Solve 2/frac{2{3}*3/10+7/25*5}+4

$$\frac { 2 } { \frac { 2 } { 3 } \cdot \frac { 3 } { 10 } + \frac { 7 } { 25 } \cdot 5 } + 4$$

Evaluate

$$\frac{21}{4}=5.25$$

Solution Steps

Multiply \frac{2}{3} times \frac{3}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{\frac{2\times 3}{3\times 10}+\frac{7}{25}\times 5}+4$$

Cancel out 3 in both numerator and denominator.

$$\frac{2}{\frac{2}{10}+\frac{7}{25}\times 5}+4$$

Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$\frac{2}{\frac{1}{5}+\frac{7}{25}\times 5}+4$$

Express \frac{7}{25}\times 5 as a single fraction.

$$\frac{2}{\frac{1}{5}+\frac{7\times 5}{25}}+4$$

Multiply 7 and 5 to get 35.

$$\frac{2}{\frac{1}{5}+\frac{35}{25}}+4$$

Reduce the fraction \frac{35}{25} to lowest terms by extracting and canceling out 5.

$$\frac{2}{\frac{1}{5}+\frac{7}{5}}+4$$

Since \frac{1}{5} and \frac{7}{5} have the same denominator, add them by adding their numerators.

$$\frac{2}{\frac{1+7}{5}}+4$$

Add 1 and 7 to get 8.

$$\frac{2}{\frac{8}{5}}+4$$

Divide 2 by \frac{8}{5} by multiplying 2 by the reciprocal of \frac{8}{5}.

$$2\times \frac{5}{8}+4$$

Express 2\times \frac{5}{8} as a single fraction.

$$\frac{2\times 5}{8}+4$$

Multiply 2 and 5 to get 10.

$$\frac{10}{8}+4$$

Reduce the fraction \frac{10}{8} to lowest terms by extracting and canceling out 2.

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

Convert 4 to fraction \frac{16}{4}.

$$\frac{5}{4}+\frac{16}{4}$$

Since \frac{5}{4} and \frac{16}{4} have the same denominator, add them by adding their numerators.

$$\frac{5+16}{4}$$

Add 5 and 16 to get 21.

$$\frac{21}{4}$$

Factor

$$\frac{3 \cdot 7}{2 ^ {2}} = 5\frac{1}{4} = 5.25$$