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 x$$^{2}$$ : y$$^{2}$$.

In other words,

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

= (m × m) : (n × n)

= m$$^{2}$$ : n$$^{2}$$

Therefore, the duplicate ratio of 4 : 7 = 4$$^{2}$$ : 7$$^{2}$$ = 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 a$$^{3}$$ : b$$^{3}$$.

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)

= m$$^{3}$$ : n$$^{3}$$

Therefore, the triplicate ratio of 4 : 7 = 4$$^{3}$$ : 7$$^{3}$$ = 64 : 343.

4. Subduplicate ratio: The subduplicate ratio m : n is the ratio √m : √n. So, the subduplicate ratio of the ratio m$$^{2}$$ : n$$^{2}$$ 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 $$\sqrt[3]{m}$$ : $$\sqrt[3]{n}$$ is the ratio m : n.

For example:

The subtriplicate ratio of 125 : 729 = $$\sqrt[3]{125}$$ : $$\sqrt[3]{729}$$ = 5 : 9

6. Reciprocal ratio: The reciprocal ratio of the ratio m : n (m ≠ 0, n ≠ 0) is the ratio $$\frac{1}{m}$$ :  $$\frac{1}{n}$$.

For any ratio x : y, where x, y ≠ 0, its reciprocal ratio = $$\frac{1}{x}$$ :  $$\frac{1}{y}$$ = 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 = $$\frac{1}{7}$$ : $$\frac{1}{13}$$ = 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.

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.

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

Recent Articles

1. Shifting of Digits in a Number |Exchanging the Digits to Another Place

May 19, 24 06:35 PM

What is the Effect of shifting of digits in a number? Let us observe two numbers 1528 and 5182. We see that the digits are the same, but places are different in these two numbers. Thus, if the digits…

2. Formation of Greatest and Smallest Numbers | Arranging the Numbers

May 19, 24 03:36 PM

the greatest number is formed by arranging the given digits in descending order and the smallest number by arranging them in ascending order. The position of the digit at the extreme left of a number…

3. Formation of Numbers with the Given Digits |Making Numbers with Digits

May 19, 24 03:19 PM

In formation of numbers with the given digits we may say that a number is an arranged group of digits. Numbers may be formed with or without the repetition of digits.

4. Arranging Numbers | Ascending Order | Descending Order |Compare Digits

May 19, 24 02:23 PM

We know, while arranging numbers from the smallest number to the largest number, then the numbers are arranged in ascending order. Vice-versa while arranging numbers from the largest number to the sma…