Definition for ratio:
In mathematics, a ratio expresses the magnitude of quantities relative to each other. Specifically, the ratio of two quantities indicates how many times the first quantity is contained in the second and may be expressed algebraically as their quotient. I like to share this What is a Ratio? with you all through my article.
Example:
For every Spoon of sugar, you need 2 spoons of flour (1:2)
Source :Wikipedia
Ratio formula:
Let A and B be two given points. Let P be a point on the line segment `barA``barB` or on `barA` `barB` produced. Then P divides `barA` `barB` into two segments `barA` `barP` and `barP` `barB`. The lengths of `barA` `barP` and `barP``barB` are AP and PB.
These lengths are in some ratio: n; that is AP : PB = m : n or `(AP)/(PB)` `(m)/(n)`
If P lies inside `barA` `barB` we say that P divides `barA``barB` internally in the ratio m : n. If P lies outside `barA` `barB`, that is, P lies on `barA` `barB` produced, then we say that P divides `barA``barB` externally in the ratio m : n. With a given ratio m : n, `barA``barB` can be divided either internally or externally. Understanding Dividing Radicals with Variables is always challenging for me but thanks to all math help websites to help me out.
Example for ratio:
Example :
Divide the line segment `barA` `barB` of length 16 units in the ratio 3:5
Solution:
i) Let C be the point inside `barA``barB` such that `(AC)/(CB)`= `(3)/(5)`. Since the numerator is smaller than the denominator, C is closer to A than to B . Then
5AC=3 BC or 5AC=3(AB–AC) or 8AC=3AB =3(16)=48
AC=6 units and so CB=AB–AC =16–6 = 10 units.
Hence C lies inside `barA` `barB` 6 units distance from A and 10 units distance from B. The point C is unique and it divides `barA``barB` internally in the given ratio 3:5.
ii) Let D be the point outside `barA``barB` such that `(AD)/(DB)`=`(3)/(5)`?. Since the numerator is smaller than the denominator, D is closer to A than to B. Now we have
5 AD = 3DB or 5 AD = 3(AD + AB) or 5 AD = 3AD + 3AB
2 AD = 3AB = 3(16) = 48 or AD = 24 Then DB = DA + AB = 24 + 16 = 40
Therefore, D lies outside `barA``barB` 24 units distance from A and 40 units distance from B. The point D is unique and it divides `barA``barB` externally in the given ratio 3:5.
In mathematics, a ratio expresses the magnitude of quantities relative to each other. Specifically, the ratio of two quantities indicates how many times the first quantity is contained in the second and may be expressed algebraically as their quotient. I like to share this What is a Ratio? with you all through my article.
Example:
For every Spoon of sugar, you need 2 spoons of flour (1:2)
Source :Wikipedia
Ratio formula:
Let A and B be two given points. Let P be a point on the line segment `barA``barB` or on `barA` `barB` produced. Then P divides `barA` `barB` into two segments `barA` `barP` and `barP` `barB`. The lengths of `barA` `barP` and `barP``barB` are AP and PB.
These lengths are in some ratio: n; that is AP : PB = m : n or `(AP)/(PB)` `(m)/(n)`
If P lies inside `barA` `barB` we say that P divides `barA``barB` internally in the ratio m : n. If P lies outside `barA` `barB`, that is, P lies on `barA` `barB` produced, then we say that P divides `barA``barB` externally in the ratio m : n. With a given ratio m : n, `barA``barB` can be divided either internally or externally. Understanding Dividing Radicals with Variables is always challenging for me but thanks to all math help websites to help me out.
Example for ratio:
Example :
Divide the line segment `barA` `barB` of length 16 units in the ratio 3:5
Solution:
i) Let C be the point inside `barA``barB` such that `(AC)/(CB)`= `(3)/(5)`. Since the numerator is smaller than the denominator, C is closer to A than to B . Then
5AC=3 BC or 5AC=3(AB–AC) or 8AC=3AB =3(16)=48
AC=6 units and so CB=AB–AC =16–6 = 10 units.
Hence C lies inside `barA` `barB` 6 units distance from A and 10 units distance from B. The point C is unique and it divides `barA``barB` internally in the given ratio 3:5.
ii) Let D be the point outside `barA``barB` such that `(AD)/(DB)`=`(3)/(5)`?. Since the numerator is smaller than the denominator, D is closer to A than to B. Now we have
5 AD = 3DB or 5 AD = 3(AD + AB) or 5 AD = 3AD + 3AB
2 AD = 3AB = 3(16) = 48 or AD = 24 Then DB = DA + AB = 24 + 16 = 40
Therefore, D lies outside `barA``barB` 24 units distance from A and 40 units distance from B. The point D is unique and it divides `barA``barB` externally in the given ratio 3:5.
