# 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 EIGHT

TOPIC: ALGEBRAIC PROCESSES

CONTENT

1. Use of symbols open sentences with two arithmetic operators
2. Word problems involving the use of symbols

Use of symbols, solving open sentences with two arithmetic operators

Algebra is a branch of mathematics where alphabets and symbols are used to represent numbers.

The Use of Symbols

Consider the following mathematical expression.

1. 4 + 5 = 9. This statement is true
2. 5 – 6 = 15. This statement is not true
3. 4 x 5 = 20. This statement  is true.

If the number 5 in (i), (ii) and (iii) is replaced by a symbol ¥, we will have the following: 4 + ¥ = 9. The following value of the symbol ¥ can be obtained by subtracting 4 from 9, ¥ = 9- 4 = 5.

¥ - 6 = 15.

The value of the symbol can be obtained by adding 6 to both sides: ¥ = 15 + 6 =21.

4 x ¥= 20.

The value of the symbol ¥ can be obtained by dividing both sides  by 4; ¥ = 20/4 = 5

Evaluation:

Find the value of the symbol ¥ in the following:

1. ¥ + 7 = 14
2. 4 x ¥ = 44
3. ¥ + 6 = 8
4. 80 + ¥ + 5 = 15

The use of letters

It should be noted that in representing numbers with letters in algebra, small letters of alphabets are used. For instance, x + 8 = 14; subtracting 8 from both sides of the equation, we have, x = 14 – 8 = 6.

WORD PROBLEMS INVOLVING THE USE OF SYMBOLS.

Consider the following mathematical statements:

1. Add 5 to a certain number, ‘if the certain’for instance is represented by x, then this statement can be interpreted to be x+5
2. ‘’Add a certain number to 8. If the certain number is represented by a letter y,then this can be interpreted as 8+y.
3. ‘p years ago’ can be interpreted as ‘minus p’(-p)years.
4. ‘x years to come or x years time can be interpreted as plus x(+x)years time.
5. The word ‘is’, ‘gives’, ‘result to’, are interpreted to mean equals
6. ‘Double’ means 2 times or (x2)and thrice’ means (x3).
9. ‘The product’means multiplication

Example 1

A man is x years old and his son is 10 years old.(a)what is their total age? (b)if the difference between their ages is 22 years,what is the value of x?

Solution:

(a)The man’s age=x years

The son’s age=10 years.

The sum (addition)of their ages=x years +10 years=(x+10)years

(b)The difference between their ages, (x-10).

‘is’means equal to

X-10=22.

Add 10 to both sides of the equation.

X=22+10=32years

Example 2

Think of a number’add 5 to it, the result is 15.What is the number?

Solution:

Let the number be y.

‘add 5 to it’ means y+5.

‘the result is 15 means ‘=15’.

Therefore y +5=15, subtract 5 from both sides of the equation .y=15-5=10.

Example 3

A woman is three times as old as her daughter. If the woman is x years old, (a) how old is her daughter? (b) How old were they 7 years ago? (c) How old would the girl be in 15 years time?

Solution:

1. If the woman’s age is x years and she is three times the age of her daughter, then her daughter’s age will be x3 years.
2. ‘7 years ago’ means minus 7 or (- 7) years, the woman’s age be (x -7) while daughter’s age will be ( x-7)/ 3
3. ( x+15) years while the daughter’s age would be  x-73+ 15 years.

Evaluation:

1. Think of a number, double it, the result is 14. What is the number?
2. A man is three times old as his son. If the man’s age is x years, (a) How old is the son? (b) How old were they 3 years ago? (c) How old will the son be in y years time? (d) How old will the man be in 5 years’ time?

Essential Mathematics for JSS 1 Pages 68- 72

General Evaluation:

1. Find the value of each letter that will make the following sentences true.
1. 17 – 6 = x (b) n x n = 49   (c) 12 – x = 9    (d) x + x = 24.
1. Find the value of each of the following when x = 3.
1. x + 7     (b) x + 9   (c) x3 - 32

Weekend Assignment

1. Three subtracted from double a certain number divided by 6 can be interpreted as (a)  (3-2x)6  (b)  (3x-3)6   (c)  (2x-3)6   (d) ) ( 2-3x)6
2. What is the value of x in the equation x – 14 = 2?  (a) 20   (b) 16    (c)  9   (d)  24
3. Find the value of ‘a’ if 3 x a = 27 (a) 20   (b)  16   (c)  9   (d) 24
4. Find the value of x if 7 + x = 9. (a) 16  (b) 4   (c)  10    (d)  2
5. An SS3 student told a JSS1 student that he is the senior to him in age by 8 years. If the junior student is x years old, how old is the senior student? (a) 8x   (b) x + 8  (c) 8 –x   (d) 16

Theory

1. A man earns N 5000.00 in a month and his wife earns N z. If the couple earns N 9500 altogether in a month, what is the value of z?
2. Think of a number that when 10 is subtracted from it, the result is 8.