Math Proportions
Hi friends, today I am here to teach you about a very interesting and important topic of maths which is Math Proportions.
A ratio is one thing compared to or related to another thing; it is just a station or an expression.
A proportion is when two ratios when written in a form in which they are equal to each other.
Proportions are represented as
or can also be written in the form like a:b = c:d
A proportion can be easily solved.
Like For Example – 5/10 = ½.
This method could also be used to find the missing values in the fractions like –
1. 6/18 = 14/x
so 1/3 = 14/x.
x = 14 x 3
= 42.
2. x/10 = ½.
x = 5.
So by this method we can easily find the values of the missing component.
Let’s solve some word problems based on proportions.
In a park there were 16 ducks to 9 geese, now if in another park the ratio to ducks and geese was same and there were 192 ducks, then find the number of geese.
To solve this we will have to first convert it in the proportion form –
ducks/ geese = 16/9 = 192/x, where x is the number of geese in the second park.
16/9 = 192/x
multiply both the sides by x.
16 x /9 = 192.
now multiply both sides by 9.
16 x = 192 x 9.
16 x = 1728.
divide both sides by 16.
16 x /16 = 1728 / 16.
x =108.
so the number of geese in the second park are 108.
if two gallons of water costs Rs. 250/-, then how much will 100 gallons cost?
In this case also we will first form the proportion,
2/250 = 100/x.
So now multiplying both sides by 250.
2/250 x 250 = 100 x 250 / x
2 = 100 x 250 / x.
x = 250 x 100.
Divide both sides by 2.
x = 250 x 100 / 2
x = Rs. 12500/-.
we can also check proportionality by a simple method.
In our terminology when we write in general form
a/b = c/d, the values b and c are called as the means of the proportion and a and d are called as the extremes of the proportion. From this we can say ad = bc. So if this condition is satisfied then we can say the given proportion is correct.
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