Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$4 \frac{ 7777777 }{ \frac{ 8888888 }{ \frac{ 9999999 }{ 4.4.4.4 } } }$$

Answer

$$(3.1111104888889*10^14)/(8888888*4.4.4.4)$$

Solution


Invert and multiply.
\[4\times \frac{7777777}{8888888\times \frac{4.4.4.4}{9999999}}\]
Use this rule: \(a \times \frac{b}{c}=\frac{ab}{c}\).
\[4\times \frac{7777777}{\frac{8888888\times 4.4.4.4}{9999999}}\]
Invert and multiply.
\[4\times 7777777\times \frac{9999999}{8888888\times 4.4.4.4}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{4\times 7777777\times 9999999}{8888888\times 4.4.4.4}\]
Simplify  \(4\times 7777777\)  to  \(31111108\).
\[\frac{31111108\times 9999999}{8888888\times 4.4.4.4}\]
Simplify  \(31111108\times 9999999\)  to  \(3.111110\times {10}^{14}\).
\[\frac{3.111110\times {10}^{14}}{8888888\times 4.4.4.4}\]
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