Math Is Fun Forum

choelrich

Member

Registered: 2008-06-10

Posts: 1

Long Division

Please help me this is driving me mad!!!

Please can someone show me how to work out in full the following long division sum:-

180 divided by 250

I shall be eternally grateful!

Thanks
Carl

integer

Member

Registered: 2008-02-21

Posts: 79

Re: Long Division

How old are you?

Long division is the stuff introduced in the 4th grade of elementary school.
Judging by the sentence structure it looks as if you are at least a 5th grader.

Anyway.

First you should (must) understand positional notation.
[I won't attempt to explain numbers & numerals or why you should know the difference.]

The same numeral in the ones, tens, hundreds, thousands positions will mean different numbers.
If you do not understand positional notation and what the numbers mean
you will need to do some study before comprehending division.

Simply:  You have 180 divided by 250, short hand:  180/250

Your numerator is 180, denominator is 250.
Since this is elementary math, the concept of negative numbers will not be covered.  That is, for this lesson you cannot take two apples if there is only one apple on the tree.  That should make sense.

Now,
The 1 in the numerator represents hundreds.
How many times can you subtract 250 from 1.   Answer: Zero.  You have no hundreds in the result.

the 18 represents tens.
How many times can you subtract 250 from 18.   Answer: Zero.  You have no tens in the result.

the 180 represents units or ones.
How many times can you subtract 250 from 180.   Answer: Zero.  You have no ones or whole numbers in the result.

the 180.0  or  1800 represents tenths
How many times can you subtract 250 from 1800.   Answer: seven.  You have 7 tenths in the result.
7*250 = 1750
1800 - 7*250 = 50.  50 is your remainder.  50 tenths.

50 tenths is equivalent to 500 hundredths.  Does that make sense.

How many times can you subtract 250 from 500.  Answer: two.  You have two hundredths in the result.

500 - 2*250 = 0     You have no remainder.  You have an exact value.

To summarize.  0 hundreds, 0 tens, 0 ones, 7 tenths, 2 hundredths.

or:  000.72

graphically:
step 1.
                       0.7
                   _________________                0.7 times 250 = 175.0
               250 | 180.00000000
                    -175.00000000
                   -----------------
                   =   5.00000000

step 2.
                       0.72
                   _________________                0.2 times 250 = 50.0
               250 | 180.00000000
                    -175.00000000
                   -----------------
                   =   5.00000000
                      -5.00000000
                   -----------------
                   =   0.00000000

You can see the alignment of the numbers.

Multiplication is many additions or multiple additions.
Long division (or short division) is nothing more than extended subtraction.

Once you comprehend positional notation of numbers in the decimal system, then it is relatively easy to
transfer the concept to octal and hexadecimal numbering systems.

That's rather pedantic,
but that is just about the stuff that Mrs. Campbell taught when I was in the 4th grade of elementary school.

atut

Member

Registered: 2008-04-23

Posts: 30

Re: Long Division

180 / 250 = 0.72