HOW TO SOLVE PROPORTIONS WITH VARIABLES

We can use cross product rule to solve proportions with variables.

Let us consider the proportion

a : b = c : d

To know the cross product rule, first we have to know about extremes and means.

It has been explained in the picture given below.

Cross product rule :

Product of extremes  =  Product of means

ad  =  bc 

Example 1 :

Solve for k :

10 : k  =  8 : 4

Solution :

10 : k  =  8 : 4

Use Cross product rule. 

10 x 8  =  4k

Divide each side by 4.

20  =  k

Example 2 :

Solve for m : 

m/10  =  10/3

Solution :

m/10  =  10/3

Use Cross product rule. 

3m  =  10 x 10

3m  =  100

Divide each side by 3.

m  =  100/3

Example 3 :

Solve for n : 

3/n  =  7/10

Solution :

3/n  =  7/10

Use Cross product rule. 

3 x 10  =  7n

30  =  7n

Divide each side by 7.

30/7  =  n

Example 4 :

Solve for p :

p : 8  =  13 : 2

Solution :

p : 8  =  13 : 2

Use Cross product rule. 

2p  =  13 x 8

Divide each side by 2.

p  =  52

Example 5 :

Solve for a :  

7/9  =  a/5

Solution :

7/9  =  a/5

Use Cross product rule. 

7 x 5  =  9a

35  =  9a

Divide each side by 9.

35/9  =  a

Example 6 :

Solve for r : 

10 : 11  =  r : 11

Solution :

10 : 11  =  r : 11

Use Cross product rule. 

10 x 11  =  11r

Divide each side by 11.

10  =  r

Example 7 :

Solve for v : 

v/10  =  10/12

Solution :

v/10  =  10/12

Use Cross product rule. 

12v  =  10 x 10

12v  =  100

Divide each side by 12.

v  =  100/12

v  =  25/3

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