Division and remainders

Here’s an example of division: 18 divided by 3. Easy peasy, 6! Because 6 times 3 is 18. Here’s another one: 22 divided by 5. Hey, wait a moment.

22 is not in 5’s multiplication table. Is it possible to divide 22 by 5? Yes, you can, but you can’t divide it evenly. Here are 22 penguins and five sheets of ice. Let’s see if we can get an equal number of penguins on each sheet.

Shoo shoo, spread out, little birds! There you go! Four penguins on each of the five sheets of ice, that’s 4 times 5, which equals 20. But, we have two penguins left. We don’t want to split any cute penguins in pieces, so we just decide to call these last two a remainder.

22 divided by 5 equals 4, with a remainder of 2. Let’s try another one! 40 divided by 6. Try thinking like this: how many times can you fit 6 into 40? Let’s see, 5 times 6 is 30, so at least five times.

And 6 times 6 is 36, so we can fit 6 sixes in there too. But can we fit seven? 7 times 6 equals 42. No, you can’t fit 7 sixes inside 40. So, 40 divided by 6 equals 6, and then a remainder.

How large is that remainder? Since 6 times 6 is 36, we have four more to go before we reach 40. The remainder is 4. Are you following so far? We are trying to figure out how many times the denominator fits inside the numerator, and then how much is left of the numerator.

Let’s try two more, where you get to work more on your own. 61 divided by 8. 8 times 7 equals 56. 56 is pretty close to 61, so 8 fits 7 times inside 61, but no more than that. And 61 minus 56 equals 5.

So, we get a remainder of 5. One last example? Yes! 100 divided by 9. Hmm, large numbers now!

9 times 9 is 81. 9 times 10 is 90. Still more than 9 steps from 100. What is 11 times 9? 99!

11 times 9 is 99. And that is just one less than 100. So, 100 divided by 9 is 11, with a remainder of 1.