Long multiplication

Hello, and welcome to Myriora Maths! What is three hundred and forty-seven, times twenty-six? Long multiplication can do any multiplication, step by step. Let's learn how!

Twenty-six is twenty plus six. So we do two easy rows: three hundred and forty-seven times six, and three hundred and forty-seven times twenty. Then we add the two rows together.

First row: times six. Start with the ones: seven times six is forty-two. Write two, and carry four. Four times six is twenty-four, plus the carried four, is twenty-eight. Write eight, and carry two. Three times six is eighteen, plus two is twenty. Write twenty. The first row is two thousand and eighty-two.

Second row: times twenty. Twenty is two times ten, so first, write a nought in the ones column. Then times by two: seven twos are fourteen, so write four, and carry one. Four twos are eight, plus one is nine. Three twos are six. The second row is six thousand, nine hundred and forty.

Now add the two rows. Two thousand and eighty-two, plus six thousand, nine hundred and forty, is nine thousand and twenty-two.

Why the nought? The two in twenty-six means two tens. Three hundred and forty-seven times two is six hundred and ninety-four, so times twenty is six thousand, nine hundred and forty. Times ten moves every digit one place to the left, and the nought keeps them in the right places.

Always check with an estimate. Three hundred and forty-seven is about three hundred and fifty, and twenty-six is about twenty-five. Three hundred and fifty times twenty-five is eight thousand, seven hundred and fifty. That's close to nine thousand and twenty-two, so our answer is sensible!

Here's a question that catches lots of people. Some people forget the nought in the second row, and add six hundred and ninety-four instead. They get two thousand, seven hundred and seventy-six. That's far too small: the estimate was about nine thousand! It's times twenty, not times two, so write the nought first.

Your turn! What is a hundred and twenty-eight times twenty-four? Pick the right card. You've got twenty seconds, or pause the video. Go!

Time's up! First row: a hundred and twenty-eight times four is five hundred and twelve. Second row: a hundred and twenty-eight times twenty is two thousand, five hundred and sixty. Add them: three thousand and seventy-two!

Quick review. Split the second number into tens and ones. Do one row for each part. In the tens row, write a nought first. Then add the rows, and check with an estimate. See you next time!