Only the last digit

About this video

A market seller has 1,235 marbles and wants to put them in bags of five. Will any be left over? You don't need to divide: one glance at the last digit tells you, and this short animation shows why. Ten dots split into five pairs, and into two fives, with nothing left over. So when 1,235 is written as 123 tens and 5 ones, every one of those tens splits into fives with nothing over, and only the 5 ones are left to decide. They make one more bag, so 1,235 divides by 5.

That gives three quick tests. A number divides by 10 if its last digit is 0, by 5 if it ends in 0 or 5, and by 2 if it ends in 0, 2, 4, 6 or 8, which means it is even. The last digit even tells you what is left over: 1,237 ends in 7, which is a five and 2 more, so 1,237 marbles in bags of five leave 2. But be careful: the tests work only for 2, 5 and 10, the numbers that split ten exactly. 13 ends in 3, yet 13 divided by 3 leaves 1 over. This video goes with the Tests for 2, 5 and 10 lesson of Number Theory Level 1 on Knaph.

Transcript

1. 0:00Twelve hundred and thirty-five marbles, in bags of five. Any left over?
2. 0:04Ten splits into five twos, and into two fives. Nothing left over.
3. 0:11So all the tens are fine. Only the last digit decides.
4. 0:17Ends in zero, divides by ten. Zero or five, by five. Even, by two.
5. 0:23Twelve thirty-seven ends in seven. A five, and two left over.
6. 0:29But not for three. Thirteen leaves one over.
7. 0:34Every ten splits, so only the last digit decides.