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MENTAL MATH: TiPs & TrIcKs for...

Division II

Dividing by 7: take the last digit, double it, then subtract it from the rest of the number. If it's divisible by 7, the number is too.

 

 
     

406 ÷ 7 = 58 (6 x 2 = 12 ; 40 - 12 = 28 ; 28 ÷ 7 = 4)
 3,983 ÷ 7 = 569 (3 x 2 = 6 ; 398 - 6 = 392 ; 392 ÷ 7 = 56)

Dividing by 8: if the last three digits are divisible by 8, so is the number. The three digit number (XYZ) will be divisible by 8 if: X is even and YZ are divisible by 8 or if X is odd and YZ - 4 is divisible by 8.

24,472 ÷ 8 = 3,059
(4 is even and 72 is divisible by 8)

65,184 ÷ 8 = 8,148
(1 is odd and 84 - 4 = 80, which is divisible by 8)
 

 


Dividing by 9: if the sum of all digits is divisible by 9, the number will also be divisible by 9 (and 3).
180 ÷ 9 = 20
(1 + 8 = 9)
[180 ÷ 3 = 60]


64,773 ÷ 9 = 7,197
(6 + 4 + 7 + 7 + 3 = 27)
[64,772 ÷ 3 = 21,591]

Dividing by 10: if the number ends in cero (0).
120 ÷ 10 = 12
87,760 ÷ 10 = 8,776

 

     
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