First thing, this stuff in NOT intuitive. Practice is the only way to get better at it. buy one of those 'for dummies' books or the like and have fun.
quick lesson:
placement:
The decimal determines the tens etc. place as follows: 987,654,321.ABCDEFG (I used letters after the decimal for ease of reference).
every set of three digits is collected in the naming scheme. The first triplet is unique in that it really defined the prefixes of the other groups to the left of the decimal (and all but the first to the right). When I mention a digit or capital letter I am making reference to that particular location. The alphanumeric is just a placeholder. Now, to begin.
1 = ones place (this place in each triplet usually has no prefix. Since the 1 position has no root word
than 'ones' takes its place)
2 = Tens
3 = Hundreds
Now for the more common triplets
4 - 6 = thousands
4 = thousands
5 = ten-thousands
6 = hundred-thousands
7-9 = millions
7 = millions
8 = ten-millions
9 = hundred-millions
This would go on for the remainder of the left side digits. Practice with Billions, etc.
Now the right side:
The first triplet actually includes the decimal (well... it works to think of it that way)
A = tenth (1/10)
B = hundredth (1/100)
C - E = Thousandths
C = thousandth (1/1000)
D = ten-thousandths (1/10,000)
etc.
Put the decimal where it will make the number you want to make.
Fractions:
A/B is the fraction of A over B. It is also A divided by B. Fractions are really just a short hand for that operation. Looking at fractions that way it is simple to see that
1/3 < 2/3
because 1 divided by three is half of 2 divided by three. If ever you need to compare two fractions then just divide them out and compare the decimal forms.
0.33333 vs. 0.666667 is clear
Now for fraction operations.
Multiply (and divide):
Multiplication and division is easier to grasp with fractions because you don't first need to manipulate the fractions.
A/B*C/D = ?
5/6*8/9 = ?
Here you just multiply the numerators together to get the new numerator, and do the same with the denominator.
A/B*C/D = A*B/(C*D)
5/6*8/9 = 5*8/(6*9)
for division
(A/b)/(c/d) = ?
(5/6)/(8/9) = ?
I forget the proof, but dividing by a fraction is the same as multiplying by the reciprocal of said fraction.
(A/b)/(c/d) = A/b*c/d = (A*d)/(b*c)
(5/6)/(8/9) = 5/6*9/8 = (5*9)/(6*8)
addition (and subtraction):
A/B + C/D = ?
5/6 + 8/9 = ?
B and D need to be equal. How? see below.
multiply the first fraction (A/B) by D/D and the second fraction (C/D) by (B/B).
Quote:
[NOTE: if you have the addition of many fractions where the denominator of each respectively are B,D,F,H,I,etc. then you would multiply each fraction by each denominator over itself until all fractions have the same denominator:
A/B*(D/D*F/F*H/H*I/I) and G/H*(B/B*D/D*F/F*I/I) ]
Now we have the following
A*D/(B*D) + C*B/(B*D)
5*9/(6*9) + 8*6/(6*9)
now that we have the same denominator we can combine the two fractions
(A*D + B*C)/(B*D)
(5*9 + 8*6)/(6*9)
Fractions can be more exact because 1/3 written in decimal form in infinitely long.
1/3 = 0.33333333333333333333333333333...3333333333333...3333333...333333333...(you get the idea)
Hope that help at least a little.
27 Jul 2008, 1:41 am
= 36 = x*12
