All of us know that division is mainly about subtraction, but can we do it in a relaxing way. The answer is affirmative!

Assume that a division question does not have a remainder. Questions to be analysed: 4-digit divides 2-digit.

divisor x quotient = dividend, p x q = r, e.g. 13x65=0845

- Find the tens-digit

</py code>

# find tens-digit

# round the dividend to nearest 100

```
r2 = round(r, -2)
```

# round the divisor to 0/5

```
if p%10 in [0, 1, 2]:
p2 = p//10*10
elif p%10 in [3, 4, 5, 6, 7]:
p2 = p//10*10+5
else:
p2 = p//10*10+10
print(r2//10, '/', p2)
q2 = math.floor(r2/p2)
```

- Find the units-digit

### 9x9 multiplication table modolus of 10

This is just the traditional multiplication table we learnt, so no worries!

Just look at the units-digit as 4x9=36 â†’ 6

**1 2 3 4 5 6 7 8 9**

**2** 4 6 8 0 2 4 6 8

**3** 6 9 2 5 8 1 4 7

**4** 8 2 6 0 4 8 2 6

**5** 0 5 0 5 0 5 0 5

**6** 2 8 4 0 6 2 8 4

**7** 4 1 8 5 2 9 6 3

**8** 6 4 2 0 8 6 4 2

**9** 8 7 6 5 4 3 2 1

e.g. 1472 / 16 = 92

left column = 6 (from divisor 16)

element = 2 (from dividend 1472)

top row = 2/7 (from quotient 92)

example 1 :

50 x 37 = 1850

1850 / 50 = ?

1800 / 50

36

final decision: 36 â†’ 37 bc 1850>1800

example 2 :

67 x 44 = 2948

2948 / 67 = ?

2900 / 65

44

[4]

final decision: 4 4

example 3 :

76 x 63 = 4788

4788 / 76 = ?

4800 / 75

6**4**

[**3**, 8] //4 is closer to 3 than 8

final decision: 6 3

example 4 :

89 x 52 = 4628

4628 / 89 = ?

4600 / 90

51

[2]

final decision: 5 2

example 5 :

32 x 49 = 1568

1568 / 32 = ?

1600 / 30

5**3**

[**4**, 9] // 3 is closer to 4 than 9

final decision: 5 4

example 6 :

56 x 34 = 1904

1904 / 56 = ?

1900 / 55

3**4**

[**4**, 9]

final decision: 3 4

example 7 :

45 x 87 = 3915

3915 / 45 = ?

3900 / 45

8**6**

[1, 3, 5, 7, 9] // this is what makes this method so-called relaxing game

final decision: 8 5 â†’ 87 because 3915>3900

example 8 :

65 x 72 = 4680

4680 / 65 = ?

4700 / 65

72

final decision: 72

example 9 :

11 x 54 = 594

594 / 11 = ?

600 / 10

60

[4]

final decision: 6 4

example 10 :

73 x 62 = 4526

4526 / 73 = ?

4500 / 75

60

[2]

final decision: 6 2

To conclude, it is a quick approximation to get a division answer for the Non-remainder type question.