Solve 71/2*22/3-121/4:frac{7/2}{110:frac{3}{5}}+frac{3frac{3}{8}+2frac{3}{4}}{24:2frac{2}{5}}

$$\frac { 7 \frac { 1 } { 2 } \cdot 2 \frac { 2 } { 3 } - 12 \frac { 1 } { 4 } : \frac { 7 } { 2 } } { 110 : \frac { 3 } { 5 } } + \frac { 3 \frac { 3 } { 8 } + 2 \frac { 3 } { 4 } } { 24 : 2 \frac { 2 } { 5 } }$$

Evaluate

$$\frac{281}{400}=0.7025$$

Solution Steps

Multiply 7 and 2 to get 14.

$$\frac{\frac{14+1}{2}\times \frac{2\times 3+2}{3}-\frac{\frac{12\times 4+1}{4}}{\frac{7}{2}}}{\frac{110}{\frac{3}{5}}}+\frac{\frac{3\times 8+3}{8}+\frac{2\times 4+3}{4}}{\frac{24}{\frac{2\times 5+2}{5}}}$$

Add 14 and 1 to get 15.

$$\frac{\frac{15}{2}\times \frac{2\times 3+2}{3}-\frac{\frac{12\times 4+1}{4}}{\frac{7}{2}}}{\frac{110}{\frac{3}{5}}}+\frac{\frac{3\times 8+3}{8}+\frac{2\times 4+3}{4}}{\frac{24}{\frac{2\times 5+2}{5}}}$$

Multiply 2 and 3 to get 6.

$$\frac{\frac{15}{2}\times \frac{6+2}{3}-\frac{\frac{12\times 4+1}{4}}{\frac{7}{2}}}{\frac{110}{\frac{3}{5}}}+\frac{\frac{3\times 8+3}{8}+\frac{2\times 4+3}{4}}{\frac{24}{\frac{2\times 5+2}{5}}}$$

Add 6 and 2 to get 8.

$$\frac{\frac{15}{2}\times \frac{8}{3}-\frac{\frac{12\times 4+1}{4}}{\frac{7}{2}}}{\frac{110}{\frac{3}{5}}}+\frac{\frac{3\times 8+3}{8}+\frac{2\times 4+3}{4}}{\frac{24}{\frac{2\times 5+2}{5}}}$$

Multiply \frac{15}{2} times \frac{8}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{15\times 8}{2\times 3}-\frac{\frac{12\times 4+1}{4}}{\frac{7}{2}}}{\frac{110}{\frac{3}{5}}}+\frac{\frac{3\times 8+3}{8}+\frac{2\times 4+3}{4}}{\frac{24}{\frac{2\times 5+2}{5}}}$$

Do the multiplications in the fraction \frac{15\times 8}{2\times 3}.

$$\frac{\frac{120}{6}-\frac{\frac{12\times 4+1}{4}}{\frac{7}{2}}}{\frac{110}{\frac{3}{5}}}+\frac{\frac{3\times 8+3}{8}+\frac{2\times 4+3}{4}}{\frac{24}{\frac{2\times 5+2}{5}}}$$

Divide 120 by 6 to get 20.

$$\frac{20-\frac{\frac{12\times 4+1}{4}}{\frac{7}{2}}}{\frac{110}{\frac{3}{5}}}+\frac{\frac{3\times 8+3}{8}+\frac{2\times 4+3}{4}}{\frac{24}{\frac{2\times 5+2}{5}}}$$

Divide \frac{12\times 4+1}{4} by \frac{7}{2} by multiplying \frac{12\times 4+1}{4} by the reciprocal of \frac{7}{2}.

