# Lesson Notes By Weeks and Term - Junior Secondary School 1

ALGEBRAIC PROCESSES

SUBJECT: MATHEMATICS

CLASS:  JSS 1

DATE:

TERM: 2nd TERM

REFERENCE BOOKS

• New General Mathematics, Junior Secondary Schools Book 1
• Essential Mathematics for Junior Secondary Schools Book 1

WEEK NINE

TOPIC: ALGEBRAIC PROCESSES

Content

1. Identification of coefficient of terms
2. Collection and simplification of like terms
3. Multiplication and division of algebra
4. Use of brackets in algebra.

• Identification of Coefficients of Terms

Consider the following algebraic expression: 8x + 2y – 4p. The letter x, y, and p are called variables while the numbers 8, +2 and -4 are called coefficients.

Variables: a variable is a letter used to represent a number.

Coefficient: A coefficient is a number place before a variable or a group of variables.

Example:

Write out the variables and coefficients of the following:

1. –  12x + 5y – z      - 12x (- 12 is the coefficient, x is the variable)

+ 5y ( +5 is the coefficient, y is the variable)

-z ( -1 is the coefficient, z is the variable)

1. –p3 + q2r – 7          -p3 ( -1 is the coefficient, p3 is the variable)

+q2r ( q2r are variables)

-7 (no variables and therefore no coefficient, -7 is a constant)

• Collection and simplification of like terms

Like terms are terms that have same letter or arrangement of letters. For instance, a + 3a – 2a are like terms.

Unlike terms are terms which do not have the same letter or arrangement of letters, for instance, 2a + 3b are unlike terms.

Example

Simplify the following (a) 12b – 5b  (b) 16x + x +x +2x  (c) 20x -6x-x- 3x + 2x

Solution

1. 12b – 5b

Subtract the coefficients: 12 – 5 = 7

Therefore, 12b – 5b = 7b

1. 16x + x + x +2x

Add all their coefficients: 16 + 1 + 1 + 2 = 20

Therefore, 16x +x +x + 2x = 20x

1. 20x – 6x – x – 3x + 2x
2. Rearrange: 20x + 2x – 6x -3x –x

Rearrange: 20x – 10x = 12x

Evaluation:

Simplify the following:

1. 7x + 4x + 3x + 6x  (2) 3w -6w – w + 18w  (3) – 18b – 2b + 40b + 10b – 5b

MULTIPLICATION AND DIVISION OF ALGEBRA

Example

1. 2pqr = 2 x p x q x r
2. 2 x 3a = 2 x 3 x a = 6 x a = 6a
3. 3p x 5q x 2r = 3 x p x 5 x q x 2 x r = 3 x 5 x 2 x p x q x r = 30pqr
4. 16ab 2ab = 16ab2ab = 16× a ×b2×a ×b = 8
5. 25pqr2 5qr = 25× p ×q ×r22×a ×b = 5pr

Evaluation

Simplify the following: (a) 3y3z ÷ y2z   (b) 5x2m x2n    (c) 27 of 21xy2    (d) 7abc 14ab

Use the brackets in Algebra

BODMAS

B- Brackets ( )

O- of

D- Division ()

M- Multiplication (x)

S- Subtraction (-)

Examples: Simplify the following using bodmas

1. 18a + 12a – 8a – ( 15a -2a)
2. 12 of ( 9-5) + 7 – 3 x 6
3. 28x ÷ 2 + ( 8x + 4x) + 6

Solution

1. 18a + 12a – 8a – ( 15a – 2a)

Applying bodmas, let’s solve the terms in the bracket. ( 15a – 2a) = 13a

18a + 4a – 13a

Since there is no ‘of ’, the next is addition 18a + 4a = 22a

Therefore, 22a – 13a = 9a

1. 12 of ( 9-5) + 7 – 3 x 6

Using BODMAS

12 of 4 + 7 – 18

2 + 7 – 18 = -9

1. 28x ÷ 2 + ( 8x + 4x) + 6

Solve the terms in the bracket, 8x + 4x = 12x

28x 2 + 12x 6

Solve the division

14x + 2x = 16x

Evaluation

1. 6 + ( 7x – 3x ) 2
2. 0.5x + x 2
3. 6 ×5x-3x×0+6x ÷2

REMOVING BRACKETS

There are cases where the terms in a bracket cannot be simplified immediately until the bracket is removed. The sign rule is applied in such a situation.

RULES:

1. If a positive sign comes before the bracket, the signs in the bracket remain the same when the bracket is removed. For instance, 2p + ( 8p – 3z) = 2p + 8p – 3z = 10p – 3z
2. If a negative sign comes before the bracket, the signs in the bracket will change as the bracket is being removed. For instance, 12x – ( - 6x + 2y) = 12x + 6x – 2y = 18x – 2y.

Note that the negative sign (-) before the bracket multiplies everything in the bracket; (-) x ( -6x) = +6x and (-) x ( +2y) = -2y

Essential Mathematics JSS1 pages 156 – 159

General Evaluation

1. Olu bought x number of exercise books yesterday. Today he bought 5 more. How many exercise books has Olu now?
2. A man is x years old and his son is 10 years. (a) What is their total age?  (b) If the difference between their ages is 22 years, what is the value of x?
3. A boy gave 5 seeds to a friend from a certain number of seeds. How many seeds did he have now?
4. Dele is x years old. How old was he 7 years ago?

Weekend Assignment

• What is the coefficient of the variable x in the equation 4x – 3y + z (a) 1  (b) -3   (c) 4  (d) 5
• Simplify 6x2y 2y2x.  (a) 6xy  (b) 3xy   (c) 3xy   (d) 3y
• Simplify 5x×2y ×z   (a) 7xyz    (b) 10xyz  (c) 10xy  (d) 5xyz
• Simplify 2 x 9x + 12x 3. (a) 18x    (b) 22x   (c) 6x   (d) 15
• Simplify 7x – 6 – ( 2- x)  (a) 8x – 8    (b) 7x -8    (c) 7x + 12   (d)  8x – 4

Theory

1. A girl is x years old and her brother is 5 years older than her. (a) find the sum of their ages  (b) if their father is 25 years older than the  girl, what is the difference between the sum of the children’s ages and their father’s age?
2. The greater of two consecutive numbers ix x + 5. (a) find the sum of the two numbers (b) Find their difference  (c) subtract their sum from x + 12