Solve 0.4+31/2-11/2+0.3-11/5+1/6-1frac{1}{2}+2frac{1}{4}

$$0.4 + 3 \frac { 1 } { 2 } - 1 \frac { 1 } { 2 } + 0.3 - 1 \frac { 1 } { 5 } + \frac { 1 } { 6 } - 1 \frac { 1 } { 2 } + 2 \frac { 1 } { 4 }$$

Evaluate

$$\frac{29}{12}\approx 2.416666667$$

Solution Steps

Multiply 3 and 2 to get 6.

$$0.4+\frac{6+1}{2}-\frac{1\times 2+1}{2}+0.3-\frac{1\times 5+1}{5}+\frac{1}{6}-\frac{1\times 2+1}{2}+\frac{2\times 4+1}{4}$$

Add 6 and 1 to get 7.

$$0.4+\frac{7}{2}-\frac{1\times 2+1}{2}+0.3-\frac{1\times 5+1}{5}+\frac{1}{6}-\frac{1\times 2+1}{2}+\frac{2\times 4+1}{4}$$

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.

$$\frac{2}{5}+\frac{7}{2}-\frac{1\times 2+1}{2}+0.3-\frac{1\times 5+1}{5}+\frac{1}{6}-\frac{1\times 2+1}{2}+\frac{2\times 4+1}{4}$$

Least common multiple of 5 and 2 is 10. Convert \frac{2}{5} and \frac{7}{2} to fractions with denominator 10.

$$\frac{4}{10}+\frac{35}{10}-\frac{1\times 2+1}{2}+0.3-\frac{1\times 5+1}{5}+\frac{1}{6}-\frac{1\times 2+1}{2}+\frac{2\times 4+1}{4}$$

Since \frac{4}{10} and \frac{35}{10} have the same denominator, add them by adding their numerators.

$$\frac{4+35}{10}-\frac{1\times 2+1}{2}+0.3-\frac{1\times 5+1}{5}+\frac{1}{6}-\frac{1\times 2+1}{2}+\frac{2\times 4+1}{4}$$

Add 4 and 35 to get 39.

$$\frac{39}{10}-\frac{1\times 2+1}{2}+0.3-\frac{1\times 5+1}{5}+\frac{1}{6}-\frac{1\times 2+1}{2}+\frac{2\times 4+1}{4}$$

Multiply 1 and 2 to get 2.

$$\frac{39}{10}-\frac{2+1}{2}+0.3-\frac{1\times 5+1}{5}+\frac{1}{6}-\frac{1\times 2+1}{2}+\frac{2\times 4+1}{4}$$

Add 2 and 1 to get 3.

$$\frac{39}{10}-\frac{3}{2}+0.3-\frac{1\times 5+1}{5}+\frac{1}{6}-\frac{1\times 2+1}{2}+\frac{2\times 4+1}{4}$$

Least common multiple of 10 and 2 is 10. Convert \frac{39}{10} and \frac{3}{2} to fractions with denominator 10.

$$\frac{39}{10}-\frac{15}{10}+0.3-\frac{1\times 5+1}{5}+\frac{1}{6}-\frac{1\times 2+1}{2}+\frac{2\times 4+1}{4}$$

Since \frac{39}{10} and \frac{15}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{39-15}{10}+0.3-\frac{1\times 5+1}{5}+\frac{1}{6}-\frac{1\times 2+1}{2}+\frac{2\times 4+1}{4}$$

Subtract 15 from 39 to get 24.

$$\frac{24}{10}+0.3-\frac{1\times 5+1}{5}+\frac{1}{6}-\frac{1\times 2+1}{2}+\frac{2\times 4+1}{4}$$

Reduce the fraction \frac{24}{10} to lowest terms by extracting and canceling out 2.

$$\frac{12}{5}+0.3-\frac{1\times 5+1}{5}+\frac{1}{6}-\frac{1\times 2+1}{2}+\frac{2\times 4+1}{4}$$

Convert decimal number 0.3 to fraction \frac{3}{10}.

$$\frac{12}{5}+\frac{3}{10}-\frac{1\times 5+1}{5}+\frac{1}{6}-\frac{1\times 2+1}{2}+\frac{2\times 4+1}{4}$$

