Squaring the Ratio

Squaring the Ratio is on the syllabus for both PCS2/SY2 and ASY.To Square the ratio,you must 1st find out the real ratio,this means the real amounts that each person will get and you must then times together the amounts that both people are getting and divide it by the number of parts/total amount and this is the value of the ratio symbol.

You must then square the value of the ratio symbol and times it with the real amounts,both people are getting to get the amount of parts/total amount that the new ratio is set for and then divide this by the value of the ratio symbol ,to get what both of their amounts,in the new ratio must times together to make and the number of parts/total amount,of thenew ratio is what they add together to make.

Now,that we have found out what the 2 values times together to equal and add together to equal this can then be substitued into the quadratic formula,using the quadratic expression x squared+what the two values add to make lots of x + what the two values times to make and when put into the quadratic formula,you will get the valuesd of x and you must minus these to get the 2 missing values and they are the values,in the new ratio,the highest value will always be the original highest ratio part because they contributed more to the squaruing of the ratio.

The numbers should then be simplified to their nearest whole number and even if the question asks,cconverted to their real ratio,which means that the ratio parts of bothsides must add up to the original amount,in the original ratio and to do this divideeach value in the ratio,by the total amount in the ratio and times by the amount in the original ratio-this will then give you the amount each person will get if the ratio,they are sharing to is squared.

Worked Example
Common Error-You must use the unit that the question specifies or uses,using 67p instyead of 2/3 of a pound will result in a different squaring of the ratio.

Error on the working out I should have rounded to 427,instead of 426,in the simplified ratio of the squared ratio.

Applications
The main use of Squaring the Ratio is in Chemistry,where in unstable mixtures different amounts of stabilisers,eg.emulsions for emulsifiers,will need to be used to keep the substance stable and Chemists will need to know the right mixture of the compunds they are stabilising,in the right ratio,to keep the substance stable,otherwise it wouldn't have the right properties rich,flavourous texture for water and oil emulsions and a hard surface for an alloy and a miscalculation could also cause a dangerous chain reaction.Also,Squaring the Ratio can be used to further understand the affect of the ratio symbol and symbols on a numeric,algebraic or calucus exprsssion.It can also be used in currency exchange calculations,where a conversion rate,eg.ratio,will change resulting in different ratios of the value of diffferent currencies all over the world.