**Do the ratios form a proportion :**

When two ratios expressed in its simplest form are equal they are said to be in proportion.

Proportion is represented by the symbol ‘ = ‘ or ‘:: ‘

If the ratio a:b is equal to the ratio c : d then a,b,c,d are said to be in proportion.

Using symbols we write as a:b = c:d or a:b :: c:d

In a proportion, the product of extremes is equal to the product of means.

- Compare the given fractions with the fractions a/b and c/d.
- Multiply the values which are in the places of "a" and "d"
- Multiply the values which are in the places of "b" and "c"
- Check whether the value of ad is equal to bc.
- If yes, then we say that the two fractions are in proportion.
- Otherwise they are not in proportion.

Let us see some example problems based on the above concept.

**Example 1 :**

State if the following pair of ratios forms a proportion

4/2 and 20/6

**Solution : **

**Step 1 :**

**Comparing the first fraction 4/2 with a/b and the second fraction 20/6 with c/d.**

**Step 2 :**

**a = 4, b = 2, c = 20 and d = 6.**

**Step 3 :**

**ad = 4(4), bc = 2(20)**

**ad = 16, bc = 40**

**Step 4 :**

**ad **≠ **bc**

**Hence the given fractions will not form a proportion.**

**Example 2 :**

State if each pair of ratios forms a proportion

6/9 and 2/3

**Solution : **

**Step 1 :**

**Comparing the first fraction 6/9 with a/b and the second fraction 2/3 with c/d.**

**Step 2 :**

**a = 6, b = 9, c = 2 and d = 3**

**Step 3 :**

**ad = 6(3), bc = 9(2)**

**ad = 18, bc = 18**

**Step 4 :**

**ad = ** **bc **

**Hence the given fractions form a proportion.**

**Example 3 :**

State if each pair of ratios forms a proportion

4/3 and 16/12

**Solution : **

**Step 1 :**

**Comparing the first fraction 4/3 with a/b and the second fraction 16/12 with c/d.**

**Step 2 :**

**a = 4, b = 3, c = 16 and d = 12**

**Step 3 :**

**ad = 4(12), bc = 3(16)**

**ad = 48, bc = 48**

**Step 4 :**

**ad = ** **bc **

**Hence the given fractions form a proportion.**

**Example 4 :**

State if each pair of ratios forms a proportion

12/24 and 3/4

**Solution : **

**Step 1 :**

**Comparing the first fraction 12/24 with a/b and the second fraction 3/4 with c/d.**

**Step 2 :**

**a = 12, b = 24, c = 3 and d = 4**

**Step 3 :**

**ad = 12(4), bc = 24(3)**

**ad = 48, bc = 72**

**Step 4 :**

**ad **≠** ** **bc **

**Hence the given fractions will not form a proportion.**

After having gone through the stuff given above, we hope that the students would have understood "Do the ratios form a proportion".

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