Solve 5/4+2{1+frac{3/4}}=

$$\frac { 5 } { 4 + \frac { 2 } { 1 + \frac { 3 } { 4 } } } =$$

Evaluate

$$\frac{35}{36}\approx 0.972222222$$

Solution Steps

Convert 1 to fraction \frac{4}{4}.

$$\frac{5}{4+\frac{2}{\frac{4}{4}+\frac{3}{4}}}$$

Since \frac{4}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\frac{5}{4+\frac{2}{\frac{4+3}{4}}}$$

Add 4 and 3 to get 7.

$$\frac{5}{4+\frac{2}{\frac{7}{4}}}$$

Divide 2 by \frac{7}{4} by multiplying 2 by the reciprocal of \frac{7}{4}.

$$\frac{5}{4+2\times \frac{4}{7}}$$

Express 2\times \frac{4}{7} as a single fraction.

$$\frac{5}{4+\frac{2\times 4}{7}}$$

Multiply 2 and 4 to get 8.

$$\frac{5}{4+\frac{8}{7}}$$

Convert 4 to fraction \frac{28}{7}.

$$\frac{5}{\frac{28}{7}+\frac{8}{7}}$$

Since \frac{28}{7} and \frac{8}{7} have the same denominator, add them by adding their numerators.

$$\frac{5}{\frac{28+8}{7}}$$

Add 28 and 8 to get 36.

$$\frac{5}{\frac{36}{7}}$$

Divide 5 by \frac{36}{7} by multiplying 5 by the reciprocal of \frac{36}{7}.

$$5\times \frac{7}{36}$$

Express 5\times \frac{7}{36} as a single fraction.

$$\frac{5\times 7}{36}$$

Multiply 5 and 7 to get 35.

$$\frac{35}{36}$$

Factor

$$\frac{5 \cdot 7}{2 ^ {2} \cdot 3 ^ {2}} = 0.9722222222222222$$