Solve 31/8+11/4/2frac{5{8}-13/4}=frac{1frac{5}{7}*1frac{2}{5}}{2frac{1}{4}:3frac{1}{3}}

$$\frac { 3 \frac { 1 } { 8 } + 1 \frac { 1 } { 4 } } { 2 \frac { 5 } { 8 } - 1 \frac { 3 } { 4 } } = \frac { 1 \frac { 5 } { 7 } \cdot 1 \frac { 2 } { 5 } } { 2 \frac { 1 } { 4 } : 3 \frac { 1 } { 3 } }$$

Verify

Solution Steps

Multiply 3 and 8 to get 24.

$$\frac{\frac{24+1}{8}+\frac{1\times 4+1}{4}}{\frac{2\times 8+5}{8}-\frac{1\times 4+3}{4}}=\frac{\frac{1\times 7+5}{7}\times \frac{1\times 5+2}{5}}{\frac{\frac{2\times 4+1}{4}}{\frac{3\times 3+1}{3}}}$$

Add 24 and 1 to get 25.

$$\frac{\frac{25}{8}+\frac{1\times 4+1}{4}}{\frac{2\times 8+5}{8}-\frac{1\times 4+3}{4}}=\frac{\frac{1\times 7+5}{7}\times \frac{1\times 5+2}{5}}{\frac{\frac{2\times 4+1}{4}}{\frac{3\times 3+1}{3}}}$$

Multiply 1 and 4 to get 4.

$$\frac{\frac{25}{8}+\frac{4+1}{4}}{\frac{2\times 8+5}{8}-\frac{1\times 4+3}{4}}=\frac{\frac{1\times 7+5}{7}\times \frac{1\times 5+2}{5}}{\frac{\frac{2\times 4+1}{4}}{\frac{3\times 3+1}{3}}}$$

Add 4 and 1 to get 5.

$$\frac{\frac{25}{8}+\frac{5}{4}}{\frac{2\times 8+5}{8}-\frac{1\times 4+3}{4}}=\frac{\frac{1\times 7+5}{7}\times \frac{1\times 5+2}{5}}{\frac{\frac{2\times 4+1}{4}}{\frac{3\times 3+1}{3}}}$$

Least common multiple of 8 and 4 is 8. Convert \frac{25}{8} and \frac{5}{4} to fractions with denominator 8.

$$\frac{\frac{25}{8}+\frac{10}{8}}{\frac{2\times 8+5}{8}-\frac{1\times 4+3}{4}}=\frac{\frac{1\times 7+5}{7}\times \frac{1\times 5+2}{5}}{\frac{\frac{2\times 4+1}{4}}{\frac{3\times 3+1}{3}}}$$

Since \frac{25}{8} and \frac{10}{8} have the same denominator, add them by adding their numerators.

$$\frac{\frac{25+10}{8}}{\frac{2\times 8+5}{8}-\frac{1\times 4+3}{4}}=\frac{\frac{1\times 7+5}{7}\times \frac{1\times 5+2}{5}}{\frac{\frac{2\times 4+1}{4}}{\frac{3\times 3+1}{3}}}$$

Add 25 and 10 to get 35.

$$\frac{\frac{35}{8}}{\frac{2\times 8+5}{8}-\frac{1\times 4+3}{4}}=\frac{\frac{1\times 7+5}{7}\times \frac{1\times 5+2}{5}}{\frac{\frac{2\times 4+1}{4}}{\frac{3\times 3+1}{3}}}$$

Multiply 2 and 8 to get 16.

$$\frac{\frac{35}{8}}{\frac{16+5}{8}-\frac{1\times 4+3}{4}}=\frac{\frac{1\times 7+5}{7}\times \frac{1\times 5+2}{5}}{\frac{\frac{2\times 4+1}{4}}{\frac{3\times 3+1}{3}}}$$

Add 16 and 5 to get 21.

$$\frac{\frac{35}{8}}{\frac{21}{8}-\frac{1\times 4+3}{4}}=\frac{\frac{1\times 7+5}{7}\times \frac{1\times 5+2}{5}}{\frac{\frac{2\times 4+1}{4}}{\frac{3\times 3+1}{3}}}$$

Multiply 1 and 4 to get 4.

$$\frac{\frac{35}{8}}{\frac{21}{8}-\frac{4+3}{4}}=\frac{\frac{1\times 7+5}{7}\times \frac{1\times 5+2}{5}}{\frac{\frac{2\times 4+1}{4}}{\frac{3\times 3+1}{3}}}$$

Add 4 and 3 to get 7.

$$\frac{\frac{35}{8}}{\frac{21}{8}-\frac{7}{4}}=\frac{\frac{1\times 7+5}{7}\times \frac{1\times 5+2}{5}}{\frac{\frac{2\times 4+1}{4}}{\frac{3\times 3+1}{3}}}$$

Least common multiple of 8 and 4 is 8. Convert \frac{21}{8} and \frac{7}{4} to fractions with denominator 8.

$$\frac{\frac{35}{8}}{\frac{21}{8}-\frac{14}{8}}=\frac{\frac{1\times 7+5}{7}\times \frac{1\times 5+2}{5}}{\frac{\frac{2\times 4+1}{4}}{\frac{3\times 3+1}{3}}}$$

