Solve (5/1+1/3)-(1/4-3/1+frac{5}{4}-frac{3}{7})

$$( \frac{ 5 }{ 1 } + \frac{ 1 }{ 3 } )-( \frac{ 1 }{ 4 } - \frac{ 3 }{ 1 } + \frac{ 5 }{ 4 } - \frac{ 3 }{ 7 } )$$

Evaluate

$$\frac{305}{42}\approx 7.261904762$$

Solution Steps

Anything divided by one gives itself.

$$5+\frac{1}{3}-\left(\frac{1}{4}-\frac{3}{1}+\frac{5}{4}-\frac{3}{7}\right)$$

Convert 5 to fraction \frac{15}{3}.

$$\frac{15}{3}+\frac{1}{3}-\left(\frac{1}{4}-\frac{3}{1}+\frac{5}{4}-\frac{3}{7}\right)$$

Since \frac{15}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$\frac{15+1}{3}-\left(\frac{1}{4}-\frac{3}{1}+\frac{5}{4}-\frac{3}{7}\right)$$

Add 15 and 1 to get 16.

$$\frac{16}{3}-\left(\frac{1}{4}-\frac{3}{1}+\frac{5}{4}-\frac{3}{7}\right)$$

Anything divided by one gives itself.

$$\frac{16}{3}-\left(\frac{1}{4}-3+\frac{5}{4}-\frac{3}{7}\right)$$

Convert 3 to fraction \frac{12}{4}.

$$\frac{16}{3}-\left(\frac{1}{4}-\frac{12}{4}+\frac{5}{4}-\frac{3}{7}\right)$$

Since \frac{1}{4} and \frac{12}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16}{3}-\left(\frac{1-12}{4}+\frac{5}{4}-\frac{3}{7}\right)$$

Subtract 12 from 1 to get -11.

$$\frac{16}{3}-\left(-\frac{11}{4}+\frac{5}{4}-\frac{3}{7}\right)$$

Since -\frac{11}{4} and \frac{5}{4} have the same denominator, add them by adding their numerators.

$$\frac{16}{3}-\left(\frac{-11+5}{4}-\frac{3}{7}\right)$$

Add -11 and 5 to get -6.

$$\frac{16}{3}-\left(\frac{-6}{4}-\frac{3}{7}\right)$$

Reduce the fraction \frac{-6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{16}{3}-\left(-\frac{3}{2}-\frac{3}{7}\right)$$

Least common multiple of 2 and 7 is 14. Convert -\frac{3}{2} and \frac{3}{7} to fractions with denominator 14.

$$\frac{16}{3}-\left(-\frac{21}{14}-\frac{6}{14}\right)$$

Since -\frac{21}{14} and \frac{6}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16}{3}-\frac{-21-6}{14}$$

Subtract 6 from -21 to get -27.

$$\frac{16}{3}-\left(-\frac{27}{14}\right)$$

The opposite of -\frac{27}{14} is \frac{27}{14}.

$$\frac{16}{3}+\frac{27}{14}$$

Least common multiple of 3 and 14 is 42. Convert \frac{16}{3} and \frac{27}{14} to fractions with denominator 42.

$$\frac{224}{42}+\frac{81}{42}$$

Since \frac{224}{42} and \frac{81}{42} have the same denominator, add them by adding their numerators.

$$\frac{224+81}{42}$$

Add 224 and 81 to get 305.

$$\frac{305}{42}$$

Factor

$$\frac{5 \cdot 61}{2 \cdot 3 \cdot 7} = 7\frac{11}{42} = 7.261904761904762$$