Solve 2-3/4-5{6-frac{7/8}}

$$2 - \frac { 3 } { 4 - \frac { 5 } { 6 - \frac { 7 } { 8 } } }$$

Evaluate

$$\frac{125}{124}\approx 1.008064516$$

Solution Steps

Convert 6 to fraction \frac{48}{8}.

$$2-\frac{3}{4-\frac{5}{\frac{48}{8}-\frac{7}{8}}}$$

Since \frac{48}{8} and \frac{7}{8} have the same denominator, subtract them by subtracting their numerators.

$$2-\frac{3}{4-\frac{5}{\frac{48-7}{8}}}$$

Subtract 7 from 48 to get 41.

$$2-\frac{3}{4-\frac{5}{\frac{41}{8}}}$$

Divide 5 by \frac{41}{8} by multiplying 5 by the reciprocal of \frac{41}{8}.

$$2-\frac{3}{4-5\times \frac{8}{41}}$$

Express 5\times \frac{8}{41} as a single fraction.

$$2-\frac{3}{4-\frac{5\times 8}{41}}$$

Multiply 5 and 8 to get 40.

$$2-\frac{3}{4-\frac{40}{41}}$$

Convert 4 to fraction \frac{164}{41}.

$$2-\frac{3}{\frac{164}{41}-\frac{40}{41}}$$

Since \frac{164}{41} and \frac{40}{41} have the same denominator, subtract them by subtracting their numerators.

$$2-\frac{3}{\frac{164-40}{41}}$$

Subtract 40 from 164 to get 124.

$$2-\frac{3}{\frac{124}{41}}$$

Divide 3 by \frac{124}{41} by multiplying 3 by the reciprocal of \frac{124}{41}.

$$2-3\times \frac{41}{124}$$

Express 3\times \frac{41}{124} as a single fraction.

$$2-\frac{3\times 41}{124}$$

Multiply 3 and 41 to get 123.

$$2-\frac{123}{124}$$

Convert 2 to fraction \frac{248}{124}.

$$\frac{248}{124}-\frac{123}{124}$$

Since \frac{248}{124} and \frac{123}{124} have the same denominator, subtract them by subtracting their numerators.

$$\frac{248-123}{124}$$

Subtract 123 from 248 to get 125.

$$\frac{125}{124}$$

Factor

$$\frac{5 ^ {3}}{2 ^ {2} \cdot 31} = 1\frac{1}{124} = 1.0080645161290323$$