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A ratio is a way to compare two quantities by using division as in miles per hour.

A proportion on the other hand is an equation that says that two ratio are equivalent

If one number in a proportion is unknown you can find that number by solving the proportion

It is formulate as:

\[a:b::c:d\]

\[ \Rightarrow \dfrac{a}{b} = \dfrac{c}{d}\]

\[ \Rightarrow a \times d = b \times c\]

Therefore,

Given

\[5:15 = 4:x......(1)\]

We need to find the value of \[x\]in proportion.

We know that if two number are in proportion i.e \[a:b::c:d\] or \[a:b = c:d,\]then we can write them as\[\dfrac{a}{b} = \dfrac{c}{d}\]

Hence \[(1) \Rightarrow \dfrac{5}{{15}} = \dfrac{4}{x}\]

Cross multiplying, we get

\[5 \times x = 15 \times 4\]

\[ \Rightarrow x = \dfrac{{15 \times 4}}{5}\]

As 5 was in multiplication LHS it will be in division on RHS

\[ \Rightarrow x = 3 \times 4\]

\[ \Rightarrow x = 12\]

Hence the value of \[x\] is 12.

For four numbers a ,b, c, d if \[a:b = c:d\] then \[a:c = b:d\]if the second and third terms interchange their places, it is known as alternator property.

We can also use component do and dividend property to simply the proportion problems.

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