$$\frac{20-\frac{\left(12\times 4+1\right)\times 2}{4\times 7}}{\frac{110}{\frac{3}{5}}}+\frac{\frac{3\times 8+3}{8}+\frac{2\times 4+3}{4}}{\frac{24}{\frac{2\times 5+2}{5}}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{20-\frac{1+4\times 12}{2\times 7}}{\frac{110}{\frac{3}{5}}}+\frac{\frac{3\times 8+3}{8}+\frac{2\times 4+3}{4}}{\frac{24}{\frac{2\times 5+2}{5}}}$$

Multiply 4 and 12 to get 48.

$$\frac{20-\frac{1+48}{2\times 7}}{\frac{110}{\frac{3}{5}}}+\frac{\frac{3\times 8+3}{8}+\frac{2\times 4+3}{4}}{\frac{24}{\frac{2\times 5+2}{5}}}$$

Add 1 and 48 to get 49.

$$\frac{20-\frac{49}{2\times 7}}{\frac{110}{\frac{3}{5}}}+\frac{\frac{3\times 8+3}{8}+\frac{2\times 4+3}{4}}{\frac{24}{\frac{2\times 5+2}{5}}}$$

Multiply 2 and 7 to get 14.

$$\frac{20-\frac{49}{14}}{\frac{110}{\frac{3}{5}}}+\frac{\frac{3\times 8+3}{8}+\frac{2\times 4+3}{4}}{\frac{24}{\frac{2\times 5+2}{5}}}$$

Reduce the fraction \frac{49}{14} to lowest terms by extracting and canceling out 7.

$$\frac{20-\frac{7}{2}}{\frac{110}{\frac{3}{5}}}+\frac{\frac{3\times 8+3}{8}+\frac{2\times 4+3}{4}}{\frac{24}{\frac{2\times 5+2}{5}}}$$

Convert 20 to fraction \frac{40}{2}.

$$\frac{\frac{40}{2}-\frac{7}{2}}{\frac{110}{\frac{3}{5}}}+\frac{\frac{3\times 8+3}{8}+\frac{2\times 4+3}{4}}{\frac{24}{\frac{2\times 5+2}{5}}}$$

Since \frac{40}{2} and \frac{7}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{40-7}{2}}{\frac{110}{\frac{3}{5}}}+\frac{\frac{3\times 8+3}{8}+\frac{2\times 4+3}{4}}{\frac{24}{\frac{2\times 5+2}{5}}}$$

Subtract 7 from 40 to get 33.

$$\frac{\frac{33}{2}}{\frac{110}{\frac{3}{5}}}+\frac{\frac{3\times 8+3}{8}+\frac{2\times 4+3}{4}}{\frac{24}{\frac{2\times 5+2}{5}}}$$

Divide 110 by \frac{3}{5} by multiplying 110 by the reciprocal of \frac{3}{5}.

$$\frac{\frac{33}{2}}{110\times \frac{5}{3}}+\frac{\frac{3\times 8+3}{8}+\frac{2\times 4+3}{4}}{\frac{24}{\frac{2\times 5+2}{5}}}$$

Express 110\times \frac{5}{3} as a single fraction.

$$\frac{\frac{33}{2}}{\frac{110\times 5}{3}}+\frac{\frac{3\times 8+3}{8}+\frac{2\times 4+3}{4}}{\frac{24}{\frac{2\times 5+2}{5}}}$$

Multiply 110 and 5 to get 550.

$$\frac{\frac{33}{2}}{\frac{550}{3}}+\frac{\frac{3\times 8+3}{8}+\frac{2\times 4+3}{4}}{\frac{24}{\frac{2\times 5+2}{5}}}$$

Divide \frac{33}{2} by \frac{550}{3} by multiplying \frac{33}{2} by the reciprocal of \frac{550}{3}.

$$\frac{33}{2}\times \frac{3}{550}+\frac{\frac{3\times 8+3}{8}+\frac{2\times 4+3}{4}}{\frac{24}{\frac{2\times 5+2}{5}}}$$

Multiply \frac{33}{2} times \frac{3}{550} by multiplying numerator times numerator and denominator times denominator.

