To simplify numbers suppose that Ohio has 18 congressional districts and 12 go Republican but the state is 50 percent plus 1 for Obama.
So 2/3 are GOP for Congress.
But 1/2 are for GOP-Romney for President.
Simplifying, we assume that 2/3 – 1/2 of GOP voters voted Obama and all others voted for their party and we ignore 3rd parties.
2/3 – 1/2 = 4/6 – 3/6 = 1/6
1/6 of the total switched for president. 2/3 were for GOP to start with. This is 4/6. So 1 out of 4 of GOP voters for Congress voted for Obama.
We can get the ratio 1/4 by
Take 1/6 and divide by 4/6. The result is 1/4.
This illustrates why we divide fractions.
Projects can be to look up the exact results and to consider more exotic possibilities like more than 1/6 cross over from GOP to Obama but some cross over from Dem for Congress to Romney.
Third parties can be done as well.
There are many opportunities to subtract, add, divide and multiply fractions.
This can be done for different states.
This is very good for Wall Work. Teams can take a different state and do an illustration of dividing by fractions in this way.
Students can also be taught to round off or simply fraction ratios to make it easier for others to grasp what happened in their team’s state. This teaches them valuable communication skills.
Approximating the actual ratios by fractions like 2/3, 1/6, etc. makes it easier for others to understand what happened. They really are not interested in the exact ratios anyhow. The more extra figures you load up the greater the cognitive load. To get your message across, reducing the complexity of the fraction helps. In fact, it is usually essential.