Mental multiplication tricks

Hello, and welcome to Myriora Maths! Here are three tricks that let you multiply big numbers in your head. They look like magic, but each one has a simple reason.

Trick one: times eleven. For forty-three times eleven, split the four and the three apart. Add them: four plus three is seven. Put the seven in the middle: four hundred and seventy-three!

Why does it work? Eleven is ten plus one. Forty-three times ten is four hundred and thirty, and forty-three times one is forty-three. Add them, and the tens digit becomes four plus three.

If the middle adds up to ten or more, carry one. Seventy-eight times eleven: seven plus eight is fifteen. Write the five in the middle, and add the one to the seven. That's eight hundred and fifty-eight.

Trick two: numbers close to a hundred. Ninety-eight is two less than a hundred. A hundred sevens are seven hundred. Two sevens are fourteen. So take fourteen away: six hundred and eighty-six.

Trick three: twenty-one times nineteen. Both numbers are one away from twenty: one above, and one below. The answer is twenty times twenty, take away one times one. Four hundred take away one is three hundred and ninety-nine!

Why does it work? Twenty-one times nineteen is twenty-one times twenty, take away one twenty-one. That's four hundred and twenty, take away twenty-one: three hundred and ninety-nine. It always works out as the middle times itself, take away the gap times itself. So twenty-two times eighteen is four hundred take away four.

Here's a question that catches lots of people. Seventy-eight times eleven. Some people put the whole fifteen in the middle, and get seven thousand, one hundred and fifty-eight. But only one digit fits in the middle! Carry the one: eight hundred and fifty-eight.

Your turn! What is ninety-nine times eight? Pick the right card. You've got fifteen seconds, or pause the video. Go!

Time's up! Ninety-nine is one less than a hundred. A hundred eights are eight hundred. Take away one eight: seven hundred and ninety-two!

Quick review. Times eleven: add the two digits, and put the answer in the middle. Close to a hundred: use a hundred, then fix it. One above and one below: the middle times itself, take away one. See you next time!