Working backwards

Hello, and welcome to Myriora Maths! Ava spends half of her money on a book. Then she spends three pounds on a drink. She has seven pounds left. How much did she start with?

Here's the trick: work backwards. Start at the end, where we know the answer. Then undo each step, in the opposite order. Every step has an opposite: adding undoes taking away, and doubling undoes halving.

First, write the story as a chain. Start with her money. Halve it. Take away three. And we get seven.

Now go backwards from seven. The last step was take away three, so we add three: ten. Before that, she halved her money, so we double it: twenty. Ava started with twenty pounds!

Let's check by going forwards. Half of twenty is ten. Take away three: seven. It works!

A common mistake is undoing the steps in the wrong order. If we double seven first, we get fourteen, then add three: seventeen. But half of seventeen, take away three, is five pounds fifty, not seven! Always undo the last step first.

Your turn! I think of a number. I double it, then add five, and get thirty-three. What was my number? You've got twenty seconds, or pause the video if you need more time. Go!

Time's up! Undo the add five: thirty-three take away five is twenty-eight. Undo the double: half of twenty-eight is fourteen. My number was fourteen!

Quick review. Start from the end, where you know the answer. Always undo the last step first. Use the opposite of each step. Then check by going forwards. See you next time!