Since \frac{21}{8} and \frac{14}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{35}{8}}{\frac{21-14}{8}}=\frac{\frac{1\times 7+5}{7}\times \frac{1\times 5+2}{5}}{\frac{\frac{2\times 4+1}{4}}{\frac{3\times 3+1}{3}}}$$

Subtract 14 from 21 to get 7.

$$\frac{\frac{35}{8}}{\frac{7}{8}}=\frac{\frac{1\times 7+5}{7}\times \frac{1\times 5+2}{5}}{\frac{\frac{2\times 4+1}{4}}{\frac{3\times 3+1}{3}}}$$

Divide \frac{35}{8} by \frac{7}{8} by multiplying \frac{35}{8} by the reciprocal of \frac{7}{8}.

$$\frac{35}{8}\times \frac{8}{7}=\frac{\frac{1\times 7+5}{7}\times \frac{1\times 5+2}{5}}{\frac{\frac{2\times 4+1}{4}}{\frac{3\times 3+1}{3}}}$$

Multiply \frac{35}{8} times \frac{8}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{35\times 8}{8\times 7}=\frac{\frac{1\times 7+5}{7}\times \frac{1\times 5+2}{5}}{\frac{\frac{2\times 4+1}{4}}{\frac{3\times 3+1}{3}}}$$

Cancel out 8 in both numerator and denominator.

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

Divide 35 by 7 to get 5.

$$5=\frac{\frac{1\times 7+5}{7}\times \frac{1\times 5+2}{5}}{\frac{\frac{2\times 4+1}{4}}{\frac{3\times 3+1}{3}}}$$

Multiply 1 and 7 to get 7.

$$5=\frac{\frac{7+5}{7}\times \frac{1\times 5+2}{5}}{\frac{\frac{2\times 4+1}{4}}{\frac{3\times 3+1}{3}}}$$

Add 7 and 5 to get 12.

$$5=\frac{\frac{12}{7}\times \frac{1\times 5+2}{5}}{\frac{\frac{2\times 4+1}{4}}{\frac{3\times 3+1}{3}}}$$

Multiply 1 and 5 to get 5.

$$5=\frac{\frac{12}{7}\times \frac{5+2}{5}}{\frac{\frac{2\times 4+1}{4}}{\frac{3\times 3+1}{3}}}$$

Add 5 and 2 to get 7.

$$5=\frac{\frac{12}{7}\times \frac{7}{5}}{\frac{\frac{2\times 4+1}{4}}{\frac{3\times 3+1}{3}}}$$

Multiply \frac{12}{7} times \frac{7}{5} by multiplying numerator times numerator and denominator times denominator.

$$5=\frac{\frac{12\times 7}{7\times 5}}{\frac{\frac{2\times 4+1}{4}}{\frac{3\times 3+1}{3}}}$$

Cancel out 7 in both numerator and denominator.

$$5=\frac{\frac{12}{5}}{\frac{\frac{2\times 4+1}{4}}{\frac{3\times 3+1}{3}}}$$

Divide \frac{2\times 4+1}{4} by \frac{3\times 3+1}{3} by multiplying \frac{2\times 4+1}{4} by the reciprocal of \frac{3\times 3+1}{3}.

$$5=\frac{\frac{12}{5}}{\frac{\left(2\times 4+1\right)\times 3}{4\left(3\times 3+1\right)}}$$

Multiply 2 and 4 to get 8.

$$5=\frac{\frac{12}{5}}{\frac{\left(8+1\right)\times 3}{4\left(3\times 3+1\right)}}$$

Add 8 and 1 to get 9.

$$5=\frac{\frac{12}{5}}{\frac{9\times 3}{4\left(3\times 3+1\right)}}$$

Multiply 9 and 3 to get 27.

$$5=\frac{\frac{12}{5}}{\frac{27}{4\left(3\times 3+1\right)}}$$

Multiply 3 and 3 to get 9.

$$5=\frac{\frac{12}{5}}{\frac{27}{4\left(9+1\right)}}$$

Add 9 and 1 to get 10.

$$5=\frac{\frac{12}{5}}{\frac{27}{4\times 10}}$$

Multiply 4 and 10 to get 40.

$$5=\frac{\frac{12}{5}}{\frac{27}{40}}$$

Divide \frac{12}{5} by \frac{27}{40} by multiplying \frac{12}{5} by the reciprocal of \frac{27}{40}.

$$5=\frac{12}{5}\times \frac{40}{27}$$

Multiply \frac{12}{5} times \frac{40}{27} by multiplying numerator times numerator and denominator times denominator.

$$5=\frac{12\times 40}{5\times 27}$$

Do the multiplications in the fraction \frac{12\times 40}{5\times 27}.

$$5=\frac{480}{135}$$

Reduce the fraction \frac{480}{135} to lowest terms by extracting and canceling out 15.

$$5=\frac{32}{9}$$

Convert 5 to fraction \frac{45}{9}.

$$\frac{45}{9}=\frac{32}{9}$$

Compare \frac{45}{9} and \frac{32}{9}.

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