Solve 4/5+6/7div12/15+4/3*frac{2}{3}divfrac{1}{5}

$$\frac { 4 } { 5 } + \frac { 6 } { 7 } \div \frac { 12 } { 15 } + \frac { 4 } { 3 } \times \frac { 2 } { 3 } \div \frac { 1 } { 5 }$$

Evaluate

$$\frac{3979}{630}\approx 6.315873016$$

Solution Steps

Divide \frac{6}{7} by \frac{12}{15} by multiplying \frac{6}{7} by the reciprocal of \frac{12}{15}.

$$\frac{4}{5}+\frac{6\times 15}{7\times 12}+\frac{\frac{4}{3}\times \frac{2}{3}}{\frac{1}{5}}$$

Cancel out 6 in both numerator and denominator.

$$\frac{4}{5}+\frac{15}{2\times 7}+\frac{\frac{4}{3}\times \frac{2}{3}}{\frac{1}{5}}$$

Multiply 2 and 7 to get 14.

$$\frac{4}{5}+\frac{15}{14}+\frac{\frac{4}{3}\times \frac{2}{3}}{\frac{1}{5}}$$

Least common multiple of 5 and 14 is 70. Convert \frac{4}{5} and \frac{15}{14} to fractions with denominator 70.

$$\frac{56}{70}+\frac{75}{70}+\frac{\frac{4}{3}\times \frac{2}{3}}{\frac{1}{5}}$$

Since \frac{56}{70} and \frac{75}{70} have the same denominator, add them by adding their numerators.

$$\frac{56+75}{70}+\frac{\frac{4}{3}\times \frac{2}{3}}{\frac{1}{5}}$$

Add 56 and 75 to get 131.

$$\frac{131}{70}+\frac{\frac{4}{3}\times \frac{2}{3}}{\frac{1}{5}}$$

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

$$\frac{131}{70}+\frac{\frac{4\times 2}{3\times 3}}{\frac{1}{5}}$$

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

$$\frac{131}{70}+\frac{\frac{8}{9}}{\frac{1}{5}}$$

Divide \frac{8}{9} by \frac{1}{5} by multiplying \frac{8}{9} by the reciprocal of \frac{1}{5}.

$$\frac{131}{70}+\frac{8}{9}\times 5$$

Express \frac{8}{9}\times 5 as a single fraction.

$$\frac{131}{70}+\frac{8\times 5}{9}$$

Multiply 8 and 5 to get 40.

$$\frac{131}{70}+\frac{40}{9}$$

Least common multiple of 70 and 9 is 630. Convert \frac{131}{70} and \frac{40}{9} to fractions with denominator 630.

$$\frac{1179}{630}+\frac{2800}{630}$$

Since \frac{1179}{630} and \frac{2800}{630} have the same denominator, add them by adding their numerators.

$$\frac{1179+2800}{630}$$

Add 1179 and 2800 to get 3979.

$$\frac{3979}{630}$$

Factor

$$\frac{23 \cdot 173}{2 \cdot 3 ^ {2} \cdot 5 \cdot 7} = 6\frac{199}{630} = 6.315873015873016$$