Solve 1313/14div13+0.4-1/3

$$13 \frac { 13 } { 14 } \div 13 + 0.4 - \frac { 1 } { 3 }$$

Evaluate

$$\frac{239}{210}\approx 1.138095238$$

Solution Steps

Express \frac{\frac{13\times 14+13}{14}}{13} as a single fraction.

$$\frac{13\times 14+13}{14\times 13}+0.4-\frac{1}{3}$$

Multiply 13 and 14 to get 182.

$$\frac{182+13}{14\times 13}+0.4-\frac{1}{3}$$

Add 182 and 13 to get 195.

$$\frac{195}{14\times 13}+0.4-\frac{1}{3}$$

Multiply 14 and 13 to get 182.

$$\frac{195}{182}+0.4-\frac{1}{3}$$

Reduce the fraction \frac{195}{182} to lowest terms by extracting and canceling out 13.

$$\frac{15}{14}+0.4-\frac{1}{3}$$

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.

$$\frac{15}{14}+\frac{2}{5}-\frac{1}{3}$$

Least common multiple of 14 and 5 is 70. Convert \frac{15}{14} and \frac{2}{5} to fractions with denominator 70.

$$\frac{75}{70}+\frac{28}{70}-\frac{1}{3}$$

Since \frac{75}{70} and \frac{28}{70} have the same denominator, add them by adding their numerators.

$$\frac{75+28}{70}-\frac{1}{3}$$

Add 75 and 28 to get 103.

$$\frac{103}{70}-\frac{1}{3}$$

Least common multiple of 70 and 3 is 210. Convert \frac{103}{70} and \frac{1}{3} to fractions with denominator 210.

$$\frac{309}{210}-\frac{70}{210}$$

Since \frac{309}{210} and \frac{70}{210} have the same denominator, subtract them by subtracting their numerators.

$$\frac{309-70}{210}$$

Subtract 70 from 309 to get 239.

$$\frac{239}{210}$$

Factor

$$\frac{239}{2 \cdot 3 \cdot 5 \cdot 7} = 1\frac{29}{210} = 1.138095238095238$$