Solve 5/8:15+7:14/5-1/26:1/52=

$$\frac { 5 } { 8 } : 15 + 7 : \frac { 14 } { 5 } - \frac { 1 } { 26 } : \frac { 1 } { 52 } =$$

Evaluate

$$\frac{13}{24}\approx 0.541666667$$

Solution Steps

Express \frac{\frac{5}{8}}{15} as a single fraction.

$$\frac{5}{8\times 15}+\frac{7}{\frac{14}{5}}-\frac{\frac{1}{26}}{\frac{1}{52}}$$

Multiply 8 and 15 to get 120.

$$\frac{5}{120}+\frac{7}{\frac{14}{5}}-\frac{\frac{1}{26}}{\frac{1}{52}}$$

Reduce the fraction \frac{5}{120} to lowest terms by extracting and canceling out 5.

$$\frac{1}{24}+\frac{7}{\frac{14}{5}}-\frac{\frac{1}{26}}{\frac{1}{52}}$$

Divide 7 by \frac{14}{5} by multiplying 7 by the reciprocal of \frac{14}{5}.

$$\frac{1}{24}+7\times \frac{5}{14}-\frac{\frac{1}{26}}{\frac{1}{52}}$$

Express 7\times \frac{5}{14} as a single fraction.

$$\frac{1}{24}+\frac{7\times 5}{14}-\frac{\frac{1}{26}}{\frac{1}{52}}$$

Multiply 7 and 5 to get 35.

$$\frac{1}{24}+\frac{35}{14}-\frac{\frac{1}{26}}{\frac{1}{52}}$$

Reduce the fraction \frac{35}{14} to lowest terms by extracting and canceling out 7.

$$\frac{1}{24}+\frac{5}{2}-\frac{\frac{1}{26}}{\frac{1}{52}}$$

Least common multiple of 24 and 2 is 24. Convert \frac{1}{24} and \frac{5}{2} to fractions with denominator 24.

$$\frac{1}{24}+\frac{60}{24}-\frac{\frac{1}{26}}{\frac{1}{52}}$$

Since \frac{1}{24} and \frac{60}{24} have the same denominator, add them by adding their numerators.

$$\frac{1+60}{24}-\frac{\frac{1}{26}}{\frac{1}{52}}$$

Add 1 and 60 to get 61.

$$\frac{61}{24}-\frac{\frac{1}{26}}{\frac{1}{52}}$$

Divide \frac{1}{26} by \frac{1}{52} by multiplying \frac{1}{26} by the reciprocal of \frac{1}{52}.

$$\frac{61}{24}-\frac{1}{26}\times 52$$

Multiply \frac{1}{26} and 52 to get \frac{52}{26}.

$$\frac{61}{24}-\frac{52}{26}$$

Divide 52 by 26 to get 2.

$$\frac{61}{24}-2$$

Convert 2 to fraction \frac{48}{24}.

$$\frac{61}{24}-\frac{48}{24}$$

Since \frac{61}{24} and \frac{48}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{61-48}{24}$$

Subtract 48 from 61 to get 13.

$$\frac{13}{24}$$

Factor

$$\frac{13}{2 ^ {3} \cdot 3} = 0.5416666666666666$$