Monday, February 18, 2013

Ratio Data Definition


In mathematics,  ratio expresses the magnitude of quantities relative to each other. Specifically, the ratio of two quantities indicates how many times the first quantity is contained in the second and may be expressed algebraically as their quotient. The ratio is the numerical expression representing a part of a larger whole or proportion. A ratio consists of two numbers separated by a colon. Ratio is numbers can be compared as multiples of one another.

A study calculating ratio means Comparison of two similar quantities or numbers by division.

* Usually the symbol “:” is used to denote "ratio"

* The ratio is generally denoted in the form a: b

* Ratio should be in the lowest form.

Examples on study of calculating ratios:

Example 1. Find the ratio of quantities 2 Kg to 500g in the lowest form.

Solution:

First we find the ratio,

2 Kg = 2 × 1000 = 2000 g

In  we solving this,  we get

The required ratio = 2000: 500

= 200: 50

Ratio = 4: 1

Example 2:   A bowl  contains pink and brown color chocolates. The ratio of  pink  chocolate to brown chocolate is  4:3. If the  bowl  contains  120 brown chocolates ,how many pink  chocolates are there?

Solution:

Given:  The bowl contains 120 brown  sweets,

Now, we are going to assign the variable:

Let `x = ` pink  sweets

The item is now found to be written in ratio fraction,

`" Pink "/ "Brown" `   = `4/3` = `x/120`

Cross multiplication is to be done.

So,    `4`` *` `120 ` = `3` ` x`

` x` `= 480/3`

`x ` = 160.

Hence they are 160 pink sweets.

Example 3:   In a tank  there are golden fishes and sea horses , the  ratio of golden fishes to sea horses 3:6 . If the  tank  contains  60  sea horses , how many golden fishes are there?

Solution:

Given:  The bowl contains 60 sea horses,

Now, we are going to assign the variable:

Let `x` = golden fishes

The item is now found to be written in ratio fraction,

`"Goldenfish" / "seahorses"` =` 3/6=x / 60`

Cross multiplication is to be done.

So,     `3*60= 6 x`

`180= 6x`

`x = 180/6`

`x = 30` .

Hence there are 30 golden fishes .

Algebra is widely used in day to day activities watch out for my forthcoming posts on Division with a Remainder and final syllabus for neet 2013. I am sure they will be helpful.

Examples word problem on study calculating ratios:

Problem 1:  In a school there are 20 male teachers and 10 female teachers. What is the ratio between the number of female teachers and number of male teachers?

Solution:

First we find the ratio,

The ratio between the number of female teachers and number of male teachers =10/20

Then simplify the ratios,

Convert the lowest form is = 1: 2

And we as usual to write this ratio as 1: 2

The Ratio between the number of female teachers and male teachers = 3: 5.

Problem 2:  A boy having 40 apples and 10 mangoes. What is the ratio between the number of apples and number of mangoes?

Solution:

First we find the ratio,

The ratio between the number of apples and number of mangoes =40/10

Then simplify the ratios,

Convert the lowest form is = 4: 1

And as usual to write this ratio as 4: 1

The Ratio between the number of female teachers and male teachers = 4: 1.

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