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How do you solve \[\dfrac{3}{8} = \dfrac{x}{{24}}\]?

Last updated date: 29th Feb 2024
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IVSAT 2024
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Hint: Use the cross – multiplication method for solving the equation. Cross – multiplication method in mathematics is performed between two fractions or rational expressions. This method is used to determine the unknown number in the equation. Multiply numerator with the denominator of another side and denominator with a numerator of another side.

Complete step by step solution:
Cross – multiplication method is used to find the value of an unknown number in the equation. This can be performed between two rational expressions or fractions. For example, if the two fractions having numbers $a,b,c$ and $d$ are given –
$\dfrac{a}{b} = \dfrac{c}{d}$
In the above fraction, $b$ and $d$ are non – zero numbers.
Therefore, in the cross – multiplication method, we multiply the numerator of the first fraction with the denominator of the second fraction and the denominator of the first fraction with the numerator of the second fraction. So, after using the cross – multiplication method in the above rational expressions, we get –
$ad = bc$
We use this procedure commonly in mathematics. This method is used to reduce fractions or to calculate the value for the given variable in the fraction. For example, if we have an equation –
$\dfrac{x}{b} = \dfrac{c}{d}$
where $x$ is the variable for which we have to find the value.
Therefore, after cross – multiplication the equation becomes –
$ \Rightarrow x = \dfrac{{bc}}{d}$
Hence, after putting the values for $b,c$ and $d$, we will also get the value of variable $x$.
In the question, we are given with the equation –
 \[ \Rightarrow \dfrac{3}{8} = \dfrac{x}{{24}}\]
After using the cross – multiplication method in the above equation, we get –
$ \Rightarrow x = \dfrac{{24 \times 3}}{8}$
Therefore, dividing 24 by 8, we get the answer as 3.
$ \Rightarrow x = 3 \times 3$
$ \Rightarrow x = 9$

Hence, the value of $x$ in the equation \[\dfrac{3}{8} = \dfrac{x}{{24}}\] is 3.

We can also use the transposition method in solving the value for $x$ in the equation \[\dfrac{3}{8} = \dfrac{x}{{24}}\] . In the transposition method, when the number is moved to another side, its operation also changes. Such as multiplication changes to division and division into multiplication, addition and subtraction, and subtraction into addition. So, after using this method in the equation \[\dfrac{3}{8} = \dfrac{x}{{24}}\]. We can directly write it as –
$ \Rightarrow x = \dfrac{{24 \times 3}}{8}$
After solving the above equation, we will get our answer.
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