Vedic Maths: Base and Complement

Base and Complement are very important in Vedic Mathematics and form the basis of many calculations.


As explained above we work in a base 10 number system. In order to ease our calculations we can take any number ending with ‘0’ i.e. any multiple of 10 as our base.


The Complement of a number is the difference between that number and the next higher power of 10.

10’s complement:

This includes all 1 digit numbers. It is the number that should be added to make it 10.

The complement of 6 is 4.
The complement of 7 is 3.

100’s complement:

This includes all 2 digit numbers. It is the number that should be added to make it 100.

The complement of 55 is 45.
The complement of 89 is 11.

Finding a complement of a number:

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Grade 3 Maths (imo): Fractions


Some Basic Terms and Rules of Fractions

  • The numbers in a fraction are called the numerator, on the top, and the denominator, on the bottom. numerator/denominator
  • Proper fractions have a numerator smaller than the denominator.
    Examples include 1/23/4 and 7/8.
  • Improper fractions have a numerator larger than the denominator.
    Examples include 5/43/2 and 101/7.

fraction types

Comparing Fractions

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IMO for Class 3 : Syllabus

Syllabus for Grade 3 

Number sense

  • Comparing numbers
  • Abacus and place value
  • Word problems

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Class 3 IMO : Papers

Grade 3 IMO papers






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Grade 3 Maths (IMO) : Division

Let’s talk about what division really is — it is repeated subtraction; much the way multiplication is repeated addition.

Let’s say I have the basic problem 16 ÷  4.  I could start with 16 and then subtract 4, subtract another 4, another 4, and another 4 until I run out and reach zero.  I would have to do this 4 times. If I had 16 cookies that I wanted to share equally among 4 friends, I could do the “one for you, one for you, one for you, and one for you” process and still end up with 4 cookies for each.

But what about 375 ÷ 50? If I don’t know how to divide by double digit numbers, the repeated subtraction process might actually be a good choice . . . at least showing some number sense to know that 375 divided by 50 means “How many 50’s in 375?” I know if I subtract 50 six times, I still have 75 left. I can subtract another 50 and I have 25 left over. So 375 ÷ 50 = 7 with a remainder of 25.

Dividing using the distributive law

Division Possible Split Calculation Answer
69 ÷ 3 60 + 9 (60 ÷ 3) = 20

(9 ÷ 3)  = 3

20 + 3 = 23
391 ÷ 3 390 + 1  (390 ÷ 3) = 130

(1 ÷ 3) = cannot be divided

130 with Remainder 1

 Long Division

Before a child is ready to learn long division, he/she has to know: Continue reading

Grade 3 Maths (IMO) : Number sense

Place value and Face value

Face value of a digit  is the digit itself whereas Place value can be termed as the location of the digit in the numeral.


The value of a place in the place value chart is 10 times the value of the place just to its right.

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Grade 3 Maths (IMO) : Multiplication Strategies

A quick look at the grade 2 lesson on introduction to multiplication

Taming the tables – Tips to introduce multiplication

While multiplying always remember :

An even number  x an even number = an even number

An odd number x an even number = an even number

An odd number x an odd number = an odd number

Distributive property of multiplication

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IMO for grade 2

Have tried breaking the syllabus given by IMO into smaller parts for better understanding.

Syllabus :

Number sense

  • Numerals and number name (3 digits)
  • Comparing Numbers
  • Arranging numbers in ascending or descending order
  • Abacus and Places values
  • Expanded form
  • Even and odd numbers
  • Formation of a number from given digits/information

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