Answer:
p : q : r = 3 : 18 : 2
Step-by-step explanation:
Given:
p : q = (1/3) : 2
p : r = (3/4) : (1/2)
Find:
p : q : r
Solution:
We want to rewrite these ratios so they use the same number for p. We can do that by using the least common multiple of (1/3) and (3/4) for p. That value is 3.
p : q = (9)(1/3) : (9)(2) = 3 : 18
p : r = (4)(3/4) : (4)(1/2) = 3 : 2
Then the ratio of interest is ...
p : q : r = 3 : 18 : 2
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Additional comment
We are not often asked to find the least common multiple of fractions or mixed numbers. One way to do it is to write the numbers using a common denominator, then find the LCM of the numerators, and reduce any resulting fraction.
LCM(1/3, 3/4) = LCM(4/12, 9/12) = (1/12)·LCM(4, 9) = 36/12 = 3
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As with integers, you also have ...
LCM(1/3, 3/4) = product/GCD = (1/3)(3/4)/GCD(1/3, 3/4)
The greatest common divisor (GCD) will be the unit fraction with the least common denominator: 1/12, so this is ...
LCM(1/3, 3/4) = (1/3)(3/4)/(1/12) = (3/12)/(1/12) = 3
