The L.C.M
Good day pupils and students, today you all will know the basics mathematical formulas and how to solve them, when to apply them. Mathematics keep the world, people, organizations even an events of days lively. Without mathematics there will be no admission for further education, but here you are welcome. What do you need in this case, only formulas and ideas, lets move to some examples.
Ascending of numbers
Now you must know how to ascend any given fractions, any time you're asked to ascend fractions what you must always remember one thing (placing the given fractions from the smallest to the highest), which is the smallest denominator ,any given ascending exercise, the smallest number is the biggest among others. The lowest denominators should always be the highest to stand among others fraction.
Examples
1 2 1 2
-------- , ------- , -------, --------
2 4 3 5
Now, look at the above fractions well, if you observed, 1/2 should be the biggest and 52/5 should be the smallest , we make it this way:
1 2 1 2
= -------- , ------- , -------, ---------
2 6 3 5
First lets find the L. C . M of 2, 6, 3, and 5 = (30)
Lets find the L.C.M of the above numbers ( denominators)
2 x 15 = 30
3 x 10 = 30
5 x 6 = 30
6 x 5 = 30
that means the L C M of 2, 6 , 3, 5 is 30
Break it down
1 1 x 15 15
-------- = ----------- = --------
2 2 x 15 30
1 1 x 5 5
--------- = ------------ = ---------
6 6 x 5 30
1 1 x 10 10
--------- = ------------ = --------
3 3 x 10 30
2 2 x 6 12
-------- = --------- = -------
5 5 x 6 30
Here we have:
5 10 12 15
---------- , --------- , --------- , ---------
30 30 30 30 1 2 1 2
therefore = -------- , ------- , ------- , ---------
2 6 3 5
2 2 1 1
= -------- ,<-------- ,< -------- ,< --------
6 5 3 2
So at last the smallest fraction has became the highest fraction. , just multiply the bottom number and the top numbers with the same number.
Finding The Missing Numbers
Here you'll know what missing number is, just pay attention and make it real when its comes to practices. Any day any time you're asked to solve mathematics that involved missing numbers just bring out the biggest number before the smallest one. If in addition, we keep - sign ( subtraction sign ), but if multiplication, we keep / sign ( division sign).
Examples
1. c + 37 = 62
We bring the biggest number first, 62.
5 10 --------borrowing
6 2 -------- biggest
- 3 7 ---------smallest
---------------
2 5
----------------
= 25, the missing number
Checked
1
3 7
+ 2 5
-------------
6 2
-------------
Do not forget this.
w x 5 = 25
This means:
25
------------- 5
5
= 5
5 is the missing number.
Multiplication Of 3 digit Numbers
This is how to multiply 3 to 3 digit without a calculator, mm can you follow up, for real just pay attention.
Examples
1. 325 x 123
remember all 3 digit are H.T.U ( hundreds tens unit/units )
32500 = 325 x 100
1
3250
+ 3250
--------------
6500 = 325 x 20
--------------
And 325 x 3
1
3 2 5
+3 2 5
+3 2 5
----------------
9 7 5
---------------
Now
1
3 2 5 0 0
+ 6 5 0 0
+ 9 7 5
------------------------
3 9 9 7 5
------------------------
Wow that means 325 x 123 = 39, 975
2. 34 x 52
first = 34 x ( 50 + 2 )
= (34 x 50) + ( 34 x 2 )
= 17 0 0 + 6 8
= 1 768
just keep 34 into 5 places and add 0 to each (zero) to this 34
2
+ 3 4 0
+ 3 4 0
+ 3 4 0
+ 3 4 0
+ 3 4 0
------------------------
17 0 0
------------------------
then 34 into 2 places without zero because 2 is units, i mean
3 4
+ 3 4
-----------------
6 8
-----------------
Now
1 7 0 0
+ 6 8
---------------------
1 7 6 8
---------------------
therefore: 34 x 52 = 1 768
Can you see how i calculated that without a calculator, that's the reason i break them down just follow the simplemethod123 and your good to go...
Descending Of Numbers
descending means placing the number from the biggest to the smallest .To descend numbers, the highest numerator is always the biggest number, but you must obtain the equivalent fractions first, then you follow the top numbers.
Example
1 2 1 1
--------- , ------- , -------, --------
2 3 4 8
First the LCM of 2, 3 , 4 , 8 = 24
1 1 x 12 12
-------- = ----------- = ---------
2 2 x 12 24
2 2 x 8 16
-------- = ---------- = --------
3 3 x 8 24
1 1 x 6 6
--------- = ---------- = --------
4 4 x 6 24
1 1 x 8 8
--------- = ---------- = --------
8 8 x 3 24
1 2 1 1
therefore --------- ,------- , ------- , --------
2 3 4 8
16 12 8 6
--------- > , --------- , > ------- > --------
24 24 24 24
How to multiply decimals without a calculator
You can multiply any given decimal numbers without the use of calculator. a lots of people get it hard to multiply decimals, we know that a decimal is: a number with a point e.g 34.3 , 1.3 , 321.23 etc.. Here you have an opportunity to understand how to multiply decimals, if know this you know it forever lets go..
Examples
3 123
12.3 = 12 + -------- = ------------- = 12 . 3 one decimal point (10)
10 10
20 1 21
also 32.21 = 32 + ---------- + ------- = --------- = 0.21 two decimal point ( 100)
10 100 100
1. 2.3 x 13.12
23 1312
-------------- x -----------
10 100
23 x 1000 =23000
23 x 300 = 6000 and 900 = 6 900
23 x 10 = 230
23 x 2 = 46
this means
1 1
2 3 0 0 0
+ 6 9 0 0
+ 2 3 0
+ 4 6
----------------
3 0 1 7 6
-----------------
30176 176
-------------- = 30 ----------
1000 1000
176
therefore 2.3 x 13.12 = = 30 ----------
1000
Can you see that concept, just follow my method and you're good to go..
2. 4.6 x 3.3
46 33 1518
---------- x -------- = -----------
10 10 100
= 15.18
1
46 x 30 = 4 6 0
+ 4 6 0 ---------- the first 3 is tens that goes with 1 (0) add the 0 into 3 places
+ 4 6 0
--------------
13 8 0
---------------
1
46 x 3 4 6
+ 4 6 ---------- the second 3 is units that has no (0) just keep 3 into 3 places
+ 4 6
--------------
1 3 8
----------------
Then
1
13 8 0
+ 1 3 8
---------------
15 1 8
---------------
In mathematics, 3y = 3 x y = y x y x y .... y in three places
More formulas are coming, stay tuned if you have any question put them in the comments box.
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