Answer:
The simplest form of the complex fraction [tex]\frac{\frac{8}{9}}{8}[/tex] is [tex]\frac{1}{9}[/tex]
Step-by-step explanation:
In the complex fractions [tex]\frac{\frac{a}{b}}{c}[/tex] = [tex]\frac{a}{b}[/tex] ÷ c
To simplify it change ÷ to × and reciprocal c
- [tex]\frac{\frac{a}{b}}{c}[/tex] = [tex]\frac{a}{b}[/tex] ÷ c = [tex]\frac{a}{b}[/tex] × [tex]\frac{1}{c}[/tex] = [tex]\frac{a}{bc}[/tex]
In the complex fractions [tex]\frac{a}{\frac{b}{c}}[/tex] = a ÷ [tex]\frac{b}{c}[/tex]
To simplify it change ÷ to × and reciprocal [tex]\frac{b}{c}[/tex]
- [tex]\frac{a}{\frac{b}{c}}[/tex] = a ÷ [tex]\frac{b}{c}[/tex] = a × [tex]\frac{c}{b}[/tex] = [tex]\frac{ac}{b}[/tex]
Let us solve the question
∵ The complex fraction is [tex]\frac{\frac{8}{9}}{8}[/tex]
∵ [tex]\frac{\frac{8}{9}}{8}[/tex] = [tex]\frac{8}{9}[/tex] ÷ 8
→ Change ÷ to × and reciprocal 8
∴ [tex]\frac{8}{9}[/tex] ÷ 8 = [tex]\frac{8}{9}[/tex] × [tex]\frac{1}{8}[/tex]
→ Cancel 8 up with 8 down
∴ [tex]\frac{8}{9}[/tex] × [tex]\frac{1}{8}[/tex] = [tex]\frac{1}{9}[/tex]
∴ The simplest form of the complex fraction [tex]\frac{\frac{8}{9}}{8}[/tex] is [tex]\frac{1}{9}[/tex]
