Solve [51/7-{33/10div(24/5-7/10)}]

$$[ 5 \frac { 1 } { 7 } - \{ 3 \frac { 3 } { 10 } \div ( 2 \frac { 4 } { 5 } - \frac { 7 } { 10 } ) \} ]$$

Evaluate

$$\frac{25}{7}\approx 3.571428571$$

Solution Steps

Multiply 5 and 7 to get 35.

$$\frac{35+1}{7}-\frac{\frac{3\times 10+3}{10}}{\frac{2\times 5+4}{5}-\frac{7}{10}}$$

Add 35 and 1 to get 36.

$$\frac{36}{7}-\frac{\frac{3\times 10+3}{10}}{\frac{2\times 5+4}{5}-\frac{7}{10}}$$

Multiply 3 and 10 to get 30.

$$\frac{36}{7}-\frac{\frac{30+3}{10}}{\frac{2\times 5+4}{5}-\frac{7}{10}}$$

Add 30 and 3 to get 33.

$$\frac{36}{7}-\frac{\frac{33}{10}}{\frac{2\times 5+4}{5}-\frac{7}{10}}$$

Multiply 2 and 5 to get 10.

$$\frac{36}{7}-\frac{\frac{33}{10}}{\frac{10+4}{5}-\frac{7}{10}}$$

Add 10 and 4 to get 14.

$$\frac{36}{7}-\frac{\frac{33}{10}}{\frac{14}{5}-\frac{7}{10}}$$

Least common multiple of 5 and 10 is 10. Convert \frac{14}{5} and \frac{7}{10} to fractions with denominator 10.

$$\frac{36}{7}-\frac{\frac{33}{10}}{\frac{28}{10}-\frac{7}{10}}$$

Since \frac{28}{10} and \frac{7}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{36}{7}-\frac{\frac{33}{10}}{\frac{28-7}{10}}$$

Subtract 7 from 28 to get 21.

$$\frac{36}{7}-\frac{\frac{33}{10}}{\frac{21}{10}}$$

Divide \frac{33}{10} by \frac{21}{10} by multiplying \frac{33}{10} by the reciprocal of \frac{21}{10}.

$$\frac{36}{7}-\frac{33}{10}\times \frac{10}{21}$$

Multiply \frac{33}{10} times \frac{10}{21} by multiplying numerator times numerator and denominator times denominator.

$$\frac{36}{7}-\frac{33\times 10}{10\times 21}$$

Cancel out 10 in both numerator and denominator.

$$\frac{36}{7}-\frac{33}{21}$$

Reduce the fraction \frac{33}{21} to lowest terms by extracting and canceling out 3.

$$\frac{36}{7}-\frac{11}{7}$$

Since \frac{36}{7} and \frac{11}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{36-11}{7}$$

Subtract 11 from 36 to get 25.

$$\frac{25}{7}$$

Factor

$$\frac{5 ^ {2}}{7} = 3\frac{4}{7} = 3.5714285714285716$$