if p:q=2/3:1/6 & q:r=3/4:1/2. find p:q:r
(3/4)/(1/6) = 9/2
so,
p:q = (9/2)(2/3):(9/2)(1/6) = 3:3/4
p:q:r = 3:3/4:1/2 = 12:3:2
To find the ratio p:q:r, we need to find the values of p, q, and r first based on the given information.
Given:
p:q = 2/3 : 1/6
q:r = 3/4 : 1/2
Step 1: Find the common value of q in both ratios:
To find the common value of q, we need to find the least common multiple (LCM) of the denominators 3 and 6.
The multiples of 3 are: 3, 6, 9, 12, 15, 18, ...
The multiples of 6 are: 6, 12, 18, 24, 30, ...
The LCM of 3 and 6 is 6.
Step 2: Adjust the ratios with the common value:
Now, we need to adjust the p:q ratio to have a common value of 6. To do this, we multiply the numerator and denominator of the second fraction (1/6) by 2 since 6 divided by 3 is 2.
So the adjusted p:q ratio becomes:
p:q = 2/3 : (1/6 * 2) = 2/3 : 2/6
Simplifying the denominator:
p:q = 2/3 : 1/3
Step 3: Combine the ratios to find the overall ratio:
Since we have the adjusted p:q ratio as 2/3 : 1/3 and the q:r ratio as 3/4 : 1/2, we can multiply the fractions together to find the overall ratio.
p:q:r = (2/3) * (3/4) : (1/3) * (1/2)
Simplifying:
p:q:r = 6/12 : 1/6
Further simplifying the fractions:
p:q:r = 1/2 : 1/6
In conclusion, the ratio p:q:r is 1/2 : 1/6.