We start out with the only information we have – Kok Yang’s mass (k) expressed as a fraction of Melvin’s (m):
k=2/7m
In order to express Melvin’s mass as a fraction of Kok Yang’s, we need to find what m is equal at – and the easiest way to do this would be to remove anything but m from that side of the equation.
Now, since we can add new operations to an existing equation – the only requirement is that we have to add the same operation to both of its sides -, we’ll just divide both of them by 2/7:
k/(2/7)=(2/7)/(2/7)m
(k/1)/(2/7)=1*m
(7*k)/1*2=1*m
7/2k=m,
thus only leaving m on its side, and showing what it’s equal at on the other.
Melvin’s mass is 7/2 of Kok Yang’s.
The ratio of Kok Yang’s mass to Melvin’s mass can be expressed as k:m or k/m, and can be derived in a similar manner and using the same equation as above:
k=2/7m,
except that this time we need to find what k/m is equal at. The easiest way to do this would be to once again add a new operation to both sides of the equation – this time, dividing them by m:
k/m=2/7(m/m)
k/m=2/7
The ratio of Kok Yang’s mass to Melvin’s is 2 to 7.
The ratio of Melvin’s mass to the total mass (k+m) can be expressed as m:(k+m) or m/(k+m), and can be calculated by using one of the equations above. Since we’re looking for ratio of Melvin’s mass to something, let’s choose to use m=7/2k, and calculate the total first:
k+m=k+7/2k=(2k+7k)/2=9/2k
Now, we look for the ratio of m to the total:
m/(k+m)=(7/2k)/(9/2k)=7/9
THe ratio of Melvin’s mass to the total mass is 7 to 9.
