The Use of letters in place of Numbers

The Use of letters in place of Numbers

        We use symbols in mathematics. Using symbols, we write ‘the sum of five and nine’ in short as ‘5 + 9’.

         

Using symbols makes our writing short and clear. Use of letters, too makes mathematical writing easier.

         

Letters are used in place of numbers in two ways.

1.    The use of a letter for an unknown number.

‘ what is the number that is bigger than 8 by 4 ?” To find the answer to this question, let us add ‘8 + 4’. The sum 12 is the answer to the question.

      

 Using a sign, we write the information number that is bigger than four by eight’ as ‘8 + 4’.

      

 Now, let us see how we could write the information ‘a number that is bigger than another number by 4’ in signs.

      

We do not know exactly which number we are speaking of still, we can write this information using signs. Let us show the unknown number with the letter ‘a’. using signs, we can write ‘a’ number bigger than another number by 4’ as ‘a

+ 4’.

        

Similarly, ‘a number less than another number by 7’ can be written as ‘b – 7’. Here, b is written in place of the unknown number.

        

You will notice that when we add, subtract, multiply or divide two or more numbers, we get only one number in the end. But, the expression we get by using the sign for an operation between a letter and a number cannot be simplified any further.

     

   ‘The product  of a number and 2’ can be written as ‘m × 2’ or          2 × m by writing ‘m’ in place of ‘a number’. However, the product of a number and a letter is conventionally written with the number first and without the multiplication sign. Thus, the product m × 2 or 2 × m is written as 2m. similarly, 10 × k or k × 10 is written as 10k.

         

Some more examples of the use of a letter in place of an unknown number are given below. Study them. Note that we can choose to write any of the letters a,b,c,…,z in place of numbers.

   Information                                                      Expressed using letters

(1)  Sum of 10 and another number                              10 + p

(2)  Product of 23 and another number                         23 × d or 23d

(3) The quotient of 18 divided by a number              18 ÷ y or 18/y

(4)  The quotient of a number divided by 18           x/18 or x ÷ 18

(5)  The number obtained by subtracting                  a - 15           

15 from a number

(6)  The number obtained by subtracting                      15 – b          

a number from 15

(7)  A number less than another by 2                             (d – 2)

(8) The mangoes left after eating 6 from a                    (m – 6)               

Certain number of mangoes       

 

(9)  The number of guavas in each share if                           

3 equal shares are made of a certain                        p/3             

Number of guavas.