**How to solve proportions with variables ?**

Here we are going to see how to solve proportion with variables.

Whenever we have two fractions on either sides of the equal sign, then we have to do cross multiplication.

That is,

- Multiply the numerator of the left side fraction by the denominator of the right side fraction.
- Multiply the numerator of the right side fraction by the denominator of the left side fraction.

Let us see some examples based on the above concept.

**Example 1 :**

Solve each proportion.

10/k = 8/4

**Solution :**

Since we have two fractions on either sides of the equal sign, then we have to do cross multiplication.

10 x 8 = 4 x k

80 = 4k

Divide by 4 on both sides

80/4 = 4k/4

20 = k

Hence the value of k is 20.

**Example 2 :**

Solve each proportion.

m/10 = 10/3

**Solution :**

Since we have two fractions on either sides of the equal sign, then we have to do cross multiplication.

m x 3 = 10 x 10

3m = 100

Divide by 3 on both sides

3m/3 = 100/3

m = 33.33

Hence the value of m is 33.33

**Example 3 :**

Solve each proportion.

3/n = 7/10

**Solution :**

Since we have two fractions on either sides of the equal sign, then we have to do cross multiplication.

3 x 10 = n x 7

30 = 7n

Divide by 7 on both sides

7n/7 = 30/7

n = 4.28

Hence the value of n is 4.28

**Example 4 :**

Solve each proportion.

p/8 = 13/2

**Solution :**

p x 2 = 13 x 8

2p = 52

Divide by 7 on both sides

7n/7 = 30/7

n = 4.28

Hence the value of n is 4.28

**Example 5 :**

Solve each proportion.

7/9 = a/5

**Solution :**

7 x 5 = a x 9

35 = 9a

Divide by 9 on both sides

35/9 = 9a/9

a = 3.88

Hence the value of a is 3.88

**Example 6 :**

Solve each proportion.

10/11 = r/11

**Solution :**

10 x 11 = r x 11

110 = 11r

Divide by 11 on both sides

110/11 = 11r/11

r = 10

Hence the value of r is 10

**Example 7 :**

Solve each proportion.

v/10 = 10/12

**Solution :**

v x 12 = 10 x 10

12v = 100

Divide by 11 on both sides

12v/12 = 100/12

v = 8.33

Hence the value of v is 8.33

After having gone through the stuff given above, we hope that the students would have understood "How to solve proportions with variables".

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