Algebra Process JSS1 Mathematics Lesson Note

Algebra Process

Algebra is the branch of mathematics in which letters of the alphabet and symbols are used in place of numbers.

We can use any shape to represent our letter in order to interpret the sentence very well. 

Examples: 

Find the missing numbers that make the following open sentence true:

1.       +  7 = 14

2. + 8= 14

3. 12 ÷ =  3

4. 30 = –  9

Solution:

1. 14 – 7 = 7 [the statement is true] (7 moves to the right-hand side and the sign changes to a negative sign).
2. 14- 8 = 6 [the statement is true]( 8 moves to the right hand side  and the sign changes to negative sign).
3. 12 x 3 = 36 [the statement is true] 12 moves to the right-hand side and the sign changes to a multiplication sign.
4. 30 + 9 = 40 [the statement is true]( 9 moves to the left hand side  and the sign changes to positive sign).

EXERCISE:

1. 8 X 7 =             
2. 53 = 12 +           
3. 121 ÷11 =            
4. —- + 42 = 80

USING LETTERS TO REPRESENT NUMBERS

It is more convenient to use a letter of the alphabet to represent an unknown number instead of shapes.

The statement ʠ + 7 = 12 is called an algebraic sentence or equation. It means ʠ plus seven equals twelve. Thus for the sentence to be true, we must add 5. 

Examples: 

Find the value of each letter that will make the following sentences true.

1. B = 8 + 6
2. S x 3 = 18
3. F = 6 x 7
4. P = 25 + 37
5. 40 – x =X 

Solution:

1. B = 8 + 6 = 14. Therefore B = 14
2. S x 3  = 18 , 18 / 3 = 6. Therefore 6 x 3 = 18
3. F = 6 x 7 = 42. Therefore F = 42
4. P = 25 + 37 = 62. Therefore P = 62
5. 40 – x = x , = 40 = x + x

= 40 = 2x [divide both sides by 2]

40/2 = 2x/2

20 =x

Therefore x = 20.

SUBSTITUTING NUMBERS

The value of an expression such as x+ 3 can be found by replacing x with a given number. This is called substitution.

EXAMPLES:

1. Find the value of x – 9 if  (i) x = 23, (ii) x = 15
2. Find the value of y + 10 when y is 20
3. Find the value of t + 19 when t is 45.

Solution:

1. X – 9 = when x = 23; 23 – 9 = 12.
2. Y + 10 = when y is 20 ; 20 + 10 = 30
3. t + 19 = when 45 + 19 = 64

USING ALGEBRA FOR SOLVING WORD PROBLEMS

NOTE: Remember that you can use any letters of the alphabet to represent an unknown number.

Examples:

1. What number when added to 8 gives 20?
2. Think of a number subtract 5 from it and the result is 15. What is the number?
3. when a number is multiplied by 5 the result is 20. What is the number?

Solution:

1. let x be the number you add to 8 to give 20.

X + 8 = 20

Subtract 8 from both sides 

X + 8 – 8 = 20 – 8

X = 12

2. Let the number be y

Y – 5 = 15

Add 5 to both sides

Y – 5 + 5 = 15 + 5

Y = 20

3. Let Z be the number you multiply by 5 to get 20

Z X 5 = 20 [note that when the multiplication sign moves other side it turns      to division]

Z = 20/5

Z = 4 [this statement is true.

EVALUATION: 

1. A boy has y number of pencils. He gave 3 to his brother and 2 to his sister. How many pencils has he left?
2. Mrs Elizabeth bought M exercise books yesterday, she bought 5 others today. If she has 20 books altogether, how many exercise books did she buy yesterday?
3. 169 / X = 13
4. Y – 42 + 2Y + 60