Counting up

Hello, and welcome to Myriora Maths! What is one thousand, minus six hundred and thirty-seven? Taking away is tricky here, with all those zeros. So let's count up instead!

Remember, a take away is also a difference: the gap between two numbers. So we can start at six hundred and thirty-seven, and count up to one thousand. The size of the gap is the answer.

Jump to friendly numbers. From six hundred and thirty-seven, jump three to get to six hundred and forty. Then jump sixty to get to seven hundred. Then jump three hundred to get to one thousand.

Now add up the jumps. Three, plus sixty, plus three hundred, is three hundred and sixty-three. So one thousand minus six hundred and thirty-seven is three hundred and sixty-three. Check: six hundred and thirty-seven plus three hundred and sixty-three is one thousand.

Why does this work? The gap between two numbers is the same, whichever end you start from. Counting up uses easy jumps: to the next ten, then the next hundred. And adding is easier than taking away!

This is how shopkeepers work out change. A pencil costs thirty-seven pence, and you pay with one pound. Count up from thirty-seven: three pence makes forty, and sixty pence makes one pound. Your change is sixty-three pence.

Let's try one together. What is five hundred, minus two hundred and eighty-four? Count up from two hundred and eighty-four. Say it out loud!

Six makes two hundred and ninety. Ten makes three hundred. Two hundred makes five hundred. Six plus ten plus two hundred is two hundred and sixteen!

Here's a question that catches lots of people. What is one thousand minus six hundred and thirty-seven? Some people make every digit up to ten: six and four, three and seven, seven and three. That gives four hundred and seventy-three. But check: six hundred and thirty-seven plus four hundred and seventy-three is one thousand, one hundred and ten. That's too much! Counting up gives three hundred and sixty-three.

Your turn! What is one thousand, minus four hundred and fifty-two? Pick the right card. You've got fifteen seconds, or pause the video. Go!

Time's up! From four hundred and fifty-two, eight makes four hundred and sixty. Forty makes five hundred. Five hundred makes one thousand. Eight plus forty plus five hundred is five hundred and forty-eight!

Quick review. A take away is the gap between two numbers. Count up from the smaller number, in friendly jumps. Then add up the jumps. See you next time!