Solve 7-2/3*1-1/2/3+frac{5{2}*1-2/3}

$$\frac{ 7- \frac{ 2 }{ 3 } \times 1- \frac{ 1 }{ 2 } }{ 3+ \frac{ 5 }{ 2 } \times 1- \frac{ 2 }{ 3 } }$$

Evaluate

$$\frac{35}{29}\approx 1.206896552$$

Solution Steps

Multiply \frac{2}{3} and 1 to get \frac{2}{3}.

$$\frac{7-\frac{2}{3}-\frac{1}{2}}{3+\frac{5}{2}\times 1-\frac{2}{3}}$$

Convert 7 to fraction \frac{21}{3}.

$$\frac{\frac{21}{3}-\frac{2}{3}-\frac{1}{2}}{3+\frac{5}{2}\times 1-\frac{2}{3}}$$

Since \frac{21}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{21-2}{3}-\frac{1}{2}}{3+\frac{5}{2}\times 1-\frac{2}{3}}$$

Subtract 2 from 21 to get 19.

$$\frac{\frac{19}{3}-\frac{1}{2}}{3+\frac{5}{2}\times 1-\frac{2}{3}}$$

Least common multiple of 3 and 2 is 6. Convert \frac{19}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{\frac{38}{6}-\frac{3}{6}}{3+\frac{5}{2}\times 1-\frac{2}{3}}$$

Since \frac{38}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{38-3}{6}}{3+\frac{5}{2}\times 1-\frac{2}{3}}$$

Subtract 3 from 38 to get 35.

$$\frac{\frac{35}{6}}{3+\frac{5}{2}\times 1-\frac{2}{3}}$$

Multiply \frac{5}{2} and 1 to get \frac{5}{2}.

$$\frac{\frac{35}{6}}{3+\frac{5}{2}-\frac{2}{3}}$$

Convert 3 to fraction \frac{6}{2}.

$$\frac{\frac{35}{6}}{\frac{6}{2}+\frac{5}{2}-\frac{2}{3}}$$

Since \frac{6}{2} and \frac{5}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{35}{6}}{\frac{6+5}{2}-\frac{2}{3}}$$

Add 6 and 5 to get 11.

$$\frac{\frac{35}{6}}{\frac{11}{2}-\frac{2}{3}}$$

Least common multiple of 2 and 3 is 6. Convert \frac{11}{2} and \frac{2}{3} to fractions with denominator 6.

$$\frac{\frac{35}{6}}{\frac{33}{6}-\frac{4}{6}}$$

Since \frac{33}{6} and \frac{4}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{35}{6}}{\frac{33-4}{6}}$$

Subtract 4 from 33 to get 29.

$$\frac{\frac{35}{6}}{\frac{29}{6}}$$

Divide \frac{35}{6} by \frac{29}{6} by multiplying \frac{35}{6} by the reciprocal of \frac{29}{6}.

$$\frac{35}{6}\times \frac{6}{29}$$

Multiply \frac{35}{6} times \frac{6}{29} by multiplying numerator times numerator and denominator times denominator.

$$\frac{35\times 6}{6\times 29}$$

Cancel out 6 in both numerator and denominator.

$$\frac{35}{29}$$

Factor

$$\frac{5 \cdot 7}{29} = 1\frac{6}{29} = 1.206896551724138$$