Solve 3/4+22/5+21/4+33/8div0.1125

$$\frac{ 3 }{ 4 } +2 \frac{ 2 }{ 5 } +2 \frac{ 1 }{ 4 } +3 \frac{ 3 }{ 8 } \div 0.1125$$

Evaluate

$$35.4$$

Solution Steps

Multiply 2 and 5 to get 10.

$$\frac{3}{4}+\frac{10+2}{5}+\frac{2\times 4+1}{4}+\frac{\frac{3\times 8+3}{8}}{0.1125}$$

Add 10 and 2 to get 12.

$$\frac{3}{4}+\frac{12}{5}+\frac{2\times 4+1}{4}+\frac{\frac{3\times 8+3}{8}}{0.1125}$$

Least common multiple of 4 and 5 is 20. Convert \frac{3}{4} and \frac{12}{5} to fractions with denominator 20.

$$\frac{15}{20}+\frac{48}{20}+\frac{2\times 4+1}{4}+\frac{\frac{3\times 8+3}{8}}{0.1125}$$

Since \frac{15}{20} and \frac{48}{20} have the same denominator, add them by adding their numerators.

$$\frac{15+48}{20}+\frac{2\times 4+1}{4}+\frac{\frac{3\times 8+3}{8}}{0.1125}$$

Add 15 and 48 to get 63.

$$\frac{63}{20}+\frac{2\times 4+1}{4}+\frac{\frac{3\times 8+3}{8}}{0.1125}$$

Multiply 2 and 4 to get 8.

$$\frac{63}{20}+\frac{8+1}{4}+\frac{\frac{3\times 8+3}{8}}{0.1125}$$

Add 8 and 1 to get 9.

$$\frac{63}{20}+\frac{9}{4}+\frac{\frac{3\times 8+3}{8}}{0.1125}$$

Least common multiple of 20 and 4 is 20. Convert \frac{63}{20} and \frac{9}{4} to fractions with denominator 20.

$$\frac{63}{20}+\frac{45}{20}+\frac{\frac{3\times 8+3}{8}}{0.1125}$$

Since \frac{63}{20} and \frac{45}{20} have the same denominator, add them by adding their numerators.

$$\frac{63+45}{20}+\frac{\frac{3\times 8+3}{8}}{0.1125}$$

Add 63 and 45 to get 108.

$$\frac{108}{20}+\frac{\frac{3\times 8+3}{8}}{0.1125}$$

Reduce the fraction \frac{108}{20} to lowest terms by extracting and canceling out 4.

$$\frac{27}{5}+\frac{\frac{3\times 8+3}{8}}{0.1125}$$

Express \frac{\frac{3\times 8+3}{8}}{0.1125} as a single fraction.

$$\frac{27}{5}+\frac{3\times 8+3}{8\times 0.1125}$$

Multiply 3 and 8 to get 24.

$$\frac{27}{5}+\frac{24+3}{8\times 0.1125}$$

Add 24 and 3 to get 27.

$$\frac{27}{5}+\frac{27}{8\times 0.1125}$$

Multiply 8 and 0.1125 to get 0.9.

$$\frac{27}{5}+\frac{27}{0.9}$$

Expand \frac{27}{0.9} by multiplying both numerator and the denominator by 10.

$$\frac{27}{5}+\frac{270}{9}$$

Divide 270 by 9 to get 30.

$$\frac{27}{5}+30$$

Convert 30 to fraction \frac{150}{5}.

$$\frac{27}{5}+\frac{150}{5}$$

Since \frac{27}{5} and \frac{150}{5} have the same denominator, add them by adding their numerators.

$$\frac{27+150}{5}$$

Add 27 and 150 to get 177.

$$\frac{177}{5}$$

Factor

$$\frac{3 \cdot 59}{5} = 35\frac{2}{5} = 35.4$$