In simple way, addition means to add two or more numbers.
For example:-If anyone has one ball and his/her mother gives him/her another ball, then the total number of balls will be two. In mathematical way, 1+1=2.
The additive identity of a number x(say) is the number that when added to x provides a result of x,i.e., the additive identity of every number is zero.
For example:- The additive identity of 3 is 0.
The additive inverse of a number is the number that when added to the first number provides a result of zero.
For example:- The additive inverse of a number a(say) is going to be -a because on adding these two numbers we get a zero. Now try putting values for a. Let a be 3 then its additive inverse will be -3.
Note:- The additive inverse of a positive number is negative and that of a negative number is positive.
Mean, Mode and Median are the three most common kind of averages that you will see in your classes till near about 9th class and later there are some more bizarre averages for you in statistics.
Mean:- It is just the ordinary average that you may be familiar with but its better to revise, so, Mean is the average in which you just add all the given values and divide their sum by the number of values.
For example:- The mean of 6,12,3 is 7,i.e., 6+12+3(sum of all values) divided by 3(The number of values).
Mode:- The mode is the value that appears most often in a group of values. For simplicity you may write the digits in ascending order or descending order and find out which number appears most often.
For example:- The mode of 2,4,5,2,5,3,1,4,2 is 2. As (I prefer ascending order) 1,2,2,2,3,4,4,5,5.Clearly we can observe that 2 is coming most often that is 3 times.
Median:- It is the middle value of a set of values. For finding the median we have to arrange the values in ascending or descending order and then the value counted to be in the middle from both the sides(left and right) is called the Median.
For example:- The median of 2,4,8,1,3 is 3. As I stated above I prefer ascending order, so, 1,2,3,4,8. Clearly 3 is the middle value from both the sides.
In this case the number of values were odd but what would happen if the number of values are even because we will have two middle numbers. In that case we take the average of the two middle numbers,i.e.,add them and divide by two.
For example:- The median of 2,4,1,3 is 2.5. As on arranging we get 1,2,3,4 in this the two middle terms that appear are 2 and 3. So when we add 2 and 3 and divide by 2,i.e.,5 divided by 2, we get 2.5.
Mid range is a bit different concept than a Range. It is the arithmetic mean or simply just the mean of the highest and the smallest values of a set of values.
For example:- The mid range of 1,2,3,4,12,19 is 10. As the mean of 19(the highest value) and 1 (the smallest value) is 10,i.e., 19+1(Sum of highest and smallest values) divided by 2(the number of values).
Multiplicative identity of a number x(say) is the number which on multiplying with x provides a result of x, i.e., the multiplicative identity of every number is 1.
For example:- The multiplicative identity of 5 is 1.
Multiplicative inverse of a number x(say) is the number which on multiplying with x provides a result of 1, i.e., 1/x(this is for fraction).
For example:- The multiplicative inverse of 5 is 1/5 or 0.2.
The most important ten polynomial identities for students till class 9th are the following which are related to binomials. i. (a+b)²= a² + 2ab + b²