Math Blog on Grade VI

Here we are going to discuss one of the most interesting and a bit complex topic of mathematics: operations on fractions, decimals, integers and exponents which are usually studied in grade VI.
Now we will first start with fraction:
Fractions can be defined as the part of whole numbers having both numerator and denominator. ¼, ¾  are some examples of fractions. Generally fractions are of three types i.e. proper fractions, improper fractions and mixed fractions. Let’s see some operations on fractions:

1.    Addition fractions:

While adding two fractions we must take care of that the denominators of the fractions to be added must be same. And if the denominators are not same then find the LCM of the denominators and put each one in its equivalent form. Then simply add the numerators.

                     p/q + r/q = (p + r)/q

2.    Subtraction of fractions:

While subtracting two fractions we must take care of that the denominators of the fractions to be subtracted must be same. And if the denominators are not same then find the LCM of the denominators and put each one in its equivalent form. Then simply subtract the numerators.

                     p/q - r/q = (p - r)/q

3.    Multiplication of fractions:

While multiplying two fractions multiply the numerators together and then multiply the denominator together and simplify them.

                     p/q x r/s = (p x r)/(q x s)

4.    Division of fractions:

While dividing the fractions take reciprocal of the second fraction and multiply both the fractions together.

           p/q ÷ r/s = p/q x s/r = (p x s)/(q x r)

Now move to the next topic i.e. decimals:
Decimal number can be defined as the number which contains decimal point. To understand the decimal numbers we must have knowledge about the place values, which is very important when we write the decimal numbers. (also try fraction to decimal converter)
In the number 234:

• The "4" is at the Units position.
• The "2" is at the Tens position.
• And the "3" is at the Hundreds position.
  

In a decimal number as we move left, each position becomes 10 times bigger and as we move right, each position become 10 times smaller.
Now we move to the next topic i.e. integers:
Integer can be defined as similar to the whole number but integers also contains negative numbers and do not contain fractions.
 Let’s see some examples of integers:

·         Negative Integers =   -1, -2,-3, -4, -5, …  

·         Positive Integers = 1, 2, 3, 4, 5, …  

·         Zero =   0

We can also put the integers like this ..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ... .
Now we move to the next topic i.e. exponents:
Exponents can be defined as the power or indices of a number. The exponent of a number represents that how many times the number will be use in multiplication. Let’s understand it by an example:
Example: 12² = 12 x 12 = 144
In words: 12² can be called as "12 to the second power", "12 to the power 2" or simply "12 square".

In upcoming posts we will discuss about Proportions. Visit our website for information on syllabus for class 10th ICSE