# Thread: explain the fifth property of fractions

1. ## explain the fifth property of fractions

property: if a/b = c/d then ad = bc
description: cross-multiply

can someone explain this to me with proof? i don't understand why it works.

2. ## Re: explain the fifth property of fractions

you should be able to see this by now...

$\dfrac a b = \dfrac c d$

$bd \dfrac a b = bd \dfrac c d$

$d a = b c$

$ad = bc$

3. ## Re: explain the fifth property of fractions

it's sinking in

4. ## Re: explain the fifth property of fractions

Or "step by step": From $\frac{a}{b}= \frac{c}{d}$
multiply both sides by b: $\frac{a}{b}b= \frac{c}{d}b$ so $a= \frac{bc}{d}$

multiply both sides by d: $ad= \frac{bc}{d}d$ so $ad= bc$.