Today’s article we will be looking at division problems,dividing any number by 9:
The vedic sutra which will be :
निखीलम् नवतः चरम् दशतः
All from 9 and last from 10
Let’s take following examples
1)412 ÷9
To find the answer :
Step1: keep 4 as it is
Step2: add 4 + 1 =5
Step3: add 5 + 2 =7
quotient is 45 and remainder is 7
Decimal form = 45.7777….
2) 11352 ÷ 9
Step 1: keep 1 as it is
Step 2: 1 + 1= 2
2 + 3= 5
5 + 5 =10
10 +2 =12
Step 3: quotient has numbers
1,2,5,10 and remainder 12
Step 4: the two digit quotient 10 is not possible ,hence 1 will be carried forward to earlier number 5 and added to it which becomes 6,
Now quotient is 1260 rem.12
Remainder can’t exceed 9 ,hence we do 12÷9=quotient 1 rem.3
Step 5: this quotient is added to above quotient 1260
Hence finally Q( quotient)= 1261
(Remainder) R = 3
Decimal form is 1261.3333….
3) 342104 ÷ 9
Step 1: 3 as it is
Step 2 : 3+4=7
7+2=9
9+1=10 ( carry forward 1)
10+0=10 (carry forward 1)
10+4=14 (remaider)
Quotient: 3,7,9,10,10 Remainder 14
Taking carry forwards for 2 digit quotient
3,7,10,1,0 remainder 14
Which again becomes 38010 with remainder 14,which is re-evaluate to become quotient 1and remainder 5
Step 3: combining all, we get
Q= 38011(adding quotient part of 14 that is 1)
Remainder = 5
Decimal form: 38011.555…
4) 3214÷ 9
Step 1: keep 3 as it is
Step 2: 3+2=5
5+1=6
6+4=10
Q = 356 remainder 10
Evaluating 10,Q=1 Remainder=1
Step 3: final answer :Q= 357 R=1
Decimal form= 357.1111….
You can see that doing certain addition technique, without doing division we can find the answer and also in decimal form, because the final remainder is the number which recurrs after decimal point..
Now try following problems:
1) 3462÷9
2)184÷9
3) 6321÷9
4) 40023÷9
5)325412÷9
6) 2001235÷9
7) 32854÷9
8) 197233÷ 9
