Answer:
a. Distributive property of multiplication over addition
b. [tex]\frac{368}{495}[/tex]
Step-by-step explanation:
Given: [tex]\frac{-8}{9}\left [ \frac{1}{-5}+\left ( \frac{-7}{11} \right ) \right ][/tex]
To find: the property and the value
Solution:
a.
Property used:
Distributive property of multiplication over addition: [tex]a(b+c)=ab+ac[/tex]
b.
Take [tex]a=\frac{-8}{9}\,,\,b=\frac{1}{-5}\,,\,c=\frac{-7}{11}[/tex]
[tex]\frac{-8}{9}\left [ \frac{1}{-5}+\left ( \frac{-7}{11} \right ) \right ]\\=\frac{-8}{9}\left (\frac{1}{-5} \right )+\left ( \frac{-8}{9} \right )\left ( \frac{-7}{11} \right )\\=\frac{-8}{-45}+\frac{56}{99}\\=\frac{8}{45}+\frac{56}{99}\\=\frac{88+280}{495}\\=\frac{368}{495}[/tex]