Cross Multiplication Method
Answers
\frac a b \nwarrow \frac c d \quad \frac a b \nearrow \frac c d.
The mathematical justification for the method is from the following longer mathematical procedure. If we start with the basic equation:
{\displaystyle {\frac {a}{b}}={\frac {c}{d}}}\frac a b = \frac c d
we can multiply the terms on each side by the same number and the terms will remain equal. Therefore, if we multiply the fraction on each side by the product of the denominators of both sides—bd—we get:
{\displaystyle {\frac {a}{b}}\times bd={\frac {c}{d}}\times bd.}\frac a b \times bd = \frac c d \times bd.
We can reduce the fractions to lowest terms by noting that the two occurrences of {\displaystyle b}b on the left-hand side cancel, as do the two occurrences of d on the right-hand side, leaving:
{\displaystyle ad=bc}ad = bc
and we can divide both sides of the equation by any of the elements—in this case we will use d—getting:
{\displaystyle a={\frac {bc}{d}}.}a = \frac {bc} d.
Another justification of cross-multiplication is as follows. Starting with the given equation:
{\displaystyle {\frac {a}{b}}={\frac {c}{d}}}\frac a b = \frac c d
multiply by
d
/
d
= 1 on the left and by
b
/
b
= 1 on the right, getting:
{\displaystyle {\frac {a}{b}}\times {\frac {d}{d}}={\frac {c}{d}}\times {\frac {b}{b}}}\frac a b \times \frac d d = \frac c d \times \frac b b
and so:
{\displaystyle {\frac {ad}{bd}}={\frac {cb}{db}}.}\frac {ad} {bd} = \frac {cb} {db}.
Cancel the common denominator bd = db, leaving:
{\displaystyle ad=cb.}ad = cb.
Each step in these procedures is based on a single, fundamental property of equations. Cross-multiplication is a shortcut, an easily understandable procedure that can be taught to students.
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Answer:
In practice, the method of cross multiplying means that we multiply the numerator of each side by the denominator of the other side effectively crossing the terms over.
Step-by-step explanation:
The above pic will help u understand better......
Hope it helps :)
