th Class 7 Subject: Maths Topic: Numerical and Literal coefficient (Repeated topic of class 6th) Recap (Worksheet 1)

Meaning of coefficient: An algebraic term is written as product of two or more factors. Each factor is multiplying the remaining factors and each factor is known as coefficient of remaining factors. For eg. 1. 4ab: we write it in product form 4 x a x b So, coefficient of 4 = ab coefficient of a = 4b 2. -8 p2q2 : we write it in product form -8 x p2 x q2 So, coefficient of -8 = p2q2 coefficient of q2 = -8p2

Now we learn to separate Numerical and Literal coefficient. Numerical coefficient: A numerical factor that multiplies another factor in a term is called a Numerical coefficient. It is any constant term that is in front of one or more variables in a expression. For eg. 1. 3bc: 3 x b x c

Numerical coefficient variables (Constant)

2. -2mn: -2 x m x n It means 3 and -2 are numerical coefficient. 3. abc: It displays no any , so its factor is 1. So numerical coefficient is 1. 4. -7 x2y: It displays two -7 and 2 but 2 is an exponent and not a multiplying factor. So -7 is a constant and it is numerical coefficient of -7 x2y. 5. – 5ab2 = It displays constant term in fraction. −ퟓ 3 so numerical coefficient will be = ퟑ Literal coefficient: A factor which contains at least one letter, in product form of a term is called a literal coefficient of the remaining factor. For eg. 1. 4a2xy: 4 x a2xy , 4 is a number and a2xy has three letters a, x, y. So, a2xy is called Literal coefficient.

2. -7mnp: -7 x mnp, Literal coefficient is mnp. 2 2 Sample Sums

TERM NUMERICAL LITERAL COEFFICIENT COEFFICIENT yz 1 yz

-2abc -2 abc

-8x2y2z2 -8 x2y2z2

7pqr3 7 pqr3 6 6 -2ab -2 ab C c

Related Sums • Write down numerical as well as literal coefficient of each:

1. abc 2. 6mn 3. -4xyz 4. 9p2q2r 5. 2mn2 6. -6ab2 7 7. 5abc2 8. 8pq r

Class 7th Subject: Maths Topic: of (Repeated topic of class 6th) Recap (Worksheet 2) Addition of Monomials: • A is an algebraic expression that consists of one term. For eg. 3xy, 4abc, -7xyz. • Two or more monomials can be added only if they are Like Terms. Unlike terms can’t be added. • Like Terms are terms that have exactly the same and Exponents on those variables. The constants on like terms may be different either positive or negative. Constant 7 x2 Exponent

Variable For eg. : 7xy and -8xy, 9p2q2 and -5p2q2 are like terms • 5x2y2 and -4x2y4 are unlike terms because exponents are not same.

Now we recall the integers rules of addition:

+ , + Sign of + Add the numbers - , - Sign of - Add the numbers +, - Sign of bigger Subtract the term numbers.

To add two or more monomials: 1. Arrange the like terms in columns. 2. Add the numbers with integers rules. 3. Write the variables and their powers same.

Sample Sums Add: Q: 1 7xy and 9xy Sol. +7xy +9xy 16xy

Q: 2 -5a2b2 , 6a2b2 Sol. -5 a2b2 +6 a2b2 (if no sign then + sign) +1 a2b2

Q: 3 -10 abc2 , 8abc2 , 7abc2 first add like signs Sol. -10 abc2 +8 +8 abc2 +7 +7 abc2 +15 +5 abc2 then unlike signs + 15 - 10 + 5

Q: 4 -7x2, x2, 4x2, -5x2 Sol. -7x2 first add like signs +1x2 +1 -7 +4x2 + 4 -5 -5x2 + 5 -12 - 7x2 then unlike signs -12 +5 -7

Related Sums: Add the following expressions: 1. 7y, 8y 2. 8abc, 3abc 3. -4xyz, +9xyz 4. 6x2y2, -7x2y2 5. -4p3q3, -3p3q3, +5p3q3 6. 2a2b4, -4a2b4, 7a2b4 7. -3x, -5x, 6x, 9x 8. 6ab, -8ab, -3ab, 4ab

Class 7th Subject: Maths Topic: Addition of binomials (Repeated topic of class 6th) Recap (Worksheet 3) Addition of Binomials. • A binomial is an algebraic expression that consists of two terms. For eg. 5x + 3z, -4a2+ 6b2 • Two or more terms can be added only if they are Like Terms.

Now we recall the integers rules of addition:

+ , + Sign of + Add the numbers - , - Sign of - Add the numbers +, - Sign of bigger Subtract the term numbers.

Rules to add binomials:

1. Arrange the terms of the given expression in same order. 2. Arrange the given expressions in the form of rows in such a way that the like terms occur in the same column. 3. Add the like terms column wise. (with integers rules)

Sample Sums

Q: 1 Add: 6a + 4b, 7a – 3b Sol. +6a + 4b (Apply integers rules) +7a – 3b +13a + 1b

Q: 2 Add: -7a2 + 6b, 9a2 – 2b, -4a2 + 5b Sol. - 7a2 + 6b first add like signs + 9a2 – 2b -7 +6 - 4a2 +5b -4 +5 - 2a2 + 9b -11 +11 Now unlike signs -11 +11 +9 - 2 -2 +9

Related Sums

Add the following expressions: 1. 7a + 9b, 8a -4b 2. -3x + 5y, 6x – 10y 3. 8p – 3q, -7p -2q, -9p + 4q 4. 10a -2b, +7a +4b, -3a + 6b