Solve 14/7div7/1+15/4*2/9-frac{5}{4}=

$$\frac { 14 } { 7 } \div \frac { 7 } { 1 } + \frac { 15 } { 4 } \cdot \frac { 2 } { 9 } - \frac { 5 } { 4 } =$$

Evaluate

$$-\frac{11}{84}\approx -0.130952381$$

Solution Steps

Divide \frac{14}{7} by \frac{7}{1} by multiplying \frac{14}{7} by the reciprocal of \frac{7}{1}.

$$\frac{14}{7\times 7}+\frac{15}{4}\times \frac{2}{9}-\frac{5}{4}$$

Multiply 7 and 7 to get 49.

$$\frac{14}{49}+\frac{15}{4}\times \frac{2}{9}-\frac{5}{4}$$

Reduce the fraction \frac{14}{49} to lowest terms by extracting and canceling out 7.

$$\frac{2}{7}+\frac{15}{4}\times \frac{2}{9}-\frac{5}{4}$$

Multiply \frac{15}{4} times \frac{2}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{7}+\frac{15\times 2}{4\times 9}-\frac{5}{4}$$

Do the multiplications in the fraction \frac{15\times 2}{4\times 9}.

$$\frac{2}{7}+\frac{30}{36}-\frac{5}{4}$$

Reduce the fraction \frac{30}{36} to lowest terms by extracting and canceling out 6.

$$\frac{2}{7}+\frac{5}{6}-\frac{5}{4}$$

Least common multiple of 7 and 6 is 42. Convert \frac{2}{7} and \frac{5}{6} to fractions with denominator 42.

$$\frac{12}{42}+\frac{35}{42}-\frac{5}{4}$$

Since \frac{12}{42} and \frac{35}{42} have the same denominator, add them by adding their numerators.

$$\frac{12+35}{42}-\frac{5}{4}$$

Add 12 and 35 to get 47.

$$\frac{47}{42}-\frac{5}{4}$$

Least common multiple of 42 and 4 is 84. Convert \frac{47}{42} and \frac{5}{4} to fractions with denominator 84.

$$\frac{94}{84}-\frac{105}{84}$$

Since \frac{94}{84} and \frac{105}{84} have the same denominator, subtract them by subtracting their numerators.

$$\frac{94-105}{84}$$

Subtract 105 from 94 to get -11.

$$-\frac{11}{84}$$

Factor

$$-\frac{11}{84} = -0.13095238095238096$$