$$\frac{33\times 3}{2\times 550}+\frac{\frac{3\times 8+3}{8}+\frac{2\times 4+3}{4}}{\frac{24}{\frac{2\times 5+2}{5}}}$$

Do the multiplications in the fraction \frac{33\times 3}{2\times 550}.

$$\frac{99}{1100}+\frac{\frac{3\times 8+3}{8}+\frac{2\times 4+3}{4}}{\frac{24}{\frac{2\times 5+2}{5}}}$$

Reduce the fraction \frac{99}{1100} to lowest terms by extracting and canceling out 11.

$$\frac{9}{100}+\frac{\frac{3\times 8+3}{8}+\frac{2\times 4+3}{4}}{\frac{24}{\frac{2\times 5+2}{5}}}$$

Multiply 3 and 8 to get 24.

$$\frac{9}{100}+\frac{\frac{24+3}{8}+\frac{2\times 4+3}{4}}{\frac{24}{\frac{2\times 5+2}{5}}}$$

Add 24 and 3 to get 27.

$$\frac{9}{100}+\frac{\frac{27}{8}+\frac{2\times 4+3}{4}}{\frac{24}{\frac{2\times 5+2}{5}}}$$

Multiply 2 and 4 to get 8.

$$\frac{9}{100}+\frac{\frac{27}{8}+\frac{8+3}{4}}{\frac{24}{\frac{2\times 5+2}{5}}}$$

Add 8 and 3 to get 11.

$$\frac{9}{100}+\frac{\frac{27}{8}+\frac{11}{4}}{\frac{24}{\frac{2\times 5+2}{5}}}$$

Least common multiple of 8 and 4 is 8. Convert \frac{27}{8} and \frac{11}{4} to fractions with denominator 8.

$$\frac{9}{100}+\frac{\frac{27}{8}+\frac{22}{8}}{\frac{24}{\frac{2\times 5+2}{5}}}$$

Since \frac{27}{8} and \frac{22}{8} have the same denominator, add them by adding their numerators.

$$\frac{9}{100}+\frac{\frac{27+22}{8}}{\frac{24}{\frac{2\times 5+2}{5}}}$$

Add 27 and 22 to get 49.

$$\frac{9}{100}+\frac{\frac{49}{8}}{\frac{24}{\frac{2\times 5+2}{5}}}$$

Divide 24 by \frac{2\times 5+2}{5} by multiplying 24 by the reciprocal of \frac{2\times 5+2}{5}.

$$\frac{9}{100}+\frac{\frac{49}{8}}{\frac{24\times 5}{2\times 5+2}}$$

Multiply 24 and 5 to get 120.

$$\frac{9}{100}+\frac{\frac{49}{8}}{\frac{120}{2\times 5+2}}$$

Multiply 2 and 5 to get 10.

$$\frac{9}{100}+\frac{\frac{49}{8}}{\frac{120}{10+2}}$$

Add 10 and 2 to get 12.

$$\frac{9}{100}+\frac{\frac{49}{8}}{\frac{120}{12}}$$

Divide 120 by 12 to get 10.

$$\frac{9}{100}+\frac{\frac{49}{8}}{10}$$

Express \frac{\frac{49}{8}}{10} as a single fraction.

$$\frac{9}{100}+\frac{49}{8\times 10}$$

Multiply 8 and 10 to get 80.

$$\frac{9}{100}+\frac{49}{80}$$

Least common multiple of 100 and 80 is 400. Convert \frac{9}{100} and \frac{49}{80} to fractions with denominator 400.

$$\frac{36}{400}+\frac{245}{400}$$

Since \frac{36}{400} and \frac{245}{400} have the same denominator, add them by adding their numerators.

$$\frac{36+245}{400}$$

Add 36 and 245 to get 281.

$$\frac{281}{400}$$

Factor

$$\frac{281}{2 ^ {4} \cdot 5 ^ {2}} = 0.7025$$