[SOLVED] Laws of Numbers

**ronaldo_07** · January 17th 2009, 12:29 AM

Use the definition of addition for rational numbers to verify that it satisfies the
commutative and associative laws.

Use the definition of multiplication for complex numbers to verify that it satisfies the commutative and associative laws.

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For the first part I did this: is this correct?

$\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}$

$\frac{c}{d}+\frac{a}{b}=\frac{cb+da}{db}$

$\frac{ad+bc}{bd}=\frac{cb+da}{db}$

EDF

**running-gag** · January 17th 2009, 01:01 AM

Originally Posted by ronaldo_07

For the first part I did this: is this correct?

$\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}$

$\frac{c}{d}+\frac{a}{b}=\frac{cb+da}{db}$

$\frac{ad+bc}{bd}=\frac{cb+da}{db}$

EDF

Hi

I think it is correct.
Of course you need to suppose that multiplication and addition are commutative for integers.

a and d being integers : $ad=da$
b and c being integers : $bc=cb$
ad and bc being integers : $ad+bc=bc+ad$
Therefore $ad+bc=bc+ad=cb+da$

b and d being integers : $bd=db$

Therefore the conclusion

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