Oh no not more math ? ! Why do I sometimes write blogs about math? Sometimes parents need help with their kids' homework especially math (if they already don't know how). Math was one of my favorite subjects in school.
A direct variation in math is when if one thing increases then another thing increases as well. For example the more you buy the more you have to pay. It also applies to decreases. The less you buy the less you have to pay.
For example three apples cost you a dollar. How much would six apples cost? Yes, I know you already know the answer but let's do
the math anyway.
3 1
---- = ----
6 X
Now let's cross multiply:
3X=6
X=2
So if three apples cost one dollar then six apples cost two dollars.
Now on to the indirect variations where one thing increases while another decreases. For example when driving in a car the faster you go (increase) the less time (decrease) it would take you to get to your destination.
Let's say you are driving at 30 miles per hour and it took 8 hours to get to your destination. How long would it take if you were driving at 60 miles per hour ? Yes, I know you already know the answer, but again let's do the math anyway.
30 8
---- = ----
60 X
Hold it ! If we figure this equation as it stands now, we will get the wrong answer of 16 . Remember this time it is an indirect variation in this case we have to invert one side doesn't matter which one. Let's invert the right side changing 8/X into X/8.
30 X
---- = ----
60 8
Now let's cross multiply:
(30)(8) = 60(X)
then divide by 60 on both sides.
(30)(8)
------- = X
(60)
30/60 can be reduce to 1/2 and 1/2 of 8 is 4 which is now the correct answer. So there we have it in this indirect variation. If it took 8 hours to get to your destination driving at 30 MPH then it would take you 4 hours driving at 60 MPH
If you understand expontents see also:
click here for Doubling Pennies On A Checkerboard.
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