Least common multiple of 5 and 10 is 10. Convert \frac{12}{5} and \frac{3}{10} to fractions with denominator 10.

$$\frac{24}{10}+\frac{3}{10}-\frac{1\times 5+1}{5}+\frac{1}{6}-\frac{1\times 2+1}{2}+\frac{2\times 4+1}{4}$$

Since \frac{24}{10} and \frac{3}{10} have the same denominator, add them by adding their numerators.

$$\frac{24+3}{10}-\frac{1\times 5+1}{5}+\frac{1}{6}-\frac{1\times 2+1}{2}+\frac{2\times 4+1}{4}$$

Add 24 and 3 to get 27.

$$\frac{27}{10}-\frac{1\times 5+1}{5}+\frac{1}{6}-\frac{1\times 2+1}{2}+\frac{2\times 4+1}{4}$$

Multiply 1 and 5 to get 5.

$$\frac{27}{10}-\frac{5+1}{5}+\frac{1}{6}-\frac{1\times 2+1}{2}+\frac{2\times 4+1}{4}$$

Add 5 and 1 to get 6.

$$\frac{27}{10}-\frac{6}{5}+\frac{1}{6}-\frac{1\times 2+1}{2}+\frac{2\times 4+1}{4}$$

Least common multiple of 10 and 5 is 10. Convert \frac{27}{10} and \frac{6}{5} to fractions with denominator 10.

$$\frac{27}{10}-\frac{12}{10}+\frac{1}{6}-\frac{1\times 2+1}{2}+\frac{2\times 4+1}{4}$$

Since \frac{27}{10} and \frac{12}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27-12}{10}+\frac{1}{6}-\frac{1\times 2+1}{2}+\frac{2\times 4+1}{4}$$

Subtract 12 from 27 to get 15.

$$\frac{15}{10}+\frac{1}{6}-\frac{1\times 2+1}{2}+\frac{2\times 4+1}{4}$$

Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$\frac{3}{2}+\frac{1}{6}-\frac{1\times 2+1}{2}+\frac{2\times 4+1}{4}$$

Least common multiple of 2 and 6 is 6. Convert \frac{3}{2} and \frac{1}{6} to fractions with denominator 6.

$$\frac{9}{6}+\frac{1}{6}-\frac{1\times 2+1}{2}+\frac{2\times 4+1}{4}$$

Since \frac{9}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{9+1}{6}-\frac{1\times 2+1}{2}+\frac{2\times 4+1}{4}$$

Add 9 and 1 to get 10.

$$\frac{10}{6}-\frac{1\times 2+1}{2}+\frac{2\times 4+1}{4}$$

Reduce the fraction \frac{10}{6} to lowest terms by extracting and canceling out 2.

$$\frac{5}{3}-\frac{1\times 2+1}{2}+\frac{2\times 4+1}{4}$$

Multiply 1 and 2 to get 2.

$$\frac{5}{3}-\frac{2+1}{2}+\frac{2\times 4+1}{4}$$

Add 2 and 1 to get 3.

$$\frac{5}{3}-\frac{3}{2}+\frac{2\times 4+1}{4}$$

Least common multiple of 3 and 2 is 6. Convert \frac{5}{3} and \frac{3}{2} to fractions with denominator 6.

$$\frac{10}{6}-\frac{9}{6}+\frac{2\times 4+1}{4}$$

Since \frac{10}{6} and \frac{9}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10-9}{6}+\frac{2\times 4+1}{4}$$

Subtract 9 from 10 to get 1.

$$\frac{1}{6}+\frac{2\times 4+1}{4}$$

Multiply 2 and 4 to get 8.

$$\frac{1}{6}+\frac{8+1}{4}$$

Add 8 and 1 to get 9.

$$\frac{1}{6}+\frac{9}{4}$$

Least common multiple of 6 and 4 is 12. Convert \frac{1}{6} and \frac{9}{4} to fractions with denominator 12.

$$\frac{2}{12}+\frac{27}{12}$$

Since \frac{2}{12} and \frac{27}{12} have the same denominator, add them by adding their numerators.

$$\frac{2+27}{12}$$

Add 2 and 27 to get 29.

$$\frac{29}{12}$$

Factor

$$\frac{29}{3 \cdot 2 ^ {2}} = 2\frac{5}{12} = 2.4166666666666665$$