Solve (12/25-0.28)*5/13+1div(0.75+1/3)

$$( 1 \frac { 2 } { 25 } - 0.28 ) \times \frac { 5 } { 13 } + 1 \div ( 0.75 + \frac { 1 } { 3 } )$$

Evaluate

$$\frac{16}{13}\approx 1.230769231$$

Solution Steps

Multiply 1 and 25 to get 25.

$$\left(\frac{25+2}{25}-0.28\right)\times \frac{5}{13}+\frac{1}{0.75+\frac{1}{3}}$$

Add 25 and 2 to get 27.

$$\left(\frac{27}{25}-0.28\right)\times \frac{5}{13}+\frac{1}{0.75+\frac{1}{3}}$$

Convert decimal number 0.28 to fraction \frac{28}{100}. Reduce the fraction \frac{28}{100} to lowest terms by extracting and canceling out 4.

$$\left(\frac{27}{25}-\frac{7}{25}\right)\times \frac{5}{13}+\frac{1}{0.75+\frac{1}{3}}$$

Since \frac{27}{25} and \frac{7}{25} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27-7}{25}\times \frac{5}{13}+\frac{1}{0.75+\frac{1}{3}}$$

Subtract 7 from 27 to get 20.

$$\frac{20}{25}\times \frac{5}{13}+\frac{1}{0.75+\frac{1}{3}}$$

Reduce the fraction \frac{20}{25} to lowest terms by extracting and canceling out 5.

$$\frac{4}{5}\times \frac{5}{13}+\frac{1}{0.75+\frac{1}{3}}$$

Multiply \frac{4}{5} times \frac{5}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 5}{5\times 13}+\frac{1}{0.75+\frac{1}{3}}$$

Cancel out 5 in both numerator and denominator.

$$\frac{4}{13}+\frac{1}{0.75+\frac{1}{3}}$$

Convert decimal number 0.75 to fraction \frac{75}{100}. Reduce the fraction \frac{75}{100} to lowest terms by extracting and canceling out 25.

$$\frac{4}{13}+\frac{1}{\frac{3}{4}+\frac{1}{3}}$$

Least common multiple of 4 and 3 is 12. Convert \frac{3}{4} and \frac{1}{3} to fractions with denominator 12.

$$\frac{4}{13}+\frac{1}{\frac{9}{12}+\frac{4}{12}}$$

Since \frac{9}{12} and \frac{4}{12} have the same denominator, add them by adding their numerators.

$$\frac{4}{13}+\frac{1}{\frac{9+4}{12}}$$

Add 9 and 4 to get 13.

$$\frac{4}{13}+\frac{1}{\frac{13}{12}}$$

Divide 1 by \frac{13}{12} by multiplying 1 by the reciprocal of \frac{13}{12}.

$$\frac{4}{13}+1\times \frac{12}{13}$$

Multiply 1 and \frac{12}{13} to get \frac{12}{13}.

$$\frac{4}{13}+\frac{12}{13}$$

Since \frac{4}{13} and \frac{12}{13} have the same denominator, add them by adding their numerators.

$$\frac{4+12}{13}$$

Add 4 and 12 to get 16.

$$\frac{16}{13}$$

Factor

$$\frac{2 ^ {4}}{13} = 1\frac{3}{13} = 1.2307692307692308$$