**What is Proportion ?**

When Two Ratios are equal then we say that they are in Proportion and use the symbol “: :” or “=” to equate two ratios.

__Four Numbers in Proportion__

Let a, b, c, d are four numbers said to be in proportion.

then, a : b = c : d or a : b :: c : d

here a and d are called the extreme terms or extremes.

b and c are called the middle terms or means.

When Four numbers are in proportion

then, **Product of extremes = Product of means. **i.e, In proportion a : b :: c : d,

(a x d) = (b x c)

**Proportion Examples**

**Example 1**

Are the ratios 90 cm : 270 cm and 70 m : 210 m in proportion?

**Explanation:**

We have 90 cm : 270 cm

= 90 : 270

= 90/270

= (90÷90)/(270÷90) (HCF of 90 and 270 is 90 )

= 1/3

70 m : 210 m

= 70 : 210

= 70/210

= (70÷70)/(210÷70) ( HCF of 70 and 210 is 70 )

= 1/3

Since, the ratios 90 cm : 270 cm and 70 m : 210 m are equal to 1/3 . So, they are in proportion.

**Example 2**

Are 6, 12, 4, 8 in proportion?

**Explanation:**

We have, 6 : 12 = 6/12 = (6÷6)/(12÷6) = 1/2

and 4 : 8 = 4/8 = (4÷4)/(8÷4) = 1/2

Since, 6 : 12 = 4 : 8

Hence, 6 , 12 , 4 , 8 are in Proportion

Alternative method: Product of extremes = Product of means

Here, Means are 12 and 4

Extremes are 6 and 8

Product of extremes = 6 x 8 = 48

Product of means = 12 x 4 = 48

Since, Product of extremes = Product of means

Hence, 6 , 12 , 4 , 8 are in Proportion

**Example 3**

If 12 : 20 : : y : 10, find the value of y?

**Explanation:**

We know that, Product of means = Product of extremes

In the given numbers, we can say that 20 , y are means and 12 , 10 are extremes

20 x y = 12 x 10

y = (12 x 10)/20

y = 6

Hence, y = 6

**Example 4**

If 12 : y : : y : 48, find the value of y?

**Explanation:**

Clearly, Product of means = Product of extremes

y x y = 12 x 48

y² = 12 x 48

y² = 576

Hence, y = 24

**Example 5**

If 3 , 9 , y are in proportion, find the value of y?

**Explanation:**

3 , 9 , y are in proportion

Which means 3 , 9 , 9 , y are in proportion

i.e, 3 : 9 : : 9 : y

Product of Means = Product of Extremes

here,

Means = 9 and 9

Extremes = 3 and y

9 x 9 = 3 x y

81 = 3 x y

y = 81/3

Hence, y = 27

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