Explanation:
To work out the ratio eg, we need to first find a common term between f and g.
We can do this by finding the least common multiple (LCM) of their respective ratios.
The ratio for f: g is given as 2:3, which means that for every 2 parts of f, there are 3 parts of g.
The ratio for e: f is given as 3:7, which means that for every 3 parts of e, there are 7 parts of f.
To find a common term between f and g, we can multiply the ratio for f: g by 3 (since 3 is a common multiple of 2 and 3):
f: g = 2:3
3f: 3g = 2(3): 3(3)
3f: 3g = 6: 9
Now we can see that the ratio of f to g is 3:4 (by dividing both sides of the above equation by 3):
f: g = 3:4
Therefore, the ratio of e: g can be found by combining the ratios of e: f and f: g:
e: f = 3:7
f: g = 2:3
Multiplying both ratios together, we get:
e: f: g = 3:7:21
Simplifying this ratio by dividing each term by 3, we get:
e: f: g = 1:2⅓:7
Therefore, the ratio eg is 1:7 in its simplest form.