Kilometers to Miles
This is a useful method for when travelling between imperial and metric countries and
need to know what kilometres to miles are.
The formula to convert kilometres to miles is number of (kilometres / 8 ) X 5
So lets try 80 kilometres into miles
80/8 = 10
multiplied by 5 is 50 miles!
Another example
40 kilometers
40 / 8 = 5
5 X 5= 25 miles
Temperature Conversions
This is a shortcut to convert Fahrenheit to Celsius and vice versa.
The answer you will get will not be an exact one, but it will give you an idea of the
temperature you are looking at.
Fahrenheit to Celsius:
Take 30 away from the Fahrenheit, and then divide the answer by two. This is your
answer in Celsius.
Example:
74 Fahrenheit - 30 = 44. Then divide by two, 22 Celsius.
So 74 Fahrenheit = 22 Celsius.
Celsius to Fahrenheit just do the reverse:
Double it, and then add 30.
30 Celsius double it, is 60, then add 30 is 90
30 Celsius = 90 Fahrenheit
Remember, the answer is not exact but it gives you a rough idea.
Wednesday, April 01, 2009
Decimals Equivalents of Fractions
With a little practice, it's not hard to recall the decimal equivalents of fractions up to 10/11!
First, there are 3 you should know already:
1/2 = .5
1/3 = .333...
1/4 = .25
Starting with the thirds, of which you already know one:
1/3 = .333...
2/3 = .666...
You also know 2 of the 4ths, as well, so there's only one new one to learn:
1/4 = .25
2/4 = 1/2 = .5
3/4 = .75
Fifths are very easy. Take the numerator (the number on top), double it, and stick a decimal in front of it.
1/5 = .2
2/5 = .4
3/5 = .6
4/5 = .8
There are only two new decimal equivalents to learn with the 6ths:
1/6 = .1666...
2/6 = 1/3 = .333...
3/6 = 1/2 = .5
4/6 = 2/3 = .666...
5/6 = .8333...
What about 7ths? We'll come back to them at the end. They're very unique. 8ths aren't that hard to learn, as they're just smaller steps than 4ths. If you have trouble with any of the 8ths, find the nearest 4th, and add .125 if needed:
1/8 = .125
2/8 = 1/4 = .25
3/8 = .375
4/8 = 1/2 = .5
5/8 = .625
6/8 = 3/4 = .75
7/8 = .875
9ths are almost too easy:
1/9 = .111...
2/9 = .222...
3/9 = .333...
4/9 = .444...
5/9 = .555...
6/9 = .666...
7/9 = .777...
8/9 = .888...
10ths are very easy, as well. Just put a decimal in front of the numerator:
1/10 = .1
2/10 = .2
3/10 = .3
4/10 = .4
5/10 = .5
6/10 = .6
7/10 = .7
8/10 = .8
9/10 = .9
Remember how easy 9ths were? 11th are easy in a similar way, assuming you know your multiples of 9:
1/11 = .090909...
2/11 = .181818...
3/11 = .272727...
4/11 = .363636...
5/11 = .454545...
6/11 = .545454...
7/11 = .636363...
8/11 = .727272...
9/11 = .818181...
10/11 = .909090...
As long as you can remember the pattern for each fraction, it is quite simple to work out
the decimal place as far as you want or need to go!
Oh, I almost forgot! We haven't done 7ths yet, have we?
One-seventh is an interesting number:
1/7 = .142857142857142857...
For now, just think of one-seventh as: .142857
See if you notice any pattern in the 7ths:
1/7 = .142857...
2/7 = .285714...
3/7 = .428571...
4/7 = .571428...
5/7 = .714285...
6/7 = .857142...
Notice that the 6 digits in the 7ths ALWAYS stay in the same order and the starting digit is the only thing that changes! If you know your multiples of 14 up to 6, it isn't difficult to work out where to begin the decimal number. Look at this:
For 1/7, think "1 * 14", giving us .14 as the starting point.
For 2/7, think "2 * 14", giving us .28 as the starting point.
For 3/7, think "3 * 14", giving us .42 as the starting point.
For 4/14, 5/14 and 6/14, you'll have to adjust upward by 1:
For 4/7, think "(4 * 14) + 1", giving us .57 as the starting point.
For 5/7, think "(5 * 14) + 1", giving us .71 as the starting point.
For 6/7, think "(6 * 14) + 1", giving us .85 as the starting point.
Practice these, and you'll have the decimal equivalents of everything from 1/2 to 10/11 at
your finger tips!
