Question

properties of ratio​

Answer 1

Properties of Ratios:

1. The ratio of a number ‘P’ to the another number ‘Q’ (Q ≠ 0) is a fraction P/Q, and it is written as P : Q.

2. In the ratio P : Q, the first term is P and second term is Q.

3. In the ratio P : Q, the first term P is called antecedent and the second term Q is called consequent.

4. The two quantities compared in a ratio must have the same units of measurement.

In order to find the ratio between two quantities, both the quantities must be in the same unit e.g., ratio between 30 cm and 2 metre

                   = 30 cm : 200 cm [Since, 2 metre = 200 cm]

                    = 30/200

                    = 3/20

                    = 3 : 20

5. The ratio of two numbers is always expressed in its lowest terms in simplest form.

6. When two ratio P : Q is in its lowest term, P and Q are co-prime, or their HCF is 1.

7. The ratio of two quantities is an abstract quantity, i.e., it has no units in itself.

8. A ratio is a pure number.

9. The order of a ratio is important. By reversing the antecedent and the consequent of a ratio, a different ratio is obtained.

10. The ratio can be expressed as a fraction and a decimal.

11. The antecedent and the consequent of a ratio are always expressed as whole numbers. When they are not, they are converted into whole numbers.

Answer 2

Answer:

$\huge\boxed{\fcolorbox{blue}{orange}{αɳនƜ៩Ʀ}}$

Some useful properties of ratio and proportion are invertendo property, alternendo property, componendo Property, dividendo property, convertendo property, componendo-dividendo property, addendo property and equivalent ratio property. These properties are explained below with examples.

I. Invertendo Property: For four numbers a, b, c, d if a : b = c : d, then b : a = d : c; that is, if two ratios are equal, then their inverse ratios are also equal.

If a : b :: c : d then b : a :: d : c.

II. Alternendo Property: For four numbers a, b, c, d if a : b = c : d, then a : c = b : d; that is, if the second and third term interchange their places, then also the four terms are in proportion.

If a : b :: c : d then a : c :: b : d.

III. Componendo Property: For four numbers a, b, c, d if a : b = c : d then (a + b) : b :: (c + d) : d.

${\huge{\sf{\blue{\underline {\underline {⚠ƒοℓℓοω ↯}}}}}}$