Mathematics - Rules of Addition & Multiplication

Arithmetic Operations

Addition

Addition involves combining groups of 1 into a bigger group. Examples :
4 + 5 is 1111 + 11111 = 111111111 ( 9 )
6 + 7 is 111111 + 1111111 = 1111111111111 ( 1 3 )

Rules of Addition

Let’s perform a simple addition. I want to drop oranges into a fruit basket and count the total when I am done. If you do not have enough oranges or a fruit basket you can roll small paper balls and use a cup or a bowl.

Pick up the oranges 1 group, (start with the left group first), at a time and throw them into the fruit basket. When you are done count the number of oranges in the basket. If your answer is 9 then well done you got it right. Next, again starting with the same groups of oranges and an empty basket perform the same action except that this time you start with the group of 3 oranges. Count the oranges in the basket when you are done.
Did you get 9 oranges ? What have you learned from this simple exercise?

Rule 1

When you perform addition, it does not matter which group or number you start with first. In the end you will still get the same answer. In the language of Mathematics, it is known as the Commutative law of Addition.
Big and sophisticated sounding , but bah! don’t bother just store the name somewhere in your brain. Even if you should forget, it is alright. I bring it out just in case it comes out in any of your conversation.

6 + 3 = 9 111111 111 111111111
3 + 6 = 9 111 111111 111111111
As illustrated the groups of 9 (1s) are non-distinguishable. The numbering system makes them look unalike - try putting them together 36 or 63 (disaster).

This rule applies to any number of groups or numbers that you are adding.
5 + 6 + 2 = 13
6 + 2 + 5 = 13
2 + 5 + 6 = 13
You can discover for yourself by making several groups of oranges and then dropping them in the basket and counting the total. In other words, order does not matter when you are performing addition.
If you still have any difficulty understanding this rule think of it this way.

Perhaps your class has 35 students and each day they enter the class in groups or individual and at different time. This routine will change from day to day, and each day the group size may be different and the order in which they enter the classroom will also vary. However, the total number of students ( total count ) will be the same ( barring any not coming to school.). Students entering the class is akin to putting oranges into a basket.

Rule 2

When performing Addition, you may consider splitting up each or all of the groups involved into smaller groups and then perform the summing or adding. Or, you can even shuffle the small groups around, then do the adding.This rule is a combination of the Associative and Distributive rule. Again, don’t lose sleep over the terms just understand the application. In fact, during day to day application the rules fade into oblivion.

Always make groups of 10 whenever possible (This is my rule )

Multiplication

Multiplication is just repetitive addition. It is a special case of addition and that is why all the rules of addition is exactly applicable to Multiplication. Schools inadvertently lead students into thinking that Multiplication is an independent operator.
6 x 7 = 7 + 7 + 7 + 7 + 7 + 7
The multiplicand is added a number of times equal to the value of the multiplier, both terms I believe you know so I will not extend on those.

Difference between Addition and Multiplication

When we add several numbers in normal addition the numbers tend to be different in values and rather random eg. 4 + 7 + 12 + 3 whereas when we multiply, a number (the multiplicand) is added several times eg. 7 + 7 + 7 + 7 + 7 + 7. This is the only difference.

Hence there is nothing difficult or scary about multiplication. Multiplication sounds and act different from Addition just because you have been pre-programmed to remember the result of such Additions from very young and you have a vast store of such results in your long term memory. Addition unlike Multiplication tend to be very random and there are just too many combinations to memorize and hence never done. I debate if remembering such results do us good today because all of us including little kids are walking around with calculators ( handphone ). However, I hesitate to recommend not remembering tables as our examination system still depends on such.