High School Math - What am i doing wrong here?

Question

Can someone please explain me what is the wrong with the Example2 below. Eventhough the same approach, Example 1 is giving me the correct answer but Example2 is giving me the wrong answer.

**Note: If you find the below data is not properly formated, please see the attachment for the same ***
 Example1 : Divide 113 by 4

Step1: 
 4)113(
Step2:
 4)113( 2 
 8
 -------
 3 /* 11 – 8 = 3 */
Step3: 
 4)113( 2 
 8
 -----
 33 /* Import 3 from Top */
Step4:
 4)113( 28 
 8
 -----
 33 
 32
 -------
 1
Step5:
 4)113( 28. 
 8
 -----
 33 
 32
 -------
 10 /* Place a point after 28 and put a Zero after 1 -  Do you agree with this? Atleast i agree!*/

Step6:
 4)113( 28.25 
 8
 -----
 33 
 32
 -------
 10
 8
 --------
 20
 20
 --------
 0
To make sure what we got is correct: 28.25 * 4 = 113

Now, Example2 : Divide 123 by 4
Step1: 
 4)123(
Step2:
 4)123( 3 
 12
 ----
 0 /* 12 –128 = 0 */
Step3: 
 4)123( 3 
 12
 -----
 03 /* Import 3 from Top */
Step4:
 4)123( 3. 
 12
 -----
 30 /* Put a point after 3 in Left brackt and place a zero after 3 (As i agreed in Example 1) */
 
Step5:
 4)123( 3.7 
 12
 -----
 30 
 28
 -------
 2

Step6:
 4)123( 3.75 
 12
 -----
 30 
 28
 -------
 20 
 20
 --------
 0
Answer Validation: 4 * 3.75  IS NOT EQUAL  TO 123

What is the wrong I am doing here?

Cheers!
Ravi

whiplash2411 · Answer

Well for starters, once you're done dividing the 12 part of 123 by 4, and you bring the 3 down, you have to put a zero on the quotient side before you can add a zero to the 3 to make it 30.

So it should be

4)123(30.75
 12
--------------
 03 
 0
------------
 030
 028
------------
 0020
 0020
------------
 0

So the answer is 30.75. I mean this is basic math and you don't need to do long division at all. 4*3 = 12, so 4*30 = 120 < 123, so you know that your answer has to be greater than 30.

nravi4 · Answer

Mr whiplash2411,

Thank you for response. But why do i have to put 0 first in quotient side? I didn't do the same thing in Example1 before putting a point in quotient side.

Cheers!
Ravi

whiplash2411 · Answer

The basic rule is, everytime you bring one digit down for division, you check for divisibility. So in this case, 12 is divisible and you get 3 on the side. When you bring the 3 down, 3 is NOT divisible by 4, so you put a zero on the quotient, before adding a 0 to the 3, making it 30 and then proceeding with the decimal point. In the first example, when you divide 11 by 4, you get 2, and you get a REMINDER from this which is 3, and then you bring the 3 down and hence check for divisibility of 33. And 33 > 4 so you add the 8 there.

Whenever you bring a digit down from the main number you're dividing you must check for divisibility. If the number you've brought down is less than the divisor itself, you add a zero. But in terms of checking for results, think about in terms of common sense. Does 3.75*4 being equal to something near 120 make sense? No. That's a way to cross check.

And just for reference, it's a miss. Not Mr.

Hope this helps. If not, refer the math book at GMAT Club for further references on the number properties and divisibility and so on.

You didn't add the zero because when you brought the 3 down, there was already a reminder there. So you made the number 33 and then added an 8 there. Here the initial reminder is a 0 and when you bring the 3 down, it stays as 03 and hence you add a 0 to the quotient because obviously 3 is not divisible by 4, being smaller than it.

nravi4 · Answer

Miss whiplash2411,

I am more worreid about the mistake i am doing in Example2, rather than results or answer validations, and your above explanation spot on clarified my doubt.

Appreciate your inputs.

Cheers!
Ravi

High School Math - What am i doing wrong here?

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