Long division

Hello, and welcome to Myriora Maths! What is nine hundred and thirty-six divided by twenty-four? Dividing by a two-digit number is harder, because the remainders get big. Long division keeps everything tidy, by writing the working underneath. Let's go!

Set it out like the bus stop: nine hundred and thirty-six inside, and twenty-four outside. But this time, leave lots of room underneath for the working.

First, a tip that makes it much easier. Write out the multiples of twenty-four. Twenty-four, forty-eight, seventy-two, ninety-six, and so on, up to nine twenty-fours: two hundred and sixteen. Now you can just look them up!

How many twenty-fours are in nine? None. Nine is too small. So look at ninety-three instead. How many twenty-fours are in ninety-three? Three twenty-fours are seventy-two. Four would be ninety-six: too big. So write three on the roof, above the three.

Write seventy-two under the ninety-three, and take it away. Ninety-three minus seventy-two is twenty-one. That's smaller than twenty-four, so we chose the right number. Good!

Now bring down the next digit, the six. Write it next to the twenty-one, to make two hundred and sixteen.

How many twenty-fours are in two hundred and sixteen? Look at the list: nine twenty-fours are exactly two hundred and sixteen. Write nine on the roof. Take it away, and there's nothing left. So nine hundred and thirty-six divided by twenty-four is thirty-nine!

Why does bringing down work? The twenty-one left over is twenty-one tens. That's two hundred and ten ones. Add the six ones, and you get two hundred and sixteen ones to share. It's just like carrying in short division!

Always check. Thirty-nine times twenty-four is nine hundred and thirty-six. And estimate: about a thousand, divided by about twenty-five, is forty. That's close to thirty-nine, so it makes sense!

Here's a question that catches lots of people. How many twenty-fours are in ninety-three? Ninety-three is close to ninety-six, so some people say four. But four twenty-fours are ninety-six, and that's more than ninety-three! You can't take ninety-six away from ninety-three. It's three: seventy-two, with twenty-one left.

Your turn! What is six hundred and seventy-two divided by thirty-two? Use long division. Pick the right card. You've got twenty seconds, or pause the video. Go!

Time's up! Six is too small, so start with sixty-seven. Two thirty-twos are sixty-four, with three left. Bring down the two: thirty-two. One thirty-two is thirty-two, with nothing left. The answer is twenty-one!

Quick review. List the multiples of the number you divide by. See how many fit, and write it on the roof. Multiply, take away, and bring down the next digit. Then check by multiplying back, and with an estimate. See you next time!