Solve (10/frac{1{4}}+4-1/2/frac{1{4}})div(7div[5/3*frac{6}{5}))=

$$( \frac { 10 } { \frac { 1 } { 4 } } + 4 - \frac { \frac { 1 } { 2 } } { \frac { 1 } { 4 } } ) \div ( 7 \div [ \frac { 5 } { 3 } * \frac { 6 } { 5 } ) ) =$$

Evaluate

$$12$$

Solution Steps

Divide 10 by \frac{1}{4} by multiplying 10 by the reciprocal of \frac{1}{4}.

$$\frac{10\times 4+4-\frac{\frac{1}{2}}{\frac{1}{4}}}{\frac{7}{\frac{5}{3}\times \frac{6}{5}}}$$

Multiply 10 and 4 to get 40.

$$\frac{40+4-\frac{\frac{1}{2}}{\frac{1}{4}}}{\frac{7}{\frac{5}{3}\times \frac{6}{5}}}$$

Add 40 and 4 to get 44.

$$\frac{44-\frac{\frac{1}{2}}{\frac{1}{4}}}{\frac{7}{\frac{5}{3}\times \frac{6}{5}}}$$

Divide \frac{1}{2} by \frac{1}{4} by multiplying \frac{1}{2} by the reciprocal of \frac{1}{4}.

$$\frac{44-\frac{1}{2}\times 4}{\frac{7}{\frac{5}{3}\times \frac{6}{5}}}$$

Multiply \frac{1}{2} and 4 to get \frac{4}{2}.

$$\frac{44-\frac{4}{2}}{\frac{7}{\frac{5}{3}\times \frac{6}{5}}}$$

Divide 4 by 2 to get 2.

$$\frac{44-2}{\frac{7}{\frac{5}{3}\times \frac{6}{5}}}$$

Subtract 2 from 44 to get 42.

$$\frac{42}{\frac{7}{\frac{5}{3}\times \frac{6}{5}}}$$

Multiply \frac{5}{3} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{42}{\frac{7}{\frac{5\times 6}{3\times 5}}}$$

Cancel out 5 in both numerator and denominator.

$$\frac{42}{\frac{7}{\frac{6}{3}}}$$

Divide 6 by 3 to get 2.

$$\frac{42}{\frac{7}{2}}$$

Divide 42 by \frac{7}{2} by multiplying 42 by the reciprocal of \frac{7}{2}.

$$42\times \frac{2}{7}$$

Express 42\times \frac{2}{7} as a single fraction.

$$\frac{42\times 2}{7}$$

Multiply 42 and 2 to get 84.

$$\frac{84}{7}$$

Divide 84 by 7 to get 12.

$$12$$

Factor

$$2^{2}\times 3$$