Solve 7/4div5/3-(1/4+2/3)

$$\frac{ 7 }{ 4 } \div \frac { 5 } { 3 } -( \frac{ 1 }{ 4 } + \frac{ 2 }{ 3 } )$$

Evaluate

$$\frac{2}{15}\approx 0.133333333$$

Solution Steps

Divide \frac{7}{4} by \frac{5}{3} by multiplying \frac{7}{4} by the reciprocal of \frac{5}{3}.

$$\frac{7}{4}\times \frac{3}{5}-\left(\frac{1}{4}+\frac{2}{3}\right)$$

Multiply \frac{7}{4} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 3}{4\times 5}-\left(\frac{1}{4}+\frac{2}{3}\right)$$

Do the multiplications in the fraction \frac{7\times 3}{4\times 5}.

$$\frac{21}{20}-\left(\frac{1}{4}+\frac{2}{3}\right)$$

Least common multiple of 4 and 3 is 12. Convert \frac{1}{4} and \frac{2}{3} to fractions with denominator 12.

$$\frac{21}{20}-\left(\frac{3}{12}+\frac{8}{12}\right)$$

Since \frac{3}{12} and \frac{8}{12} have the same denominator, add them by adding their numerators.

$$\frac{21}{20}-\frac{3+8}{12}$$

Add 3 and 8 to get 11.

$$\frac{21}{20}-\frac{11}{12}$$

Least common multiple of 20 and 12 is 60. Convert \frac{21}{20} and \frac{11}{12} to fractions with denominator 60.

$$\frac{63}{60}-\frac{55}{60}$$

Since \frac{63}{60} and \frac{55}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{63-55}{60}$$

Subtract 55 from 63 to get 8.

$$\frac{8}{60}$$

Reduce the fraction \frac{8}{60} to lowest terms by extracting and canceling out 4.

$$\frac{2}{15}$$

Factor

$$\frac{2}{3 \cdot 5} = 0.13333333333333333$$