The actual principle of counting, adding, subtracting, multiplying and dividing is so complex it would take pages to describe, luckily we seem to be able to grasp it when we are young, and you probably know the basics anyway. Here we'll just look at a few basic principles.
Adding[]
'Adam has 1 apple, 10 oranges, and 230 grapes, how many peices of fruit does he have in total?'
A good method is:
1 Add the 1 unit Add the 0 tens Add the 0 hundreds 10 to 0 units to 1 ten to 0 hundreds 230 to 0 units to 3 tens to 2 hundreds --- 241 equals 1 unit equals 4 tens equals 2 hundreds ---
This can be used for ALL columns from trillions to triollionths(actually more than just those).
No more than 9[]
It is important to note that you CANNOT have more than 9 or LESS than 1 in each column as having 10 or 0.1 would actually mean that you have 0 in that colum and 1 in the column to the left or right of it. Therefore:
'Adam has 12 trucks and 19 barbies, how many toys does he have in total?'
12 Add the 2 units Add the 1 ten 19 to 9 units to 1 ten -- + 1 ten from the units 30 equals 11 units, so 1 equals 3 tens -- + 1 ten 1
Try some addition:
101 2 1346 12.253 2.234 99 11 239 113 2.987 --- --- ---- ------- ----- --- --- ---- ------- -----
Answers:
200 13 1585 125.253 5.221
Subtracting[]
Same principle but in reverse 'Lauren has 32 pairs of shoes, she decides to bin 13 of them, how many shoes will she have?'
A good method is:
32 2 units 2 tens (we stole one for the units) 13 minus 3 minus 1 ten -- nick 1 ten 19 equals 12-3=9 equals 1 -- 1
Negative numbers[]
When a subtraction takes you below 0 you go into negative numbers, these are exactly like normal numbers but negative, the signs are the key:
-1 + -2 = -3 1 less and 2 less gives 3 less -1 + 2 = 1 1 less and 2 more gives 1 1 - -2 = 3 1 and the removal of 2 less gives 3 -1 - 2 = -3 1 less and 2 less gives 3 less
Try some subtraction:
201 12 7.45 -12 -12 39 19 6.99 -19 19 --- -- ---- -- -- --- -- ---- -- --
Answers:
162 -7 0.46 7 -31
Multiplying[]
A good way to think of multiplication is to think of it as repetition of addition. Common elementary notation is to use "x" as a symbol for times. However it should be recomended to use "•" or parentheses, i.e. 4(3).
With arithmetic addition you would show something like so , 3+4+5= , and answer with the sum , or total value of all integers, the answer being 12. Now take into account 4+4+4= , count the amount of times the 4 is repeated , 3 "times".
therefore , it is 4x3 or 4(3).
Lets try the reverse now , given 7(5) or 7x5 find the product( the product is the number you get by multiplying numbers together , this will later include variables in algebra). Try to figure out what would be written in each step of the two steps before revealing it.
Step 1 . extend the multiplication into addition
| 7(5) |
|---|
| 7+7+7+7+7 OR 5+5+5+5+5+5+5 |
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either will work but try and lean for the lower number being total repetitions of the higher number. |
Step 2. Addition
| 7+7+7+7+7 |
|---|
| 7+7+7+7+7=35 |
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Don't worry that i didn't show my work , with addition as soon as you get used to it it can be done in the head. Until you can do that stay with the usual work on paper. Also it is okay to use the multiple 5's , you should get the same answer. |