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Ratio

• What is Ratio?

In Mathematics, a Ratio Shows the relationship between two or more numbers in its simplest form.

We generally separate the two numbers in the ratio with a colon (:). The ratio of numbers A and B can be expressed as:

• the ratio of A to B

• A is to B

• A:B

The ratio of three numbers, A, B and C is written as A:B:C.

Here A, B and C are whole numbers

Example: The ratio for 3 pizzas to 4 cupcakes is written as

Pizzas : Cupcakes

      3   :   4

In Fraction this relation we can express as ¾ .

One quantity can be expressed as a fraction of another when their ratio is given and vice versa.

• Comparing Ratio

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To compare ratios, write them as fractions. The ratios are equal, if they are equal when written as fractions.

Example:Are the ratio 5 to 8 and 10 to 16 equal?

The ratios are equal if 5/8 = 10/16

To find out two ratios are equal or not we have to find out their cross products. And if cross products are equal that means ratios are equal.

In this case, if 5 x 16 = 8 x 10. Since both of these products equal 80, the answer is yes, the ratios are equal.

Here 5 : 16 and 8 : 10 are equivalent ratios.

Are 4 :3 and 1 : 8 Equivalent Ratio?

NO because 4/3 > 1 while 1/8 < 1 So the Ratios cannot be equal.

Ratio is always given in whole numbers, in its lowest terms.

ratio

ratio

* Comparing more than two quantities.

For Example : If in one farm ratio of Hen to Rabbit is 5 : 6. And The Ratio of Rabbit to Duck is 1 : 4. Find ratio of Hen to Rabbit to Duck.

Important Thing to note here in both cases Number of Rabbit remain same Keeping this in mind we can solve this problem like this.

ratio

The ratio of Hen to Rabbit to Duck is 5 : 6 : 24.

• Ratio and Proportion

When we says, July mixes 6 litres of water with 2 litres of rose syrup. The amount of water and rose syrup is mixed in proportion. They are mixed in the Ratio of 6 : 2 or in simplest form 3 : 1 .

• Expressing Ratio with Models

Ratio can be easily expressed by models.

The ratio of the number of balloons Tom has to the number of balloons Rocky has is 2 : 5, can be expressed by the models as follows.

ratio