a number which does not have a fixed value. Variable are generalised numbers or unknown numbers. As variables are usually denoted by letters, so variables are also known as literal (or literal numbers).
ALGEBRAIC EXPRESSIONS:- A collection of constants and literals connected by one or more of the operations of addition, subtractions, multiplication and division is called an algebraic expression. TERMS OF ALGEBRAIC EXPRESSION:- The various parts of an algebraic expression separated by + or - Sign are called the terms of the algebraic expression. CONSTANT TERM:- The term of an algebraic expression having no literal is called its constant term. PRODUCT:- When two or more constants or literals (or both) are multiplied, then the result so obtained is called the product. FACTORS:- Each of the quantity (constant or literal) multiplied together to form a product is called a factor of the product. A constant factor is called a numerical factor and other factors are called variable (or literal) factors. COEFFICIENTS:- Any factor of a (non constant) term of an algebraic expression is called the coefficient of the remaining factor of the term. In particular, the constant part is called the numerical coefficient or simply the coefficient of the term and the remaining part is called the literal coefficient of the term. LIKE AND UNLIKE TERMS:- The terms having same literal coefficient are called like terms, otherwise, the terms are called unlike terms. TYPES OF ALGEBRAIC EXPRESSIONS:- Some algebraic expressions have only one term while some other expressions have more than one terms. Various types of algebraic expressions are: MONOMIAL:- An algebraic expression having only one term is called a monomial. BINOMIAL:- An algebraic expression having two terms is called binomial. TRINOMIAL:- An algebraic expression having three terms is called trinomial. MULTINOMIAL:- An algebraic expression having two or more than two terms is called multinomial. POLYNOMIALS IN ONE VARIABLE:- An algebraic expression containing one variable is called a polynomial in that variable if the powers of the variable in each term are non negative integer. Thus, an algebraic expression of the form a + bx + c +d +...... Where a, b, c, d,...... are constants and x is a variable, is called a polynomial in the variable X. The greatest power of X present in the polynomial is called the degree of polynomial. EXAMPLES:- 1- Write down the algebraic expressions whose terms are (a) 3a, -4b, 7c
(b) 5 , -2 , - , 8
SOLUTION:- (a) 3a-4b+ 7c
(b) 5 -2 - + 8
2- Identify monomials , binomials and trinomials from the following algebraic expressions (a) - 3 (b) 9 - 5 + 7 (c) 2x-3 (d) Pq + rst (e) -5 + ab + bc + ca
SOLUTIONS:- (a) As the given expression has only one term , it is a monomial (b) As the given expression has not only three terms it is a trinomial. (c) As the given expression has two terms it is a binomial. (d) As the given expression has two terms it is a binomial. (e) As the given expression has four terms it is a multinomial.
3- Raja scored 30 marks in math , X marks in science and Y marks in English. What is his total score in these three subjects?
SOLUTIONS:-
Score in maths = 30 Score in science= X Score in English= Y Therefore, total score in these three subjects = 30 + X + Y
4- The length of a rectangular hall is 5 meter less than 3 times the breath of the hall. What is its length, if the breath is b metres? SOLUTIONS:-
Breath of the hall = b metres As the length of the hall is 5 metres less than 3 times the breath of the hall , its length = (3×b – 5) metres = (3b-5) metres 5- If meera’s presented age is X years , determine: (a) Meera’s age 5 years from now (b) Meera’s age 3 years ago. (c) Meera’s grandfathers age which is 6 times her age. (d) Meera’s grandmother is two years younger than her grandfather. What is grandmothers age? (e) Meera’s fathers age is 5 years more than 3 times her age. What is her father’s age? SOLUTIONS:- Meera’s present age is X years (a) Meera’s age 5 years from now = (X + 5) years (b) Meera’s age 3 years ago = (X-3) years (c) Meera’s grandfathers age = 6X years (d) Meera’s grandmothers age= (6X – 2) years (e) Meera’s father age = (3X + 5) years
Exercise 9.3
1- Write all the terms of each of the following algebraic expressions: (a) 3 – 7x
(b) 2 – 5a + b
(c) 3 + 4 - 7 + 3
(d) 2 - + + 9
2- Write down the algebraic expression whose terms are: (a) 5, -2x (b) -3, 5 , -7 (c) , - 2 , 3 , 7 3- State the number of term in each of the following algebraic expressions: (a) x÷2 + y-3
(b)
(c) 5×ab-7 (d) 7×a+b÷3-c+5 4- Identify monomials, binomials and trinomials from the following algebraic expressions: (a) (b) (c) 5+5x (d) 5x
(e) +3
(f) (g) - - + 5abc (h) (i) + (j) (k) 5p ×ab (l) 3÷a - 2×b+c 5- Write down the numerical as well as literal coefficient of each of the following monomials: (a) -7x (b) -2 (c) 6abc 6- Write the numerical coefficient of each term of the expression:
- 5x +7 - x -
7- In – 7x , write down the coefficient of (a) X (b) 7x (c) -x (d) Xy (e) (f) (g) (h) 7y 8- In the following , which pairs contain like terms? (a) 5x, -2x (b) 5x, 5y (c) -2xyz, -3 (d) 10xyz , -10xyz (e) 2 (f) 2xy, -3yx (g) X, (h) 6,6x (i) 2xy, 3xyz 9- Identify which of the following algebraic expressions are polynomials. If so , write their degrees:
(a) - x –
(b) 3 -3
10- Which out of the following are expressions with numbers only? (a) 2y + 3 (b) (7×20)-8z (c) 5×(21-7)+9×2 (d) 5-11n 11- Write expression for the following : (a) 11 added to 2 m (b) 11 subtracted from 2 m (c) 3 added to 5 times y (d) 3 subtracted from 5 times y (e) Y is multiplied by -8 and then 5 is added to the result (f) Y is multiplied by 5 and then the result is subtracted from 16 12- Write the following in mathematical form using signs and symbols: (a) 6 more than thrice a number x (b) 7 taken away from y (c) 3 less than quotient of x by y 13- Form six expressions using t and 4.use not more than one number operation and every expression must have t in it. 14- A student scored x marks in English but the teacher deducted 5 marks for bad handwriting. What was the students final score in English? 15- Raju’s fathers age is two years more than 3 times Raju’s age . if Raju’s present age is y years, then what is his fathers age? 16- Mohini is x years old. Express the following in algebraic form. (a) 3 times Mohini’s age next year (b) 4 times Mohini’s age three years ago (c) The present age of mohini’s uncle, if her uncle is five times as old as Mohini will be 2 years from now. 17- A bus travels at v km per hour. It is going from delhi to jaipur. After the bus has travelled five hours , jaipur is still 20 km away. What is the distance from delhi to jaipur?