Checking your answers

Hello, and welcome to Myriora Maths! You've finished the paper, and there are five minutes left. How do you check your answers, without just doing every sum again? Here are four quick checks.

Check one: undo it. Five hundred and four minus two hundred and sixty-seven is two hundred and thirty-seven. To check, add it back: two hundred and thirty-seven plus two hundred and sixty-seven. That's five hundred and four. It matches, so it's right!

Here's one that's wrong. Five hundred and three minus two hundred and seventy-eight: someone wrote three hundred and thirty-five. Check: three hundred and thirty-five plus two hundred and seventy-eight is six hundred and thirteen. That's not five hundred and three, so something went wrong! Do it again, and the answer is two hundred and twenty-five.

Multiplying and dividing undo each other too. Seven hundred and twenty-eight divided by eight is ninety-one. Check: ninety-one times eight is seven hundred and twenty-eight. Yes!

Check two: does it make sense? You worked out a child's height, and got one point four kilometres. That's taller than the tallest building in the world! It should be one point four metres. A pencil that costs forty-five pounds? It's probably forty-five pence.

Check three: the last digit. Look at twenty-three times fourteen. Three times four is twelve, so the answer must end in two. Twenty-three times fourteen is three hundred and twenty-two: it ends in two. If yours ends in anything else, look again.

Check four: check a different way. If you do the same sum the same way again, you often make the same slip again! So undo it, estimate it, or check the last digit instead.

A common mistake is checking just by looking. Two hundred and forty-seven plus one hundred and eighty-six, written as three hundred and twenty-three, can look fine at a glance. Your eyes see what you expect to see! Undo it: three hundred and twenty-three minus one hundred and eighty-six is a hundred and thirty-seven, not two hundred and forty-seven. The real answer is four hundred and thirty-three.

Your turn! Ben worked out six hundred and twelve divided by four, and got a hundred and sixty-three. Is he right? Check it! You've got twenty seconds, or pause the video. Go!

Time's up! Undo it: a hundred and sixty-three times four is six hundred and fifty-two. That's not six hundred and twelve, so Ben is wrong. The right answer is a hundred and fifty-three, because a hundred and fifty-three times four is six hundred and twelve.

Quick review. Undo it: add back, or multiply back. Ask: does it make sense? Check the last digit. And check a different way, not the same way twice. See you next time!