Solve 113/14-(7-611/35)div9/27+4/21

$$1 \frac { 13 } { 14 } -(7- 6 \frac { 11 } { 35 } ) \div \frac { 9 } { 27 } + \frac{ 4 }{ 21 }$$

Evaluate

$$\frac{13}{210}\approx 0.061904762$$

Solution Steps

Multiply 1 and 14 to get 14.

$$\frac{14+13}{14}-\frac{7-\frac{6\times 35+11}{35}}{\frac{9}{27}}+\frac{4}{21}$$

Add 14 and 13 to get 27.

$$\frac{27}{14}-\frac{7-\frac{6\times 35+11}{35}}{\frac{9}{27}}+\frac{4}{21}$$

Multiply 6 and 35 to get 210.

$$\frac{27}{14}-\frac{7-\frac{210+11}{35}}{\frac{9}{27}}+\frac{4}{21}$$

Add 210 and 11 to get 221.

$$\frac{27}{14}-\frac{7-\frac{221}{35}}{\frac{9}{27}}+\frac{4}{21}$$

Convert 7 to fraction \frac{245}{35}.

$$\frac{27}{14}-\frac{\frac{245}{35}-\frac{221}{35}}{\frac{9}{27}}+\frac{4}{21}$$

Since \frac{245}{35} and \frac{221}{35} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27}{14}-\frac{\frac{245-221}{35}}{\frac{9}{27}}+\frac{4}{21}$$

Subtract 221 from 245 to get 24.

$$\frac{27}{14}-\frac{\frac{24}{35}}{\frac{9}{27}}+\frac{4}{21}$$

Reduce the fraction \frac{9}{27} to lowest terms by extracting and canceling out 9.

$$\frac{27}{14}-\frac{\frac{24}{35}}{\frac{1}{3}}+\frac{4}{21}$$

Divide \frac{24}{35} by \frac{1}{3} by multiplying \frac{24}{35} by the reciprocal of \frac{1}{3}.

$$\frac{27}{14}-\frac{24}{35}\times 3+\frac{4}{21}$$

Express \frac{24}{35}\times 3 as a single fraction.

$$\frac{27}{14}-\frac{24\times 3}{35}+\frac{4}{21}$$

Multiply 24 and 3 to get 72.

$$\frac{27}{14}-\frac{72}{35}+\frac{4}{21}$$

Least common multiple of 14 and 35 is 70. Convert \frac{27}{14} and \frac{72}{35} to fractions with denominator 70.

$$\frac{135}{70}-\frac{144}{70}+\frac{4}{21}$$

Since \frac{135}{70} and \frac{144}{70} have the same denominator, subtract them by subtracting their numerators.

$$\frac{135-144}{70}+\frac{4}{21}$$

Subtract 144 from 135 to get -9.

$$-\frac{9}{70}+\frac{4}{21}$$

Least common multiple of 70 and 21 is 210. Convert -\frac{9}{70} and \frac{4}{21} to fractions with denominator 210.

$$-\frac{27}{210}+\frac{40}{210}$$

Since -\frac{27}{210} and \frac{40}{210} have the same denominator, add them by adding their numerators.

$$\frac{-27+40}{210}$$

Add -27 and 40 to get 13.

$$\frac{13}{210}$$

Factor

$$\frac{13}{2 \cdot 3 \cdot 5 \cdot 7} = 0.06190476190476191$$