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

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

Evaluate

$$\frac{14}{3}\approx 4.666666667$$

Solution Steps

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

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

Since \frac{2}{2} and \frac{5}{2} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 5 from 2 to get -3.

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

Anything divided by one gives itself.

$$\frac{7}{-\frac{3}{2}+3}$$

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

$$\frac{7}{-\frac{3}{2}+\frac{6}{2}}$$

Since -\frac{3}{2} and \frac{6}{2} have the same denominator, add them by adding their numerators.

$$\frac{7}{\frac{-3+6}{2}}$$

Add -3 and 6 to get 3.

$$\frac{7}{\frac{3}{2}}$$

Divide 7 by \frac{3}{2} by multiplying 7 by the reciprocal of \frac{3}{2}.

$$7\times \frac{2}{3}$$

Express 7\times \frac{2}{3} as a single fraction.

$$\frac{7\times 2}{3}$$

Multiply 7 and 2 to get 14.

$$\frac{14}{3}$$

Factor

$$\frac{2 \cdot 7}{3} = 4\frac{2}{3} = 4.666666666666667$$