Algebraic process: Use of symbol

CONTENT

• Use of symbols open sentences with two arithmetic operators
• 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.

• 4 + 5 = 9. This statement is true
• 5 – 6 = 15. This statement is not true
• 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:

• ¥ + 7 = 14
• 4 x ¥ = 44
• ¥ + 6 = 8
• 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:

• 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
• ‘’Add a certain number to 8. If the certain number is represented by a letter y,then this can be interpreted as 8+y.
• ‘p years ago’ can be interpreted as ‘minus p’(-p)years.
• ‘x years to come or x years time can be interpreted as plus x(+x)years time.
• The word ‘is’, ‘gives’, ‘result to’, are interpreted to mean equals
• ‘Double’ means 2 times or (x2)and thrice’ means (x3).
• ‘the difference’means addition
• ‘The sum means addition
• ‘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:

• 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 years.
• ‘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
• ( x+15) years while the daughter’s age would be  + 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?

Reading Assignment

Essential Mathematics for JSS 1 Pages 68- 72

Weekend Assignment

1. What is the value of x in the equation x – 14 = 2?  (a) 20   (b) 16    (c)  9   (d)  24
2. Find the value of ‘a’ if 3 x a = 27 (a) 20   (b)  16   (c)  9   (d) 24
3. Find the value of x if 7 + x = 9. (a) 16  (b) 4   (c)  10    (d)  2
4. 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

• 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?
• Think of a number that when 10 is subtracted from it, the result is 8.