Solve (0.25+1/3)*6/7+(15/6-0.5)div11/3

$$( 0.25 + \frac { 1 } { 3 } ) \times \frac { 6 } { 7 } + ( 1 \frac { 5 } { 6 } - 0.5 ) \div 1 \frac { 1 } { 3 }$$

Evaluate

$$1.5$$

Solution Steps

Convert decimal number 0.25 to fraction \frac{25}{100}. Reduce the fraction \frac{25}{100} to lowest terms by extracting and canceling out 25.

$$\left(\frac{1}{4}+\frac{1}{3}\right)\times \frac{6}{7}+\frac{\frac{1\times 6+5}{6}-0.5}{\frac{1\times 3+1}{3}}$$

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

$$\left(\frac{3}{12}+\frac{4}{12}\right)\times \frac{6}{7}+\frac{\frac{1\times 6+5}{6}-0.5}{\frac{1\times 3+1}{3}}$$

Since \frac{3}{12} and \frac{4}{12} have the same denominator, add them by adding their numerators.

$$\frac{3+4}{12}\times \frac{6}{7}+\frac{\frac{1\times 6+5}{6}-0.5}{\frac{1\times 3+1}{3}}$$

Add 3 and 4 to get 7.

$$\frac{7}{12}\times \frac{6}{7}+\frac{\frac{1\times 6+5}{6}-0.5}{\frac{1\times 3+1}{3}}$$

Multiply \frac{7}{12} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 6}{12\times 7}+\frac{\frac{1\times 6+5}{6}-0.5}{\frac{1\times 3+1}{3}}$$

Cancel out 7 in both numerator and denominator.

$$\frac{6}{12}+\frac{\frac{1\times 6+5}{6}-0.5}{\frac{1\times 3+1}{3}}$$

Reduce the fraction \frac{6}{12} to lowest terms by extracting and canceling out 6.

$$\frac{1}{2}+\frac{\frac{1\times 6+5}{6}-0.5}{\frac{1\times 3+1}{3}}$$

Multiply 1 and 6 to get 6.

$$\frac{1}{2}+\frac{\frac{6+5}{6}-0.5}{\frac{1\times 3+1}{3}}$$

Add 6 and 5 to get 11.

$$\frac{1}{2}+\frac{\frac{11}{6}-0.5}{\frac{1\times 3+1}{3}}$$

Convert decimal number 0.5 to fraction \frac{5}{10}. Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{1}{2}+\frac{\frac{11}{6}-\frac{1}{2}}{\frac{1\times 3+1}{3}}$$

Least common multiple of 6 and 2 is 6. Convert \frac{11}{6} and \frac{1}{2} to fractions with denominator 6.

$$\frac{1}{2}+\frac{\frac{11}{6}-\frac{3}{6}}{\frac{1\times 3+1}{3}}$$

Since \frac{11}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}+\frac{\frac{11-3}{6}}{\frac{1\times 3+1}{3}}$$

Subtract 3 from 11 to get 8.

$$\frac{1}{2}+\frac{\frac{8}{6}}{\frac{1\times 3+1}{3}}$$

Reduce the fraction \frac{8}{6} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}+\frac{\frac{4}{3}}{\frac{1\times 3+1}{3}}$$

Multiply 1 and 3 to get 3.

$$\frac{1}{2}+\frac{\frac{4}{3}}{\frac{3+1}{3}}$$

Add 3 and 1 to get 4.

$$\frac{1}{2}+\frac{\frac{4}{3}}{\frac{4}{3}}$$

Divide \frac{4}{3} by \frac{4}{3} to get 1.

$$\frac{1}{2}+1$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{1}{2}+\frac{2}{2}$$

Since \frac{1}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

$$\frac{1+2}{2}$$

Add 1 and 2 to get 3.

$$\frac{3}{2}$$

Factor

$$\frac{3}{2} = 1\frac{1}{2} = 1.5$$