Solve 1 / [4 - 1 / \{2 - 1 / (1 - 5/13)\}]

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Question

$$1\div[4-1\div\{2-1\div(1-\frac{5}{13})\}]$$

Evaluate

$\frac{3}{4}=0.75$

Solution Steps

Convert $1$ to fraction $\frac{13}{13}$.

$$\frac{1}{4-\frac{1}{2-\frac{1}{\frac{13}{13}-\frac{5}{13}}}}$$

Since $\frac{13}{13}$ and $\frac{5}{13}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{4-\frac{1}{2-\frac{1}{\frac{13-5}{13}}}}$$

Subtract $5$ from $13$ to get $8$.

$$\frac{1}{4-\frac{1}{2-\frac{1}{\frac{8}{13}}}}$$

Divide $1$ by $\frac{8}{13}$ by multiplying $1$ by the reciprocal of $\frac{8}{13}$.

$$\frac{1}{4-\frac{1}{2-1\times \frac{13}{8}}}$$

Multiply $1$ and $\frac{13}{8}$ to get $\frac{13}{8}$.

$$\frac{1}{4-\frac{1}{2-\frac{13}{8}}}$$

Convert $2$ to fraction $\frac{16}{8}$.

$$\frac{1}{4-\frac{1}{\frac{16}{8}-\frac{13}{8}}}$$

Since $\frac{16}{8}$ and $\frac{13}{8}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{4-\frac{1}{\frac{16-13}{8}}}$$

Subtract $13$ from $16$ to get $3$.

$$\frac{1}{4-\frac{1}{\frac{3}{8}}}$$

Divide $1$ by $\frac{3}{8}$ by multiplying $1$ by the reciprocal of $\frac{3}{8}$.

$$\frac{1}{4-1\times \frac{8}{3}}$$

Multiply $1$ and $\frac{8}{3}$ to get $\frac{8}{3}$.

$$\frac{1}{4-\frac{8}{3}}$$

Convert $4$ to fraction $\frac{12}{3}$.

$$\frac{1}{\frac{12}{3}-\frac{8}{3}}$$

Since $\frac{12}{3}$ and $\frac{8}{3}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{\frac{12-8}{3}}$$

Subtract $8$ from $12$ to get $4$.

$$\frac{1}{\frac{4}{3}}$$

Divide $1$ by $\frac{4}{3}$ by multiplying $1$ by the reciprocal of $\frac{4}{3}$.

$$1\times \frac{3}{4}$$

Multiply $1$ and $\frac{3}{4}$ to get $\frac{3}{4}$.

$$\frac{3}{4}$$

Show Solution

Factor

$\frac{3}{2 ^ {2}} = 0.75$