Ratio :- When the relation between two quantities of the same kind is indicated by division or a fraction then the relation is called ratio.
For eg. ratio of 8m to 4m is
$\frac{8}{4}$ or $\frac{2}{1}$ or 2:1
Here, 2 is called antecedent and 1 is consequent.
Note:- A ratio has no units in itself.
Proportion:- A proportion is defined as a statement which shows that two ratios are equal.
If a:b=c:d, then we say that a, b, c and d are in proportion
Here, a and b are called extreme terms.
b and c are called middle terms or means.
d is called fourth proportional to a, b and c.
Note:- a:b=c:d is also written as a:b::d or $\frac{a}{b}=\frac{c}{d}$.
Condition for Proportionality:- If a, b, c and are in proportion then
$\frac{a}{b}=\frac{c}{d}$
or ad = bc
Note:- In a proportion the product of the extreme terms is equal to the product of the means(middle) terms.
If a:b::c:d, then d is called the fourth proportion to a, b, c.
If a:b::b:c, then c is called the third proportion to a, b.
Mean proportion between a and b = $\sqrt{ab}$
If a:b::b:c or $\frac{a}{b}=\frac{c}{d}$ or $a\times c=b\times b$ or $ac=b^{2}$
Then, a, b and c are in continued proportion.
Duplicate Ratio of (a:b) is $(a^{2}:b^{2})$.
Sub Duplicate ratio of (a:b) is $(\sqrt{a}:\sqrt{b})$.
Triplicate ratio of (a:b) is $(a^{3}:b^{3})$.
Sub Triplicate ratio of (a:b) is $(a^{\frac{1}{3}}:b^{\frac{1}{3}})$.
For eg. ratio of 8m to 4m is
$\frac{8}{4}$ or $\frac{2}{1}$ or 2:1
Here, 2 is called antecedent and 1 is consequent.
Note:- A ratio has no units in itself.
Proportion:- A proportion is defined as a statement which shows that two ratios are equal.
If a:b=c:d, then we say that a, b, c and d are in proportion
Here, a and b are called extreme terms.
b and c are called middle terms or means.
d is called fourth proportional to a, b and c.
Note:- a:b=c:d is also written as a:b::d or $\frac{a}{b}=\frac{c}{d}$.
Condition for Proportionality:- If a, b, c and are in proportion then
$\frac{a}{b}=\frac{c}{d}$
or ad = bc
Note:- In a proportion the product of the extreme terms is equal to the product of the means(middle) terms.
If a:b::c:d, then d is called the fourth proportion to a, b, c.
If a:b::b:c, then c is called the third proportion to a, b.
Mean proportion between a and b = $\sqrt{ab}$
If a:b::b:c or $\frac{a}{b}=\frac{c}{d}$ or $a\times c=b\times b$ or $ac=b^{2}$
Then, a, b and c are in continued proportion.
Duplicate Ratio of (a:b) is $(a^{2}:b^{2})$.
Sub Duplicate ratio of (a:b) is $(\sqrt{a}:\sqrt{b})$.
Triplicate ratio of (a:b) is $(a^{3}:b^{3})$.
Sub Triplicate ratio of (a:b) is $(a^{\frac{1}{3}}:b^{\frac{1}{3}})$.
No comments:
Post a Comment