Important Properties of Ratios

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

10th Grade Math

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