分數之乘法分配律

設 $a$ 、 $b$ 、 $c$ 為任意三個分數，則：

1. $a\times (b+c)=a\times b+a\times c$

例 $13\times (\dfrac{12}{13}+\dfrac{2}{39})=13\times \dfrac{12}{13}+13\times \dfrac{2}{39}=12+\dfrac23=12\dfrac23$

$\dfrac37\times \dfrac{7}{19}+\dfrac{3}{7}\times \dfrac{12}{19}=\dfrac37\times (\dfrac{7}{19}+\dfrac{12}{19})=\dfrac37\times \dfrac{19}{19}=\dfrac37$

2. $(a+b)\times c=a\times c+b\times c$

例 $(\dfrac{12}{13}+\dfrac{2}{39})\times 13=\dfrac{12}{13}\times 13+\dfrac{2}{39}\times 13=12+\dfrac23=12\dfrac23$

3. $a\times (b-c)=a\times b-a\times c$

例 $\dfrac{17}{11}\times (\dfrac{33}{34}-\dfrac{22}{17})=\dfrac{17}{11}\times \dfrac{33}{34}-\dfrac{17}{11}\times \dfrac{22}{17}=\dfrac32-2=-\dfrac12$

$\dfrac{5}{13}\times \dfrac{13}{29}-\dfrac{5}{13}\times \dfrac{42}{29}=\dfrac{5}{13}\times (\dfrac{13}{29}-\dfrac{42}{29})=\dfrac{5}{13}\times (-\dfrac{29}{29})=-\dfrac{5}{13}$

4. $(a-b)\times c=a\times c-b\times c$

例 $(\dfrac{33}{34}-\dfrac{22}{17})\times \dfrac{17}{11}=\dfrac{33}{34}\times \dfrac{17}{11}-\dfrac{22}{17}\times \dfrac{17}{11}=\dfrac32-2=-\dfrac12$