Question

Find the value of \[x\]in the following proportion \[x:4 = 6:8\]

Answer 1

Hint: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 ratios are equivalent
If one number in a proportion is unknown you can find that number by solving the proportion.
It is formulated as:
\[a:b::c:d\]
\[ \Rightarrow \dfrac{a}{b} = \dfrac{c}{d}\]
\[ \Rightarrow a \times d = b \times c\]
Therefore,

Complete step by step answer:
Given,
\[x:4 = 6:8......(1)\]
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 \[(1) \Rightarrow \dfrac{x}{4} = \dfrac{6}{8}\]
Gross multiplying, we get
\[x \times 8 = 4 \times 6\]

As S was in multiplication on LHS it will be in the division on the right-hand side.
\[ \Rightarrow x = \dfrac{6}{2}\]
\[ \Rightarrow x = 3\]
Hence the value, of \[x\] is \[3\]

Note:
 For four numbers a, b, c, d if \[a:b = c:d\] then \[b:c = d:c,\] is known as invert and properly
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 and dividend property to simplify the proportion problems.