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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