ffirs.indd

42 Speed Math for Kids
Eleven nines are 99. Nine plus 9 equals 18. Wrong answer? No, not
yet. Eighteen is a two-digit number, so we add its digits together:
1 + 8. Again, the answer is 9.
If you multiply any number by 9, the sum of the digits in the answer
will always add up to 9 if you keep adding the digits until you get
a one-digit number. Th is is an easy way to tell if a number is evenly
divisible by 9. If the digits of any number add up to 9, or a multiple
of 9, then the number itself is evenly divisible by 9.
If the digits of a number add up to any number other than 9, this
other number is the remainder you would get after dividing the
number by 9.
Let’s try 13:
1 + 3 = 4
Four is the digit sum of 13. It should be the remainder you would get
if you divided by 9. Nine divides into 13 once, with 4 remainder.
If you add 3 to the number, you add 3 to the remainder. If you
double the number, you double the remainder. If you halve the
number, you halve the remainder.
Don’t believe me? Half of 13 is 6.5. Six plus 5 equals 11. One plus
1 equals 2. Two is half of 4, the nines remainder for 13.
Whatever you do to the number, you do to the remainder,
so we can use the remainders as substitutes.
Why do we use 9 remainders? Couldn’t we use the remainders after
dividing by, say, 17? Certainly, but there is so much work involved
in dividing by 17, the check would be harder than the original
problem. We choose 9 because of the easy shortcut method for
fi nding the remainder.