# Thread: [SOLVED] Laws of Numbers

1. ## [SOLVED] Laws of Numbers

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

2. 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