A Brief Overview of Methods for Solutions to Simple Proportional Problems

Proportional can be arranged in two types Vertical  or Horizontal

The Law of Proportions applies to both types of arrangements for Proportions.

 

The Product of the Means equals The Product of the Extremes.

 

N         4                      3          9                      4          N                     2          6

---  =    ---                    ---  =    ---                    ---  =    ---                    ---  =    ---

3          6                      N         12                    5          20                    3          N

 

6N=12                         36=9N                         80=5N                         2N=18

 

N=2                             4=N                             16=N                           N=9

 

Checking

 

2          4                      3          9                      4          16                    2          6

---  =    ---                    ---  =    ---                    ---  =    ---                    ---  =    ---

3          6                      4          12                    5          20                    3          9

 

12=12                          36=36                          80=80                          18=18

 

 

The Product of the Means equals The Product of the Extremes.

 

 

N : 3 = 4 : 6                3: N = 9 :12                4 : 5 = N : 20              2 : 3 = 6 : N

 

12 = 6N                       9N = 36                       5N = 80                       18 = 2N

 

2 = N                           N = 4                           N = 16                         9 = N

 

Checking

 

2          4                      3          9                      4          16                    2          6

---  =    ---                    ---  =    ---                    ---  =    ---                    ---  =    ---

3          6                      4          12                    5          20                    3          9

 

12=12                          36=36                          80=80                          18=18

 

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Tom Love             Malone College              Fall 2003

Reference: Fundamentals of Mathematics by Edwin I. Stein