Solve [61/2-(0.4+1/3)*1:5]+0.54

$$[ 6 \frac { 1 } { 2 } - ( 0.4 + \frac { 1 } { 3 } ) \times 1 : 5 ] + 0.54$$

Evaluate

$$\frac{517}{75}\approx 6.893333333$$

Solution Steps

Multiply 6 and 2 to get 12.

$$\frac{12+1}{2}-\frac{\left(0.4+\frac{1}{3}\right)\times 1}{5}+0.54$$

Add 12 and 1 to get 13.

$$\frac{13}{2}-\frac{\left(0.4+\frac{1}{3}\right)\times 1}{5}+0.54$$

Convert decimal number 0.4 to fraction \frac{4}{10}. Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$\frac{13}{2}-\frac{\left(\frac{2}{5}+\frac{1}{3}\right)\times 1}{5}+0.54$$

Least common multiple of 5 and 3 is 15. Convert \frac{2}{5} and \frac{1}{3} to fractions with denominator 15.

$$\frac{13}{2}-\frac{\left(\frac{6}{15}+\frac{5}{15}\right)\times 1}{5}+0.54$$

Since \frac{6}{15} and \frac{5}{15} have the same denominator, add them by adding their numerators.

$$\frac{13}{2}-\frac{\frac{6+5}{15}\times 1}{5}+0.54$$

Add 6 and 5 to get 11.

$$\frac{13}{2}-\frac{\frac{11}{15}\times 1}{5}+0.54$$

Multiply \frac{11}{15} and 1 to get \frac{11}{15}.

$$\frac{13}{2}-\frac{\frac{11}{15}}{5}+0.54$$

Express \frac{\frac{11}{15}}{5} as a single fraction.

$$\frac{13}{2}-\frac{11}{15\times 5}+0.54$$

Multiply 15 and 5 to get 75.

$$\frac{13}{2}-\frac{11}{75}+0.54$$

Least common multiple of 2 and 75 is 150. Convert \frac{13}{2} and \frac{11}{75} to fractions with denominator 150.

$$\frac{975}{150}-\frac{22}{150}+0.54$$

Since \frac{975}{150} and \frac{22}{150} have the same denominator, subtract them by subtracting their numerators.

$$\frac{975-22}{150}+0.54$$

Subtract 22 from 975 to get 953.

$$\frac{953}{150}+0.54$$

Convert decimal number 0.54 to fraction \frac{54}{100}. Reduce the fraction \frac{54}{100} to lowest terms by extracting and canceling out 2.

$$\frac{953}{150}+\frac{27}{50}$$

Least common multiple of 150 and 50 is 150. Convert \frac{953}{150} and \frac{27}{50} to fractions with denominator 150.

$$\frac{953}{150}+\frac{81}{150}$$

Since \frac{953}{150} and \frac{81}{150} have the same denominator, add them by adding their numerators.

$$\frac{953+81}{150}$$

Add 953 and 81 to get 1034.

$$\frac{1034}{150}$$

Reduce the fraction \frac{1034}{150} to lowest terms by extracting and canceling out 2.

$$\frac{517}{75}$$

Factor

$$\frac{11 \cdot 47}{3 \cdot 5 ^ {2}} = 6\frac{67}{75} = 6.8933333333333335$$