Solve 5/7+(1-3/7)*11/3+22/3=

$$\frac { 5 } { 7 } + ( 1 - \frac { 3 } { 7 } ) \times 1 \frac { 1 } { 3 } + 2 \frac { 2 } { 3 } =$$

Evaluate

$$\frac{29}{7}\approx 4.142857143$$

Solution Steps

Convert 1 to fraction \frac{7}{7}.

$$\frac{5}{7}+\left(\frac{7}{7}-\frac{3}{7}\right)\times \frac{1\times 3+1}{3}+\frac{2\times 3+2}{3}$$

Since \frac{7}{7} and \frac{3}{7} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 3 from 7 to get 4.

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

Multiply 1 and 3 to get 3.

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

Add 3 and 1 to get 4.

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

Multiply \frac{4}{7} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{4\times 4}{7\times 3}.

$$\frac{5}{7}+\frac{16}{21}+\frac{2\times 3+2}{3}$$

Least common multiple of 7 and 21 is 21. Convert \frac{5}{7} and \frac{16}{21} to fractions with denominator 21.

$$\frac{15}{21}+\frac{16}{21}+\frac{2\times 3+2}{3}$$

Since \frac{15}{21} and \frac{16}{21} have the same denominator, add them by adding their numerators.

$$\frac{15+16}{21}+\frac{2\times 3+2}{3}$$

Add 15 and 16 to get 31.

$$\frac{31}{21}+\frac{2\times 3+2}{3}$$

Multiply 2 and 3 to get 6.

$$\frac{31}{21}+\frac{6+2}{3}$$

Add 6 and 2 to get 8.

$$\frac{31}{21}+\frac{8}{3}$$

Least common multiple of 21 and 3 is 21. Convert \frac{31}{21} and \frac{8}{3} to fractions with denominator 21.

$$\frac{31}{21}+\frac{56}{21}$$

Since \frac{31}{21} and \frac{56}{21} have the same denominator, add them by adding their numerators.

$$\frac{31+56}{21}$$

Add 31 and 56 to get 87.

$$\frac{87}{21}$$

Reduce the fraction \frac{87}{21} to lowest terms by extracting and canceling out 3.

$$\frac{29}{7}$$

Factor

$$\frac{29}{7} = 4\frac{1}{7} = 4.142857142857143$$