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Method and examples
Fourth proportional calculator
 
Method  

1. If `a:b:c=2:3:5` then find value of `(a^2+b^2+c^2)/(ab+bc+ca)`
Ratio :
Find value of
  1. If `a/b=2/3`, then find `(2a-3b)/(a-2b)`
  2. If `a:2=b:3=c:5`, then find `(a^2+b^2+c^2)/(ab+bc+ca)`
  3. If `a/4=b/15`, then find `(a+b)/(a-b)`
  4. If `(2a+3b)/(a+b)=13/5`, then find `a/b`
  5. If `(x^2+1)/(x^2-1)=2`, then find `x`
  6. If `x:30=12:20`, then find `x`

2. If `a:b=2:3,b:c=4:5` then find `a:b:c`
Ratio :
Find ratio
 
  1. If `a:b=2:3,b:c=4:5`, then find `a:b:c`
  2. If `b:c=4:5,c:d=5:6`, then find `b:c:d`
  3. If `a:b=2:3,b:c=4:5,c:d=5:6`, then find `a:b:c:d`
  4. If `2a=3b`, then find `a:b`
  5. If `2a=3b=7c`, then find `a:b:c`

3. If `a/b=c/d=e/f` then prove that `(2a+3c-4e)/(2b+3d-4f)=(5a-4c+3e)/(5b-4d+3f)`
If then
prove that
 
  1. If `a/b=c/d=e/f`, then prove that `(2a+3c-4e)/(2b+3d-4f)=(5a-4c+3e)/(5b-4d+3f)`
  2. If `x/(b^2-c^2)=y/(c^2-a^2)=z/(a^2-b^2)`, then prove that `x+y+z=0`

4. If `x/(y+z)=y/(z+x)=z/(x+y)` then prove the value of each ratio is `1/2` or `-1`
If then
prove value of each ratio
 
  1. If `x/(y+z)=y/(z+x)=z/(x+y)`, then prove each ratio = `1/2,-1`
  2. If `(5a+6b)/(7c)=(6b+7c)/(5a)=(7c+5a)/(6b)`, then prove each ratio = `2,-1`
  3. If `(ax+by)/(x+y)=(ay+bz)/(y+z)=(az+bx)/(z+x)`, then prove each ratio = `(a+b)/2`

5. Geometric Mean
Method :
A = , B =
 
  1. Geometric Mean of `4/9` and `9/4`
  2. Geometric Mean of `49/4` and `16/9`
  3. Geometric Mean of `4x^3` and `9x`
  4. Geometric Mean of `8a^2` and `32b^2`
  5. Geometric Mean of `16a^4` and `81/b^4`
  6. Geometric Mean of `(a-b)^2` and `(a+b)^2`
  7. If geometric mean `6x^2` and x is `9x`, find value of x

6. Ratios(duplicate, triplicate) and proportional(mean, third, fourth)
Find
Ratio of
 
  1. Find Duplicate ratio of 2:3
  2. Find Triplicate ratio of 2:3
  3. Find Sub-Duplicate ratio of 16:25
  4. Find Sub-Triplicate ratio of 8:27
  5. Find Compounded ratio of 2:5,3:4
  6. Find Compounded ratio of 2:3,3:4,4:5
  7. Find Mean proportional of 8,32
  8. Find Third proportional of 16,36
  9. Find Fourth proportional of 3,7,15
  10. Find Compare ratios of 2:3,3:4,4:5

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