Estimate before you calculate

Hello, and welcome to Myriora Maths! Many 11 plus questions are multiple choice, so the right answer is already on the page. You don't always need to work it out exactly. A quick estimate can knock out the wrong ones!

Here's how to estimate. Round each number to something easy, like a whole ten, or a whole hundred. Forty-nine is about fifty. Twenty-one is about twenty. Then do the easy sum in your head: fifty times twenty is a thousand.

Which is forty-nine times twenty-one? A: three hundred and twenty-nine. B: one thousand and twenty-three. C: one thousand and twenty-nine. D: ten thousand, two hundred and ninety. Our estimate is about a thousand. That knocks out A, which is far too small, and D, which is ten times too big. Now it's B or C.

To choose between them, look at the last digit. Nine times one is nine, so the answer must end in nine. B ends in three, so it's out! The answer is C, one thousand and twenty-nine, and we didn't do any long multiplication!

It works for dividing too. What is six hundred and twelve divided by eighteen? Is it three point four, thirty-four, three hundred and forty, or forty-three? Estimate: six hundred divided by twenty is thirty. That knocks out three point four and three hundred and forty. And thirty-four is much closer to thirty than forty-three is. Check: thirty-four times eighteen is six hundred and twelve.

And with decimals. What is three point nine times five point one? Is it one point nine eight nine, nineteen point eight nine, or a hundred and ninety-eight point nine? Four times five is twenty, so it must be nineteen point eight nine. The estimate tells you where the decimal point goes!

A common mistake is doing the long sum, making a slip, and not noticing. Forget the zero in the tens row, and forty-nine times twenty-one comes out as a hundred and forty-seven. An estimate of a thousand shows straight away that it's wrong! So always estimate first.

Your turn! Which is two hundred and ninety-eight times thirty-one? Estimate first, then check the last digit. You've got twenty seconds, or pause the video. Go!

Time's up! Three hundred times thirty is nine thousand. That knocks out A and D. Eight times one is eight, so the answer ends in eight. That knocks out B. The answer is C: nine thousand, two hundred and thirty-eight!

Quick review. Round to easy numbers, and estimate first. Cross out answers that are far too big, or far too small. Use the last digit to choose between close ones. And let the estimate tell you where the decimal point goes. See you next time!