Types of Ratios

We will discuss here about the different types of ratios.

1. Compounded ratio: For two or more ratios, if we take antecedent as product of antecedents of the ratios and consequent as product of consequents of the ratios, then the ratio thus formed is called mixed or compound ratio. As, compound ratio of m : n and p :  q is mp : nq.

In other words,

When two or more ratios are multiplies termwise; the ratio thus obtained is called compound ratio.

For example:

The compounded ratio of the two ratios a : b and c : d is the ratio ac : bd, and that of a : b, c : d and e : f is the ratio ace : bdf.

For ratios m : n and p :  q; the compound ratio is (m × p) : (n × q).

For ratio m : n, p :  q and r : s; the compound ratio is (m × p × r) : (n × q × s).


2. Duplicate ratio: Duplicate ratio is the ratio of two equal ratios.

For example:

The duplicate ratio of the ratio x : y is the ratio x2 : y2.

In other words,

The duplicate ratio of the ratio m : n = Compound ratio of m : n and m : n

                                                  = (m × m) : (n × n)

                                                  = m2 : n2

Therefore, the duplicate ratio of 4 : 7 = 42 : 72 = 16 : 49

 

3. Triplicate ratio: The triplicate ratio is the compound ratio of three equal ratios.

The triplicate ratio of the ratio a : b is the ratio a3 : b3.

In other words,

The triplicate ratio of the ratio m : n = Compound ratio of m : n, m : n and m : n

                                                 = (m × m × m) : (n × n × n)

                                                 = m3 : n3

Therefore, the triplicate ratio of 4 : 7 = 43 : 73 = 64 : 343.

 

4. Subduplicate ratio: The subduplicate ratio m : n is the ratio √m : √n. So, the subduplicate ratio of the ratio m2 : n2 is the ratio m : n.

For example:

The subduplicate ratio of 25 : 81 = √25 : √81 = 5 : 9.

 

5. Subtriplicate ratio: The subtriplicate ratio m : n is the ratio √m : √n. So, the subduplicate ratio of the ratio 3m : 3n is the ratio m : n.

For example:

The subtriplicate ratio of 125 : 729 = 3125 : 3729 = 5 : 9

 

6. Reciprocal ratio: The reciprocal ratio of the ratio m : n (m ≠ 0, n ≠ 0) is the ratio 1m :  1n.

For any ratio x : y, where x, y ≠ 0, its reciprocal ratio = 1x :  1y = y : x

Similarly, we can say if the antecedent and consequent of a ratio be interchanged, the changed ratio is called the inverse ratio of the previous ratio.

For example:

Reciprocal ratio of 7 : 13 = 17 : 113 = 13 : 7.

5 : 7 is the inverse ratio of 7 : 5

 

7. Ratio of equalities: For a ratio, if the antecedent and consequent are equal, the ratio is called ratio of equality.

For example:  5 : 5 is the ratio of equalities.


8. Ratio of inequalities: For a ratio, if the antecedent and consequent are unequal, the ratio is called ratio of inequality.

For example:  5 : 7 is the ratio of inequalities.


9. Ratio of lesser inequalities: For a ratio, if antecedent is less than the consequent, the ratio is called the ratio of lesser inequality.

For example: 7 : 9 is a ratio of lesser inequalities.

 

10. Ratio of greater inequalities: For a ratio, if antecedent is greater than the consequent, the ratio is called the ratio of greater inequality.

For example:  13 : 10 is a ratio of greater inequalities.


Note: (i) If the ratio x : y, if x = y, we get ratio of equality. If x ≠ y, we get ratio of inequality, x > y gives ratio of greater inequality.

(ii) y : x and x : y are mutually inverse ratio to each other.






10th Grade Math

From Types of Ratios to HOME




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. Quadrilaterals | Four Sided Polygon | Closed Figure | Adjoining Figure

    Jul 14, 25 02:55 AM

    Square
    Quadrilaterals are known as four sided polygon.What is a quadrilateral? A closed figure made of our line segments is called a quadrilateral. For example:

    Read More

  2. Formation of Numbers | Smallest and Greatest Number| Number Formation

    Jul 14, 25 01:53 AM

    In formation of numbers we will learn the numbers having different numbers of digits. We know that: (i) Greatest number of one digit = 9,

    Read More

  3. 5th Grade Geometry Practice Test | Angle | Triangle | Circle |Free Ans

    Jul 14, 25 01:53 AM

    Name the Angles
    In 5th grade geometry practice test you will get different types of practice questions on lines, types of angle, triangles, properties of triangles, classification of triangles, construction of triang…

    Read More

  4. 5th Grade Circle Worksheet | Free Worksheet with Answer |Practice Math

    Jul 11, 25 02:14 PM

    Radii of the circRadii, Chords, Diameters, Semi-circles
    In 5th Grade Circle Worksheet you will get different types of questions on parts of a circle, relation between radius and diameter, interior of a circle, exterior of a circle and construction of circl…

    Read More

  5. Construction of a Circle | Working Rules | Step-by-step Explanation |

    Jul 09, 25 01:29 AM

    Parts of a Circle
    Construction of a Circle when the length of its Radius is given. Working Rules | Step I: Open the compass such that its pointer be put on initial point (i.e. O) of ruler / scale and the pencil-end be…

    Read More