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

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

Evaluate

$$\frac{18}{7}\approx 2.571428571$$

Solution Steps

Multiply 1 and 3 to get 3.

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

Add 3 and 2 to get 5.

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

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

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

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

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

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

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

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

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

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

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

Add 10 and 2 to get 12.

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

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

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

Multiply 2 and 4 to get 8.

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

Add 8 and 1 to get 9.

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

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

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

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

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

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

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

Least common multiple of 7 and 2 is 14. Convert \frac{4}{7} and \frac{3}{2} to fractions with denominator 14.

$$\frac{8}{14}+\frac{21}{14}+\frac{2}{3}\times \frac{3}{4}$$

Since \frac{8}{14} and \frac{21}{14} have the same denominator, add them by adding their numerators.

$$\frac{8+21}{14}+\frac{2}{3}\times \frac{3}{4}$$

Add 8 and 21 to get 29.

$$\frac{29}{14}+\frac{2}{3}\times \frac{3}{4}$$

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

$$\frac{29}{14}+\frac{2\times 3}{3\times 4}$$

Cancel out 3 in both numerator and denominator.

$$\frac{29}{14}+\frac{2}{4}$$

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

$$\frac{29}{14}+\frac{1}{2}$$

Least common multiple of 14 and 2 is 14. Convert \frac{29}{14} and \frac{1}{2} to fractions with denominator 14.

$$\frac{29}{14}+\frac{7}{14}$$

Since \frac{29}{14} and \frac{7}{14} have the same denominator, add them by adding their numerators.

$$\frac{29+7}{14}$$

Add 29 and 7 to get 36.

$$\frac{36}{14}$$

Reduce the fraction \frac{36}{14} to lowest terms by extracting and canceling out 2.

$$\frac{18}{7}$$

Factor

$$\frac{2 \cdot 3 ^ {2}}{7} = 2\frac{4}{7} = 2.5714285714285716$$