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Need help with decimal long division please

Mathematics
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313.7/13.125 having trouble with the set up and operations for decimal long division. Can you please help?

Sep 25th, 2014

Parts of Division

For the division problem 47.1 divided by 3.2, 47.1 ÷ 3.2, is equivalent to 471 divided by 32 and 47.1/3.2 = 471/32 = 14.718 calculating 3 decimal places.

[img src="http://www.calculatorsoup.com/images/divisionlongpartsdecimals.png" width="220" height="330" alt="drawing of long division with parts of division: dividend, divisor, quotient, remainder">

In this problem we will divide 47.1 by 3.2 out t0 6 decimal places in the quotient answer.

Long DivisionExplanationEquations
We set up our problem with the long division bracket. Place the dividend on the inside of the bracket and divisor on the outside, left. 
It is easier to operate on a dividend and divisor that are not decimal numbers so we turn these into integers. In this problem, we multiply both by 10 to eliminate numerical decimal places.

Since we are solving to 6 decimal places, we also added six trailing zeroes on to the dividend as "place holders" for now.

We can also pre-place a decimal point in the quotient, right above its new position in the dividend.
47.1 ÷ 3.2 
is equivalent to
471 ÷ 32

Since:
47.1/3.2 * 10/10 = 471/32 

Just like when we work with fractions, you don't change the value of a fraction if you multiply its top and bottom numbers by the same number.
Divide the left most number of the dividend by the divisor. 

The quotient result is rounded down to an integer, and since 32 does not divide into 4 at least one whole time, the first quotient digit is 0.

Multiply the divisor 32 by the quotient 0 to get the product 0.  We then subtract 0 from 4 to get the remainder 4.
4 ÷ 32 = 0

32 * 0 = 0

4 - 0 = 4

4 ÷ 32 = 0 
with a remainder of 4
Now, we carry this remainder forward and "bring down" the next digit from the dividend making 47 the next number we'll divide our divisor into.47

47 ÷ 32 = ??
Again, we note only the whole number result (1) in the quotient. To find the remainder, we multiply our divisor by our whole number result (1), and subtract the product (32) from our second dividend (47), to get a remainder of 15.47 ÷ 32 = 1

32 * 1 = 32

47 - 32 = 15

47 ÷ 32 = 1
with a remainder of 15 
Again, we bring down the next digit (1) from the dividend, and add it on to the remainder. Now we'll divide our our divisor into this new dividend (151).151

151 ÷ 32 = ??
We go through the exact same set of steps again. 32 goes into 151 four times. Multiply 32 by 4 to get 128, and subtract that product from 151 to find our remainder, 23.151 ÷ 32 = 4

32 * 4 = 128

151 - 128 = 23

151 ÷ 32 = 4
with a remainder of 23
We'll bring down the next number (0) from the dividend.

Ignore the decimal point for now, we don't bring it down, just work around it.
230

230 ÷ 32 = ??
32 goes into 230 seven times. 32 multiplied by 7 is 224. 230 take away 224 leaves us a remainder of 6.230 ÷ 32 = 7

32 * 7 = 224

230 - 224 = 6

230 ÷ 32 = 7
with a remainder of 6
Now we bring down the next zero from the dividend and we'll do the same thing all over again.60

60 ÷ 32 = ??
32 goes into 60 only one time whole. 32 multiplied by 1 is 32, subtracted from 60 leaves us 28.60 ÷ 32 = 1


32 * 1 = 32


60 - 32 = 28


60 ÷ 32 = 1
with a remainder of 28
We bring down the next digit from the quotient and continue with the same process.280

280 ÷ 32 = ??
 280 ÷ 32 = 8 

32 * 8 = 256

280 - 256 = 24

280 ÷ 32 = 8
with a remainder of 24
 240

240 ÷ 32 = ??
 240 ÷ 32 = 7

32 * 7 = 224

240 - 224 = 16

240 ÷ 32 = 7
with a remainder of 16
 160

160 ÷ 32 = ??
Wait, there's no remainder?

As 32 goes into 160 five times evenly, with no remainder, and there are no other digits in the dividend besides trailing zeroes (which have no effect on the final answer) we can actually stop here, because 014.71875 is our final answer.
160 ÷ 32 = 5

32 * 5 = 160

160 - 160 = 0

160 ÷ 32 = 5
with no remainder.
Since we wanted six decimal places we can simply add the trailing zero to the quotient.

We can go through all the steps for the final digit: zero divided by anything is zero.
00

0 ÷ 32 = ??

0 ÷ 32 = 0
We don't need to move the decimal point in the final answer. Both 471 divided by 32 and 47.1 divided by 3.2 give us the same result, 14.718750.471 ÷ 32 = 14.718750
47.1 ÷ 3.2 = 14.718750

http://www.calculatorsoup.com/calculators/math/longdivisiondecimals.php 


Sep 25th, 2014

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