Sum and difference

Hello, and welcome to Myriora Maths! Two numbers add up to forty-six. One is twelve more than the other. What are they? Guessing takes ages. But there's a neat trick!

Draw the two numbers as bars. The big bar is the small bar, plus an extra twelve. Together, they make forty-six.

Now chop off the extra twelve. Forty-six take twelve is thirty-four. That leaves two equal bars. So each one is thirty-four divided by two: seventeen!

So the small number is seventeen. Add the twelve back on: the big number is twenty-nine. Check: seventeen plus twenty-nine is forty-six!

Here's the rule. Small number: the sum minus the difference, then halve. Big number: the sum plus the difference, then halve. Forty-six plus twelve is fifty-eight. Halve it: twenty-nine. It matches!

It hides in word problems too. Amy and Ben have thirty sweets altogether. Amy has eight more than Ben. Thirty take eight is twenty-two. Halve it: Ben has eleven, and Amy has nineteen.

A common mistake is halving the sum first. Half of forty-six is twenty-three, but then the numbers aren't twelve apart. Take away the difference first, then halve.

Your turn! Two numbers add up to sixty. Their difference is fourteen. What are they? You've got twenty seconds, or pause the video if you need more time. Go!

Time's up! Sixty take fourteen is forty-six. Halve it: twenty-three. Add fourteen: thirty-seven!

Quick review. Draw two bars. Chop off the difference, and halve what's left to get the small number. Then add the difference back for the big one. See you next time!