Splitting the total when a ratio is given is a fairly basic bit of number maths. I first encounter this at middle school level, typically for an 11+ or 13+ maths ISEB entrance exam, or at GCSE maths.
I made a video three years ago on how I explain how a total is split into a given ratio.
Once you have watched the video you will notice how I use whitespace to decode the question and make the problem clearer first.
The problem is a simple one, there are 140 students at a school and the ratio of girls to boys is 3:4. How many girls and how many boys are there at the school?
I first put down the information in a very compact and clean form. Writing the ratio down, and the letter G and B above the relevant part of the ratio. I also write out the total number of students below.
The key to ratio questions is finding 1 part and then amplifying the 1 part to 3 or 4 parts later. Once you have 1 part, it is easy to find as many other parts as you want. So I work out that:
3 parts + 4 parts = 7 parts.
7 parts = 140 students
1 part = 140/7 = 20 students
3 parts = 20 students x 3 = 60 students
4 parts = 20 students x 4 = 80 students
And that’s the question done! Please let me know if you have any comments on the video or this method below.
Now this is a deep deep question. And one that we all ask. In fact, do we really know if the universe is even finite at all? Fortunately the answer to this is covered at school in the context of Astronomy in Physics. Finite or infinite, according to the latest information on Physics, and the measurements we have made so far, it is possible to get a very good picture on this. But how can one put this into context, or visualise this?
This is a video I show to all my Physics students, it is a totally mindblowing visualisation of the universe, zooming out of the earth, into the solar system, how the solar system fits into the Milky Way galaxy, and where the Milky way fits in amongst many many galaxies. Produced by the American Museum of Natural History, and with a beautiful ambient trance like soundtrack this short video will take you on a very long journey away and then back from earth.
The distances are measured in how fast light travels, because in the big scheme of things light is very slow indeed. While it takes roughly 8 minutes for light to get from the Sun to the Earth, it takes millions of years to get to us from the outer reaches of the universe.
This video fascinates all my students, it will leave you stunned and in awe knowing where you fit into the big scheme of things. It is a total joy to be able to share this with my students, and I never get bored of watching it again and again, a truly great Physics resource. Hit play and enjoy the ride.