Solve 4\div(1)/((4)/((590)/((0.25)/((1)/((4)/(.4))))))

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Question

$$4 \div \frac{ 1 }{ \frac{ 4 }{ \frac{ 590 }{ \frac{ 0.25 }{ \frac{ 1 }{ \frac{ 4 }{ .4 } } } } } }$$

Evaluate

$\frac{4}{59}\approx 0.06779661$

Solution Steps

Divide $4$ by $\frac{1}{\frac{4}{\frac{590}{\frac{0.25}{\frac{1}{\frac{4}{0.4}}}}}}$ by multiplying $4$ by the reciprocal of $\frac{1}{\frac{4}{\frac{590}{\frac{0.25}{\frac{1}{\frac{4}{0.4}}}}}}$.

$$4\times \frac{4}{\frac{590}{\frac{0.25}{\frac{1}{\frac{4}{0.4}}}}}$$

Divide $4$ by $\frac{590}{\frac{0.25}{\frac{1}{\frac{4}{0.4}}}}$ by multiplying $4$ by the reciprocal of $\frac{590}{\frac{0.25}{\frac{1}{\frac{4}{0.4}}}}$.

$$4\times \frac{4\times \frac{0.25}{\frac{1}{\frac{4}{0.4}}}}{590}$$

Divide $0.25$ by $\frac{1}{\frac{4}{0.4}}$ by multiplying $0.25$ by the reciprocal of $\frac{1}{\frac{4}{0.4}}$.

$$4\times \frac{4\times 0.25\times \frac{4}{0.4}}{590}$$

Multiply $4$ and $0.25$ to get $1$.

$$4\times \frac{\frac{4}{0.4}}{590}$$

Expand $\frac{4}{0.4}$ by multiplying both numerator and the denominator by $10$.

$$4\times \frac{\frac{40}{4}}{590}$$

Divide $40$ by $4$ to get $10$.

$$4\times \frac{10}{590}$$

Reduce the fraction $\frac{10}{590}$ to lowest terms by extracting and canceling out $10$.

$$4\times \frac{1}{59}$$

Multiply $4$ and $\frac{1}{59}$ to get $\frac{4}{59}$.

$$\frac{4}{59}$$

Show Solution

Factor

$\frac{2 ^ {2}}{59} = 0.06779661016949153$