Continued Proportion

Definition of Continued Proportion:

Three quantities are said to be in continued proportion; if the ratio between the first and the second is equal to the ratio between the second and the third.

Suppose, if we have three qualities such that the ratio of first to second is equal to the ratio of second to third, we say that the three qualities are in continued proportion. The middle term is called the mean proportional between the first the third terms.

i.e. a, b and c are in continued proportion, if a : b = b : c

The second quantity is called the mean proportional between the first and the third

i.e. in a : b = b : c; b is the mean proportional between a and c.

 The third quantity is called the third proportional to the first and the second

i.e. in a : b = b : c; c is the third proportional to a and b.

For example, let us consider the numbers 6, 12, 24.

Here the ratio of first quantity to the second = 6 : 12 = 1 : 2

And ratio of second quantity to the third = 12 : 24 = 1 : 2

We see that 6 : 12 = 12 : 24

Thus, 6, 12, 24 are in continued proportion.

The second quantity 12 is the mean proportional and third quantity 24 is the third proportional.


Solved example on continued proportion:

1. Find the mean proportion between 4 and 9.

Solution:

Let the mean proportion be x

Therefore, 4 : x = x : 9

⇒ x × x = 4 × 9

⇒ x2 = 36

⇒ x2 = 62

⇒ x = 6


2. Find, m, if 7, 14, m are in continued proportion.

Solution:

x, y and z are in continued proportion xz = y2

Let 7, 14, and m be x, y and z respectively.

Therefore, 7m = 142

or, 7m = 196         

or, m = 196/7

Therefore, m = 28.

Hence, m = 28.


3. Find the third proportional to 12 and 30.

Solution:

Let x be the third proportional

Therefore, 12 : 30 = x : 30

⇒ 12 × x = 30 × 30

⇒ 12x = 900

⇒ x = 900/12

⇒ x = 75







6th Grade Page

From Continued Proportion to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Share this page: What’s this?

Recent Articles

  1. Worksheet on Triangle | Homework on Triangle | Different types|Answers

    Jun 21, 24 02:19 AM

    Find the Number of Triangles
    In the worksheet on triangle we will solve 12 different types of questions. 1. Take three non - collinear points L, M, N. Join LM, MN and NL. What figure do you get? Name: (a)The side opposite to ∠L…

    Read More

  2. Worksheet on Circle |Homework on Circle |Questions on Circle |Problems

    Jun 21, 24 01:59 AM

    Circle
    In worksheet on circle we will solve 10 different types of question in circle. 1. The following figure shows a circle with centre O and some line segments drawn in it. Classify the line segments as ra…

    Read More

  3. Circle Math | Parts of a Circle | Terms Related to the Circle | Symbol

    Jun 21, 24 01:30 AM

    Circle using a Compass
    In circle math the terms related to the circle are discussed here. A circle is such a closed curve whose every point is equidistant from a fixed point called its centre. The symbol of circle is O. We…

    Read More

  4. Circle | Interior and Exterior of a Circle | Radius|Problems on Circle

    Jun 21, 24 01:00 AM

    Semi-circular Region
    A circle is the set of all those point in a plane whose distance from a fixed point remains constant. The fixed point is called the centre of the circle and the constant distance is known

    Read More

  5. Quadrilateral Worksheet |Different Types of Questions in Quadrilateral

    Jun 19, 24 09:49 AM

    In math practice test on quadrilateral worksheet we will practice different types of questions in quadrilateral. Students can practice the questions of quadrilateral worksheet before the examinations

    Read More