A proportion is an equation that states that two ratios or rates are equivalent.

Examples :

1/3 and 2/6 are equivalent ratios

1/3 = 2/6 is a proportion

We use cross product rule in proportion to solve many real world problems.

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 :**

If you can buy one can of pineapple chunks for $2 then how many can you buy with $10 ?

**Solution :**

From the given information, number of cans of pineapple chunks and the cost are in the ratio

1 : 2

Let 'x' be the number of cans that we buy.

Then,

1 : 2 = x : 10

1(10) = 2x

10 = 2x

5 = x

So, we can buy 5 apples with $10.

**Example 2 :**

Shawna reduced the size of a rectangle to a height of 2 in. What is the new width, if it was originally 24 in wide and 12 in tall ?

**Solution :**

From the given information, the width and height of the rectangle are in the ratio

24 : 12 = 2 : 1

Because the original width and height of the rectangle are in the ratio 2 : 1, the width and height of he resized rectangle will also be in the same ratio.

And also, the height of the rectangle is reduced to 2 inches.

Let 'x' be the width of the resized rectangle.

Then,

2 : 1 = x : 2

2(2) = 1(x)

4 = x

So, the width of the resized rectangle is 4 inches.

**Example 3 :**

One cantaloupe costs $2. How many cantaloupes can we buy for $6 ?

**Solution :**

From the given information, number of cans of pineapple chunks and the cost are in the ratio

1 : 2

Let 'x' be the number of cantaloupe that we buy.

Then,

1 : 2 = x : 6

1(6) = 2(x)

6 = 2x

3 = x

So, we can buy 3 cantaloupes for $6.

**Example 4 :**

Ming was planning a trip to Western Samoa.
Before going, she did some research and
learned that the exchange rate is 6 Tala for
$2. How many Tala would she get if she
exchanged $6?

**Solution :**

From the given information, the exchange rate of Tala and Dollar are in the ratio

6 : 2 = 3 : 1

Let 'x' be the number of Tala that Ming would expect.

Then,

3 : 1 = x : 6

3(6) = 1(x)

18 = x

So, Ming would get 18 Tala, if she exchanged $6.

**Example 5 :**

Jasmine bought 32 kiwi fruit for $16. How
many kiwi she Lisa buy, if she has $4 ?

**Solution :**

From the given information, we come to know that number of kiwi fruits to the cost is in the ratio

32 : 16 = 2 : 1

Let 'x' be the number of kiwi that jasmine buy for $4.

2 : 1 = x : 4

2(4) = 1(x)

8 = x

So, Jasmine can buy 8 kiwi fruits for $4.

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