Solve 24/13(3/8-4/15)-11:51/2

$$2 \frac { 4 } { 13 } ( \frac { 3 } { 8 } - \frac { 4 } { 15 } ) - 11 : 5 \frac { 1 } { 2 }$$

Evaluate

$$-\frac{7}{4}=-1.75$$

Solution Steps

Multiply 2 and 13 to get 26.

$$\frac{26+4}{13}\left(\frac{3}{8}-\frac{4}{15}\right)-\frac{11}{\frac{5\times 2+1}{2}}$$

Add 26 and 4 to get 30.

$$\frac{30}{13}\left(\frac{3}{8}-\frac{4}{15}\right)-\frac{11}{\frac{5\times 2+1}{2}}$$

Least common multiple of 8 and 15 is 120. Convert \frac{3}{8} and \frac{4}{15} to fractions with denominator 120.

$$\frac{30}{13}\left(\frac{45}{120}-\frac{32}{120}\right)-\frac{11}{\frac{5\times 2+1}{2}}$$

Since \frac{45}{120} and \frac{32}{120} have the same denominator, subtract them by subtracting their numerators.

$$\frac{30}{13}\times \frac{45-32}{120}-\frac{11}{\frac{5\times 2+1}{2}}$$

Subtract 32 from 45 to get 13.

$$\frac{30}{13}\times \frac{13}{120}-\frac{11}{\frac{5\times 2+1}{2}}$$

Multiply \frac{30}{13} times \frac{13}{120} by multiplying numerator times numerator and denominator times denominator.

$$\frac{30\times 13}{13\times 120}-\frac{11}{\frac{5\times 2+1}{2}}$$

Cancel out 13 in both numerator and denominator.

$$\frac{30}{120}-\frac{11}{\frac{5\times 2+1}{2}}$$

Reduce the fraction \frac{30}{120} to lowest terms by extracting and canceling out 30.

$$\frac{1}{4}-\frac{11}{\frac{5\times 2+1}{2}}$$

Divide 11 by \frac{5\times 2+1}{2} by multiplying 11 by the reciprocal of \frac{5\times 2+1}{2}.

$$\frac{1}{4}-\frac{11\times 2}{5\times 2+1}$$

Multiply 11 and 2 to get 22.

$$\frac{1}{4}-\frac{22}{5\times 2+1}$$

Multiply 5 and 2 to get 10.

$$\frac{1}{4}-\frac{22}{10+1}$$

Add 10 and 1 to get 11.

$$\frac{1}{4}-\frac{22}{11}$$

Divide 22 by 11 to get 2.

$$\frac{1}{4}-2$$

Convert 2 to fraction \frac{8}{4}.

$$\frac{1}{4}-\frac{8}{4}$$

Since \frac{1}{4} and \frac{8}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-8}{4}$$

Subtract 8 from 1 to get -7.

$$-\frac{7}{4}$$

Factor

$$-\frac{7}{4} = -1\frac{3}{4} = -1.75$$