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Basic numbers and decimals

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Ma1

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

Step 2. Addition

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