Some of the important properties of ratios are discussed here.

**1.** Ratio \(\frac{m}{n}\) has no unit and can be written as m : n (read as m is to n).

**2.** The quantities m and n are called terms of the ratio. The first quantity m is called the first term or the antecedent and the second quantity n is called the second term or the consequent of the ratio m : n.

The second term of a ratio cannot be zero.

i.e., (i) In the ratio m : n, the second term n cannot be zero (n ≠ 0).

(ii) In the ratio n : m, the second term cannot be zero (m ≠ 0).

**3.** The ratio of two unlike quantities is not defined. For example, the ratio between 5 kg and 15 meters cannot be found.

**4.** Ratio is a pure number and does not have any unit.

**5.** If both the terms of a ratio are multiplied by the same
non-zero number, the ratio remains unchanged.

If two terms of a ratio be multiplied by any number except zero, then there is no change in the value of the ratio because; m : n = \(\frac{m}{n}\) = \(\frac{km}{kn}\)= km : kn

If both the terms of a ratio are divided by the same non-zero number, the ratio remains unchanged.

m : n = \(\frac{m}{n}\) = \(\frac{\frac{m}{k}}{\frac{n}{k}}\) = \(\frac{m}{k}\) : \(\frac{n}{k}\), (k ≠ 0)

In other words, the ratio of m and n is the same as the ratio of the quantities km and kn, or \(\frac{m}{k}\) and \(\frac{n}{k}\), where k ≠ 0.

**6.** If two quantities are in the ratio m : n then the
quantities will be of the form m ∙ k and n ∙ k, where k is nay number, k ≠ 0.
Thus, if the ratio of two quantities x and y is 3 : 4, x and y can be 6 and 8
(k = 2), 9 and 12 (k = 3), and so on.

**7.** If m is k % of n then the ratio m : n = k : 100. Also, if m : n = p : q then m = \(\frac{p}{q}\) × 100% of n = \(\frac{p}{q}\) × n.

**8.** A ratio must always be expressed in its lowest terms.

The ratio is in its lowest terms, if the H.C.F. of its both the terms is 1 (unity).

For example;

(i) The ratio 3 : 7 is in its lowest terms as the H.C.F. of its terms 3 and 7 is 1.

(ii) The ratio 4 : 20 is not in its lowest terms as the H.C.F. of its terms 4 and 20 is 4 and not 1.

**9.** Ratios m : n and n : m cannot be equal unless m = n

i.e. m : n ≠ n : m, unless m = n

In other words, the order of the terms in a ratio is important.

● **Ratio and proportion**

**Basic Concept of Ratios****Important Properties of Ratios****Ratio in Lowest Term****Types of Ratios****Comparing Ratios****Arranging Ratios****Dividing into a Given Ratio****Divide a Number into Three Parts in a Given Ratio****Dividing a Quantity into Three Parts in a Given Ratio****Problems on Ratio****Worksheet on Ratio in Lowest Term****Worksheet on Types of Ratios****Worksheet on Comparison on Ratios****Worksheet on Ratio of Two or More Quantities****Worksheet on Dividing a Quantity in a Given Ratio****Word Problems on Ratio****Proportion****Definition of Continued Proportion****Mean and Third Proportional****Word Problems on Proportion****Worksheet on Proportion and Continued Proportion****Worksheet on Mean Proportional****Properties of Ratio and Proportion**

__From Important Properties 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.