Tuesday, August 21, 2012

Introduction to ratio and proportion summary

Introduction to ratio and proportion summary:

              The ratio a: b is equivalent to the quotient `a/b` . A is relation of give the equality of two ratios, in the form `a/b` = `c/d` . This relation has called as proportion. Proportion is a states in which numbers are called as proportionality relation giving of two ratios, in the form `a/b` = `c/d` . Here a & d are known as extreme and b & c are known as means.                                                    

Problems on Proportion Summary:

     The ratio a: b is equivalent to the quotient `a/b` . The ratio of two given numbers a and b is the fraction, usually expressed in reduced form.

Ratio summary - example 1:  

                  A classroom has 60 men and 20 women. What is the ratio of men and women?        

Solution:

                   Men to women = 60 to 20 or 60: 20,

                   which reduces to = 6 to 2 or 6:2

                   The ratio of men to women is 6 to 2, or `6/2` , or 6 : 2.

Ratio summary - example 2:  

              A triangle has angle measures of 30°, 60°, and 90°. In simple form, what is the ratio of the given angles to each other?

Solution:

            30: 60: 90 = 3: 6: 9 (10 is a common divisor).That is,

                     (1) Ratio of the first to the second is 3 to 6.

                     (2) Ratio of the first to the third is 3 to 9.

                     (3) Ratio of the second to the third is 6 to 9.

Some Problems for Proportion Summary:

    A is relation give the equality of two ratios, in the form `a/b ` = `c/d` . This relation has called as proportion. Proportion is a states in which numbers are called as proportionality relation giving of two ratios, in the form `a/b` = `c/d` . Here a & d are known as extreme and b & c are known as means.                                                   

Proportion summary - example 1:

           If `x/5` = `y/2` , find the ratio of  `x/y` .(proportion)

Solution:

                    `x/5` =  `y/2`                                                          

                    `x/y` =  `5/2`

       Therefore the ratio of x and y is 5:2

Proportion summary - example 2:

           If  `x/3` = `2/6` , then find x?

Solution:

           Using cross multiplication (Property 1)

                    2x = 3 `xx` 6

                    2x = 18

                     x = `18/2`

                     x = 9

            So the value of x = 9

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