Transposition and Cross-multiplication
Transposition: Any term of an equation may be taken to the other side with its sign changed, without affecting the equality. This process is called transposition.
For example: 4x – 2 = 2x – 6 4x – 2x = – 6 + 2.
Here, the term involving ‘x’ has been transposed to L.H.S. and the constant term (– 2) from L.H.S. has been transposed to R.H.S.
Cross-multiplication: If , then (a × d) = (b × c), that is, ad = bc. The numerator on L.H.S. is multiplied with denominator on R.H.S. and numerator on R.H.S. is multiplied with denominator on L.H.S., with "=" sign in tact. This process is called cross-multiplication.
Ex: Consider the equation . Then, by cross-multiplication, we get: 2(2x + 3) = 5(x – 4).