Solve (2/7*12/3+1/7*2/3)div(frac{2}{3}*2frac{1}{4}+frac{2}{3}*frac{3}{4})

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

Evaluate

$$\frac{2}{7}\approx 0.285714286$$

Solution Steps

Multiply 1 and 3 to get 3.

$$\frac{\frac{2}{7}\times \frac{3+2}{3}+\frac{1}{7}\times \frac{2}{3}}{\frac{2}{3}\times \frac{2\times 4+1}{4}+\frac{2}{3}\times \frac{3}{4}}$$

Add 3 and 2 to get 5.

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

Multiply \frac{2}{7} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{2\times 5}{7\times 3}.

$$\frac{\frac{10}{21}+\frac{1}{7}\times \frac{2}{3}}{\frac{2}{3}\times \frac{2\times 4+1}{4}+\frac{2}{3}\times \frac{3}{4}}$$

Multiply \frac{1}{7} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{10}{21}+\frac{1\times 2}{7\times 3}}{\frac{2}{3}\times \frac{2\times 4+1}{4}+\frac{2}{3}\times \frac{3}{4}}$$

Do the multiplications in the fraction \frac{1\times 2}{7\times 3}.

$$\frac{\frac{10}{21}+\frac{2}{21}}{\frac{2}{3}\times \frac{2\times 4+1}{4}+\frac{2}{3}\times \frac{3}{4}}$$

Since \frac{10}{21} and \frac{2}{21} have the same denominator, add them by adding their numerators.

$$\frac{\frac{10+2}{21}}{\frac{2}{3}\times \frac{2\times 4+1}{4}+\frac{2}{3}\times \frac{3}{4}}$$

Add 10 and 2 to get 12.

$$\frac{\frac{12}{21}}{\frac{2}{3}\times \frac{2\times 4+1}{4}+\frac{2}{3}\times \frac{3}{4}}$$

Reduce the fraction \frac{12}{21} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{4}{7}}{\frac{2}{3}\times \frac{2\times 4+1}{4}+\frac{2}{3}\times \frac{3}{4}}$$

Multiply 2 and 4 to get 8.

$$\frac{\frac{4}{7}}{\frac{2}{3}\times \frac{8+1}{4}+\frac{2}{3}\times \frac{3}{4}}$$

Add 8 and 1 to get 9.

$$\frac{\frac{4}{7}}{\frac{2}{3}\times \frac{9}{4}+\frac{2}{3}\times \frac{3}{4}}$$

Multiply \frac{2}{3} times \frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{4}{7}}{\frac{2\times 9}{3\times 4}+\frac{2}{3}\times \frac{3}{4}}$$

Do the multiplications in the fraction \frac{2\times 9}{3\times 4}.

$$\frac{\frac{4}{7}}{\frac{18}{12}+\frac{2}{3}\times \frac{3}{4}}$$

Reduce the fraction \frac{18}{12} to lowest terms by extracting and canceling out 6.

$$\frac{\frac{4}{7}}{\frac{3}{2}+\frac{2}{3}\times \frac{3}{4}}$$

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

$$\frac{\frac{4}{7}}{\frac{3}{2}+\frac{2\times 3}{3\times 4}}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\frac{4}{7}}{\frac{3}{2}+\frac{2}{4}}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{4}{7}}{\frac{3}{2}+\frac{1}{2}}$$

Since \frac{3}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4}{7}}{\frac{3+1}{2}}$$

Add 3 and 1 to get 4.

$$\frac{\frac{4}{7}}{\frac{4}{2}}$$

Divide 4 by 2 to get 2.

$$\frac{\frac{4}{7}}{2}$$

Express \frac{\frac{4}{7}}{2} as a single fraction.

$$\frac{4}{7\times 2}$$

Multiply 7 and 2 to get 14.

$$\frac{4}{14}$$

Reduce the fraction \frac{4}{14} to lowest terms by extracting and canceling out 2.

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

Factor

$$\frac{2}{7} = 0.2857142857142857$$