24.8k views
3 votes
If

p
:
q
=
1
3
:
2
and
p
:
r
=
3
4
:
1
2
, calculate the ratio
p
:
q
:
r
Giving your answer in its simplest form.

User Mle
by
8.5k points

1 Answer

3 votes

Answer:

p : q : r = 3 : 18 : 2

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

_____

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

__

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

User Gulzar
by
7.1k points

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