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Cross Multiply
To cross multiply is to go from this:8 = 2123  To this:8 × 3 = 12 × 2How Does it Work?Step 1: When you multiply the top and bottom of a fraction by the same amount, it doesn't change its value. Example (first fraction above): 8 = 8 × 31212 × 3In that example I multiplied the top and bottom of the first fraction
by the bottom number of the second fraction.
Step 2: We could also multiply the top and bottom of the second fraction by the bottom number of the first fraction.Example (second fraction above): 2 = 2 × 1233 × 12Step 3: And we would then have:8 × 3 = 2 × 1212 × 33 × 12And Magic! The bottom of both fractions is now 12 × 3 ... ! Step 4: We can get rid of the 12 × 3 (because we are dividing both sides by the same amount) and the equation is still true:8 × 3 = 12 × 2Job Done! In practice, though, it is easier to skip the steps and go straight to the "cross-multiplied" form.Using VariablesSo far I have used numbers, but we can state it more generally using variables:To cross multiply is to go from this:a = cbd  To this:ad = bc
How to remember: "cross" multiply:Example Cross multiplication can help speed up a solution. Like in this example: Find "x":x = 28x  Let's cross multiply:x2 = 8 × 2 = 16  And solvex = 4 or -4
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Cross multiplication is used in vector i.e. A <bar>× B<bar>= ABsinθ 
eg A<bar> = a₁î<cap> +a₂j<cap> +a₃k<cap>
     and  B<bar> = b₁î<cap> +b₂j<cap> +b₃k<cap>
so A<bar > × B<bar> =   \left[\begin{array}{ccc}i&j&k\\a1&a2&a3\\b1&b2&b3\end{array}\right]
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hope it helps
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