Colleagues in my dept have been looking at Ratio with year 10 and in particular, questions involving ratio that change when one quantity is shifted.

EG:

Ali and Bo share money in the ratio 7 : 5. Ali gives £24 to Bo and the ratio of their amounts is now 1 : 2. How much did they each have to start with?

I was thinking about how it can be linked to fractions that are shaded. When we want to compare fractions we can create common denominators and when we want to compare ratios we scale the ratios so they have the same number of parts… 3 : 2 has 2 parts and 7 : 8 has 15 parts. If we multiply 3 : 2 by 3 then we have a ratio 9 : 6.