In mathematics, what is it meant by "TO USE DIGIT SUMS TO CHECK YOUR ANSWER"?

Question

Thanks and I'll give you Best Answer if you provide some examples too! (: Loves!

Answer 1

Add digits in modulus 9, perform the function. The answer should match the modulus 9 value of the solution.

For example:

21 + 37 + 69 = 127

21:2 + 1 = 3

37: 3 + 7 = 10
1+ 0 = 1

69: 6 + 9 = 15
1 + 5 = 6
(As you get better, you can pick out 9's, and know instantly that 69 -> 6.)

Add together the three values you got.
3 + 1 + 6 = 10
1 + 0 = 1

127: 1 + 2 + 7 = 10
1 + 0 = 1.

If you had gotten 128 as your answer, you would know immediately that this is wrong, because the value of the addends (1) would not equal the value of the answer (2).

Subtraction works the same way, except that sometimes the value of the minuend is larger than the subtrahend. In that case, make the value of the minuend any number with the same modulo and subtract.

173 - 17 = 156

173: 1 + 7 + 3 = 11
1 + 1 = 2

17: 1 + 7 = 8

2 - 8?

Change the 2 to 20.

20 - 8 = 12
1 + 2 = 3

156: 1 + 5 + 6 = 12
1 + 2 = 3, and again the answer is correct.



Multiplication:

241 * 91 = 21931

241: 2 + 4 + 1 = 7

91: 1

7 * 1 = 7

21931: 2 + 1 + 9 + 3 + 1 = 16
1 + 6 = 7


Division is a bit harder, because in this one case you work backwards.

1291 / 17 = 75 r 16

17: 8
75: 3
16: 7

8 * 3 + 7 = 24 + 7 = 31 -> 4

1291: 1 + 2 + 1 (you can knock out the 9)
= 4

The answers match.

My mother taught me how to do this when I was in the 4th grade. When you are doing math tests and are not permitted to use calculators, it will SAVE YOUR LIFE.

Answer 2

This is the method that used to be called "Casting out nines" in the old arithmetic books...

The idea is that the digit root (Or base nine modulus) follows a simple arithmetic using only the digits 0 through 8...
FIrst, the digit root of a number ....
add all the digits together... if the answer has more than one digit, do it again to that answer until you get a number with only a single digit (if it is nine, call it zero)..

235 has a digit root of 1 because 2+3+5 = 10 and 1+0 = 1

467 has a digit root of 8 because 4+6+7 = 17 and 1+7 = 8

36 has a digit root of zero because 3+6 = 9

What you are finding is the remainder when the number is divided by nine, but using a short cut..

467 / 9 = 51 with a remainder of 8...<--- that's the modulus or digit root...

Now if you add, subtract multiply or divide numbers, the digit roots of the numbers is preserved...(ok, an example)

467 + 236 = 703 and the digit roots add up too...
8 + 2 = 1 the digit root of 703 is 1

if we multiply 467 * 236 we get a number with a digit root of 7 (8*2= 16 and 1+6 = 7)
go ahead, multiply it out and see...

It also works for subtraction and if one is a factor of the other, it works for division...(honestly, I don't remember what happens if they don't go into each other evenly, guess I'll have to play with that)..


this is a way to check to see if you have made certain types of mistakes (it won't work for everything) but it is good enough that some ID numbers on bank notes etc... use it as check code...


Find more on my web site at http://www.pballew.net/arithm17.html#castnine
good luck

Answer 3

suppose you have a number XY. For example, 27 is X = 2, Y = 7. The sum of the digits would be X + Y. For example, the sum of the digits of 27 is 2 + 7 = 9. So if the sum of the digits is a multiple of 3, then we have X + Y = 3n. Where n is some number. This applies for 3 digit numbers (and more) as well. You would just have X + Y + Z = 3n

Answer 4

I'm not sure if this is what you mean, but it's true that if you add all the digits together, and then do arithmetical operations, you'll get the same thing as if you did the operations and then added the digits together. for example:
12*11 = 132
if you add the digits of 12, you get 3, and if you add the digits of 11, you get 2.
3*2 = 6, which is equal to the sum of the digits of 132. so this provides a quick way to check your multiplication.

sometimes you have to add digits repeatedly, for example
13*3 = 39
add digits: 4*3 = 12, add digits again to get 3.

here's another example with addition:
1432 + 349 = 1781.
add digits first: 1 + 7 = 8.

Answer 5

Quite simply a digit sum of a given integer is the sum of all its digits.
the digit sum of 924031 is calculated as 9+2+4+0+3+1 = 19

Why is this useful?
It can be used along with the concept of 'casting out nines' to check the accuracy of answers in problems of addition, subtraction, multiplication and division

Let's take three numbers (982,355,867)
Digit Sums are (19,13,21)

Subtract 9 as many times as you can from each one of these numbers you are left with (1,4,3)

If I add 982,355,867 then I get 2204
Well, the digit sum of 2204 = 8 = (1+4+3)
This equality verifies the correctness of the answer.

There are similiar subtraction, multiplication and division techniques, to avoid negative numbers in subtraction verifications it is sometimes necessary to add back a 9.