16.Ratios and Proportions

Question 1

What is the Invertendo law in ratios and proportions?

Answer 1

The Invertendo law states that if a : b = c : d, then the inverted ratios a : c and b : d are also equal.

Question 2

What is the Alternendo law in ratios and proportions?

Answer 2

The Alternendo law states that if a : b = c : d, then the ratios a : d and b : c obtained by alternating the terms are also equal.

Question 3

What is the Componendo law in ratios and proportions?

Answer 3

The Componendo law states that if a : b = c : d, then the sum of the terms in the ratio a + b : b = c + d : d is also equal.

Question 4

What is the Dividendo law in ratios and proportions?

Answer 4

The Dividendo law states that if a : b = c : d, then the difference of the terms in the ratio a - b : b = c - d : d is also equal.

Question 5

What is the Componendo and Dividendo law in ratios and proportions?

Answer 5

The Componendo and Dividendo law states that if a : b = c : d, then the ratios obtained by adding or subtracting the terms in the ratio, i.e., (a + b) : (a - b) = (c + d) : (c - d), are also equal.

Question 6

How do these laws apply to proper fractions?

Answer 6

These laws can be applied to proper fractions by considering the numerators and denominators as the terms of the ratios. The same principles of invertendo, alternendo, componendo, and dividendo can be used to establish equalities between fractions.

Question 7

How do these laws apply to improper fractions?

Answer 7

These laws can also be applied to improper fractions by considering the numerators and denominators as the terms of the ratios. The laws of invertendo, alternendo, componendo, and dividendo can be used to derive equalities between improper fractions.

Question 8

For a proper fraction
𝒂/𝒃
i.e. a <b, then for a positive quantity c,
then

Answer 8

▪(𝑎+𝑐) / (𝑏+𝑐) > 𝑎/𝑏
and
(𝑎−𝑐)/(𝑏−𝑐)< 𝑎/𝑏

Question 9

For a proper fraction
𝒂/𝒃
i.e. a >b, then for a positive quantity c,
then

Answer 9

▪(𝑎+𝑐) / (𝑏+𝑐) < 𝑎/𝑏
and
(𝑎−𝑐)/(𝑏−𝑐)> 𝑎/𝑏