Question

What is cross multiplication?

Answer 1

Hint: First of all we will assume the meaning of the term cross multiplication. Now, we will consider two fractions $\dfrac{a}{b}$ and $\dfrac{c}{d}$, we will equate them. To understand cross multiplication mathematically, we will perform this operation by multiplying the numerator of the L.H.S with the denominator of the R.H.S to get the resultant term of the left hand side. Similarly, we will multiply the denominator of the L.H.S with the numerator of the R.H.S to get the resultant term of the right hand side.

Complete step by step answer:
Here we have been asked to describe the term cross multiplication. Let us understand it with the help of some examples.
Now, in mathematics cross multiplication is a method to simplify two ratios or fractions that are equal to each other. Let us consider two fractions $\dfrac{a}{b}$ and $\dfrac{c}{d}$ which are equal, so according to this method we have to multiply the numerator of the L.H.S with the denominator of the R.H.S to get the resultant term of the left hand side. Similarly, we have to multiply the denominator of the L.H.S with the numerator of the R.H.S to get the resultant term of the right hand side. Therefore, performing these operations we get,
$\begin{align}
  & \Rightarrow \dfrac{a}{b}=\dfrac{c}{d} \\
 & \Rightarrow a\times d=c\times b \\
\end{align}$
This method is used to determine the values of any variable if the other three terms are known, for example we have the expression $\dfrac{x}{4}=\dfrac{6}{5}$ so it can be simplified as: -
$\begin{align}
  & \Rightarrow 5\times x=6\times 4 \\
 & \Rightarrow 5x=24 \\
 & \Rightarrow x=\dfrac{24}{5} \\
\end{align}$

Note: Here you must not get confused with the cross multiplication method used in the linear equation in two variables to solve for the values of x and y. Remember that the denominator of a fraction cannot be 0 otherwise the fraction will become undefined. These cross multiplication operations are used in the chapter ‘ratio and proportion’.