Solve 5/4*2/3div1/5+2/5divfrac{1}{10}*frac{3}{4}+frac{1}{2}*frac{4}{3}=frac{1}{6}

$$\frac { 5 } { 4 } \times \frac { 2 } { 3 } \div \frac { 1 } { 5 } + \frac { 2 } { 5 } \div \frac { 1 } { 10 } \times \frac { 3 } { 4 } + \frac { 1 } { 2 } \times \frac { 4 } { 3 } = \frac { 1 } { 6 }$$

Verify

Solution Steps

Multiply \frac{5}{4} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{5\times 2}{4\times 3}.

$$\frac{\frac{10}{12}}{\frac{1}{5}}+\frac{\frac{2}{5}}{\frac{1}{10}}\times \frac{3}{4}+\frac{1}{2}\times \frac{4}{3}=\frac{1}{6}$$

Reduce the fraction \frac{10}{12} to lowest terms by extracting and canceling out 2.

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

Divide \frac{5}{6} by \frac{1}{5} by multiplying \frac{5}{6} by the reciprocal of \frac{1}{5}.

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

Express \frac{5}{6}\times 5 as a single fraction.

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

Multiply 5 and 5 to get 25.

$$\frac{25}{6}+\frac{\frac{2}{5}}{\frac{1}{10}}\times \frac{3}{4}+\frac{1}{2}\times \frac{4}{3}=\frac{1}{6}$$

Divide \frac{2}{5} by \frac{1}{10} by multiplying \frac{2}{5} by the reciprocal of \frac{1}{10}.

$$\frac{25}{6}+\frac{2}{5}\times 10\times \frac{3}{4}+\frac{1}{2}\times \frac{4}{3}=\frac{1}{6}$$

Express \frac{2}{5}\times 10 as a single fraction.

$$\frac{25}{6}+\frac{2\times 10}{5}\times \frac{3}{4}+\frac{1}{2}\times \frac{4}{3}=\frac{1}{6}$$

Multiply 2 and 10 to get 20.

$$\frac{25}{6}+\frac{20}{5}\times \frac{3}{4}+\frac{1}{2}\times \frac{4}{3}=\frac{1}{6}$$

Divide 20 by 5 to get 4.

$$\frac{25}{6}+4\times \frac{3}{4}+\frac{1}{2}\times \frac{4}{3}=\frac{1}{6}$$

Cancel out 4 and 4.

$$\frac{25}{6}+3+\frac{1}{2}\times \frac{4}{3}=\frac{1}{6}$$

Convert 3 to fraction \frac{18}{6}.

$$\frac{25}{6}+\frac{18}{6}+\frac{1}{2}\times \frac{4}{3}=\frac{1}{6}$$

Since \frac{25}{6} and \frac{18}{6} have the same denominator, add them by adding their numerators.

$$\frac{25+18}{6}+\frac{1}{2}\times \frac{4}{3}=\frac{1}{6}$$

Add 25 and 18 to get 43.

$$\frac{43}{6}+\frac{1}{2}\times \frac{4}{3}=\frac{1}{6}$$

Multiply \frac{1}{2} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{43}{6}+\frac{1\times 4}{2\times 3}=\frac{1}{6}$$

Do the multiplications in the fraction \frac{1\times 4}{2\times 3}.

$$\frac{43}{6}+\frac{4}{6}=\frac{1}{6}$$

Since \frac{43}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\frac{43+4}{6}=\frac{1}{6}$$

Add 43 and 4 to get 47.

$$\frac{47}{6}=\frac{1}{6}$$

Compare \frac{47}{6} and \frac{1}{6}.

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