If you want to demonstrate this skill to other people, and you know your multiplication tables up to the hundreds for each number 1-9, then give them a calculator and ask for a 2-digit number (3-digit number, if you're up to it!) to be divided by a 1-digit number. If they give you 96 divided by 7, for example, you can think, "Hmm... the closest multiple of 7 is 91, which is 13 * 7, with 5 left over. So the answer is 13 and 5/7, or:
13.7142857!"
First, there are 3 you should know already:
1/2 = .5
1/3 = .333...
1/4 = .25
Starting with the thirds, of which you already know one:
1/3 = .333...
2/3 = .666...
You also know 2 of the 4ths, as well, so there's only one new one to learn:
1/4 = .25
2/4 = 1/2 = .5
3/4 = .75
Fifths are very easy. Take the numerator (the number on top), double it, and stick a decimal in front of it.
1/5 = .2
2/5 = .4
3/5 = .6
4/5 = .8
There are only two new decimal equivalents to learn with the 6ths:
1/6 = .1666...
2/6 = 1/3 = .333...
3/6 = 1/2 = .5
4/6 = 2/3 = .666...
5/6 = .8333...
What about 7ths? We'll come back to them at the end. They're very unique. 8ths aren't that hard to learn, as they're just smaller steps than 4ths. If you have trouble with any of the 8ths, find the nearest 4th, and add .125 if needed:
1/8 = .125
2/8 = 1/4 = .25
3/8 = .375
4/8 = 1/2 = .5
5/8 = .625
6/8 = 3/4 = .75
7/8 = .875
9ths are almost too easy:
1/9 = .111...
2/9 = .222...
3/9 = .333...
4/9 = .444...
5/9 = .555...
6/9 = .666...
7/9 = .777...
8/9 = .888...
10ths are very easy, as well. Just put a decimal in front of the numerator:
1/10 = .1
2/10 = .2
3/10 = .3
4/10 = .4
5/10 = .5
6/10 = .6
7/10 = .7
8/10 = .8
9/10 = .9
Remember how easy 9ths were? 11th are easy in a similar way, assuming you know your multiples of 9:
1/11 = .090909...
2/11 = .181818...
3/11 = .272727...
4/11 = .363636...
5/11 = .454545...
6/11 = .545454...
7/11 = .636363...
8/11 = .727272...
9/11 = .818181...
10/11 = .909090...
As long as you can remember the pattern for each fraction, it is quite simple to work out
the decimal place as far as you want or need to go!
Oh, I almost forgot! We haven't done 7ths yet, have we?
One-seventh is an interesting number:
1/7 = .142857142857142857...
For now, just think of one-seventh as: .142857
See if you notice any pattern in the 7ths:
1/7 = .142857...
2/7 = .285714...
3/7 = .428571...
4/7 = .571428...
5/7 = .714285...
6/7 = .857142...
Notice that the 6 digits in the 7ths ALWAYS stay in the same order and the starting digit is the only thing that changes! If you know your multiples of 14 up to 6, it isn't difficult to work out where to begin the decimal number. Look at this:
For 1/7, think "1 * 14", giving us .14 as the starting point.
For 2/7, think "2 * 14", giving us .28 as the starting point.
For 3/7, think "3 * 14", giving us .42 as the starting point.
For 4/14, 5/14 and 6/14, you'll have to adjust upward by 1:
For 4/7, think "(4 * 14) + 1", giving us .57 as the starting point.
For 5/7, think "(5 * 14) + 1", giving us .71 as the starting point.
For 6/7, think "(6 * 14) + 1", giving us .85 as the starting point.
Practice these, and you'll have the decimal equivalents of everything from 1/2 to 10/11 at
your finger tips!
If you want to demonstrate this skill to other people, and you know your multiplication tables up to the hundreds for each number 1-9, then give them a calculator and ask for a 2-digit number (3-digit number, if you're up to it!) to be divided by a 1-digit number. If they give you 96 divided by 7, for example, you can think, "Hmm... the closest multiple of 7 is 91, which is 13 * 7, with 5 left over. So the answer is 13 and 5/7, or:
13.7142857!"
Saturday, January 03, 2009
maths essentials
Introduction
I f you’re like most other people, you use a
pocket calculator to do your basic arithmetic. The calculator is fast
and accurate as long, of course, as you punch in the right numbers.
So what could be bad about a tool that saves you so much work and gives
you the right answers?
Let me be brutally frank. You know why you bought this book, and
it’s not for the story. By working your way through this book, problem
by problem, you will be amazed by how much your math skills will
improve. But—and this is a really big BUT—I don’t want you to use your
calculator at all. So put it away for the time you spend working through
this book. And who knows—you may never want to use it again.
