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:
- Think of a number, double it, the result is 14. What is the number?
- 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
- What is the value of x in the equation x – 14 = 2? (a) 20 (b) 16 (c) 9 (d) 24
- Find the value of ‘a’ if 3 x a = 27 (a) 20 (b) 16 (c) 9 (d) 24
- Find the value of x if 7 + x = 9. (a) 16 (b) 4 (c) 10 (d) 2
- 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.
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