Your brain has its own built-in calculator, and it, too, can work
quickly and accurately. But you know the saying, “Use it or lose it.”
The book is divided into four sections—a review of basic arithmetic,
and then sections on fractions, decimals, and percentages. Each section is
subdivided into four to eight lessons, which focus on building specific
skills, such as converting fractions into decimals, or finding percentage
changes. You’ll then get to use these skills by solving word problems in the
applications section. There are 21 lessons plus four review lessons, so if
you spend 20 minutes a day working out the problems in each lesson, you
can complete the entire book in about a month.
One thing that distinguishes this book from most other math books is
that virtually every problem is followed by its full solution. I don’t believe
in skipping steps. You, of course, are free to skip as many steps as you
wish, as long as you keep getting the right answers. Indeed, there may well
be more than one way of doing a problem, but there’s only one right
answer.
When you’ve completed this book, you will have picked up some very
useful skills. You can use these skills to figure out the effect of mortgage
rate changes and understand the fluctuations in stock market prices or
how much you’ll save on items on sale at the supermarket. And you’ll
even be able to figure out just how much money you’ll save on a low-
interest auto loan.
Once you’ve mastered fractions, decimals, and percentages, you’ll be
prepared to tackle more advanced math, such as algebra, business math,
and even statistics. At the end of the book, you’ll find my list of recom-
mended books to further the knowledge you gain from this book (see
Additional Resources).
If you’re just brushing up on fractions, decimals, and percentages, you
probably will finish this book in less than 30 days. But if you’re learning
the material for the first time, then please take your time. And whenever
necessary, repeat a lesson, or even an entire section. Just as Rome wasn’t
built in a day, you can’t learn a good year’s worth of math in just a few
weeks.
While I’m doing clichés, I’d like to note that just as a building will
crumble if it doesn’t have a strong foundation, you can’t learn more
advanced mathematical concepts without mastering the basics. And it
doesn’t get any more basic than the concepts covered in this book. So put
away that calculator, and let’s get started
I f you’re like most other people, you use a
pocket calculator to do your basic arithmetic. The calculator is fast
and accurate as long, of course, as you punch in the right numbers.
So what could be bad about a tool that saves you so much work and gives
you the right answers?
Let me be brutally frank. You know why you bought this book, and
it’s not for the story. By working your way through this book, problem
by problem, you will be amazed by how much your math skills will
improve. But—and this is a really big BUT—I don’t want you to use your
calculator at all. So put it away for the time you spend working through
this book. And who knows—you may never want to use it again.
Your brain has its own built-in calculator, and it, too, can work
quickly and accurately. But you know the saying, “Use it or lose it.”
The book is divided into four sections—a review of basic arithmetic,
and then sections on fractions, decimals, and percentages. Each section is
subdivided into four to eight lessons, which focus on building specific
skills, such as converting fractions into decimals, or finding percentage
changes. You’ll then get to use these skills by solving word problems in the
applications section. There are 21 lessons plus four review lessons, so if
you spend 20 minutes a day working out the problems in each lesson, you
can complete the entire book in about a month.
One thing that distinguishes this book from most other math books is
that virtually every problem is followed by its full solution. I don’t believe
in skipping steps. You, of course, are free to skip as many steps as you
wish, as long as you keep getting the right answers. Indeed, there may well
be more than one way of doing a problem, but there’s only one right
answer.
When you’ve completed this book, you will have picked up some very
useful skills. You can use these skills to figure out the effect of mortgage
rate changes and understand the fluctuations in stock market prices or
how much you’ll save on items on sale at the supermarket. And you’ll
even be able to figure out just how much money you’ll save on a low-
interest auto loan.
Once you’ve mastered fractions, decimals, and percentages, you’ll be
prepared to tackle more advanced math, such as algebra, business math,
and even statistics. At the end of the book, you’ll find my list of recom-
mended books to further the knowledge you gain from this book (see
Additional Resources).
If you’re just brushing up on fractions, decimals, and percentages, you
probably will finish this book in less than 30 days. But if you’re learning
the material for the first time, then please take your time. And whenever
necessary, repeat a lesson, or even an entire section. Just as Rome wasn’t
built in a day, you can’t learn a good year’s worth of math in just a few
weeks.
While I’m doing clichés, I’d like to note that just as a building will
crumble if it doesn’t have a strong foundation, you can’t learn more
advanced mathematical concepts without mastering the basics. And it
doesn’t get any more basic than the concepts covered in this book. So put
away that calculator, and let’s get started
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