Solve 4/7*sqrt{49/64}+(1-3/5)div3/5+(1+frac{1}{3})g)(9)^frac{3{2}}+(32)^0,8

$$\frac { 4 } { 7 } \cdot \sqrt { \frac { 49 } { 64 } } + ( 1 - \frac { 3 } { 5 } ) \div \frac { 3 } { 5 } + ( 1 + \frac { 1 } { 3 } ) g ) ( 9 ) ^ { \frac { 3 } { 2 } } + ( 32 ) ^ { 0,8 }$$

Evaluate

$$\frac{4g}{3}+\frac{7}{6}$$

Solution Steps

Rewrite the square root of the division \frac{49}{64} as the division of square roots \frac{\sqrt{49}}{\sqrt{64}}. Take the square root of both numerator and denominator.

$$\frac{4}{7}\times \frac{7}{8}+\frac{1-\frac{3}{5}}{\frac{3}{5}}+\left(1+\frac{1}{3}\right)g$$

Multiply \frac{4}{7} times \frac{7}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 7}{7\times 8}+\frac{1-\frac{3}{5}}{\frac{3}{5}}+\left(1+\frac{1}{3}\right)g$$

Cancel out 7 in both numerator and denominator.

$$\frac{4}{8}+\frac{1-\frac{3}{5}}{\frac{3}{5}}+\left(1+\frac{1}{3}\right)g$$

Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.

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

Convert 1 to fraction \frac{5}{5}.

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

Since \frac{5}{5} and \frac{3}{5} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 3 from 5 to get 2.

$$\frac{1}{2}+\frac{\frac{2}{5}}{\frac{3}{5}}+\left(1+\frac{1}{3}\right)g$$

Divide \frac{2}{5} by \frac{3}{5} by multiplying \frac{2}{5} by the reciprocal of \frac{3}{5}.

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

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

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

Cancel out 5 in both numerator and denominator.

$$\frac{1}{2}+\frac{2}{3}+\left(1+\frac{1}{3}\right)g$$

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{2}{3} to fractions with denominator 6.

$$\frac{3}{6}+\frac{4}{6}+\left(1+\frac{1}{3}\right)g$$

Since \frac{3}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\frac{3+4}{6}+\left(1+\frac{1}{3}\right)g$$

Add 3 and 4 to get 7.

$$\frac{7}{6}+\left(1+\frac{1}{3}\right)g$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{7}{6}+\left(\frac{3}{3}+\frac{1}{3}\right)g$$

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

$$\frac{7}{6}+\frac{3+1}{3}g$$

Add 3 and 1 to get 4.

$$\frac{7}{6}+\frac{4}{3}g$$

Factor

$$\frac{8g+7}{6}$$

Solution Steps

Rewrite the square root of the division \frac{49}{64} as the division of square roots \frac{\sqrt{49}}{\sqrt{64}}. Take the square root of both numerator and denominator.

$$factor(\frac{4}{7}\times \frac{7}{8}+\frac{1-\frac{3}{5}}{\frac{3}{5}}+\left(1+\frac{1}{3}\right)g)$$

Multiply \frac{4}{7} times \frac{7}{8} by multiplying numerator times numerator and denominator times denominator.

$$factor(\frac{4\times 7}{7\times 8}+\frac{1-\frac{3}{5}}{\frac{3}{5}}+\left(1+\frac{1}{3}\right)g)$$

Cancel out 7 in both numerator and denominator.

$$factor(\frac{4}{8}+\frac{1-\frac{3}{5}}{\frac{3}{5}}+\left(1+\frac{1}{3}\right)g)$$

Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.

$$factor(\frac{1}{2}+\frac{1-\frac{3}{5}}{\frac{3}{5}}+\left(1+\frac{1}{3}\right)g)$$

Convert 1 to fraction \frac{5}{5}.

$$factor(\frac{1}{2}+\frac{\frac{5}{5}-\frac{3}{5}}{\frac{3}{5}}+\left(1+\frac{1}{3}\right)g)$$

Since \frac{5}{5} and \frac{3}{5} have the same denominator, subtract them by subtracting their numerators.

$$factor(\frac{1}{2}+\frac{\frac{5-3}{5}}{\frac{3}{5}}+\left(1+\frac{1}{3}\right)g)$$

Subtract 3 from 5 to get 2.

$$factor(\frac{1}{2}+\frac{\frac{2}{5}}{\frac{3}{5}}+\left(1+\frac{1}{3}\right)g)$$

Divide \frac{2}{5} by \frac{3}{5} by multiplying \frac{2}{5} by the reciprocal of \frac{3}{5}.

$$factor(\frac{1}{2}+\frac{2}{5}\times \frac{5}{3}+\left(1+\frac{1}{3}\right)g)$$

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

$$factor(\frac{1}{2}+\frac{2\times 5}{5\times 3}+\left(1+\frac{1}{3}\right)g)$$

Cancel out 5 in both numerator and denominator.

$$factor(\frac{1}{2}+\frac{2}{3}+\left(1+\frac{1}{3}\right)g)$$

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{2}{3} to fractions with denominator 6.

$$factor(\frac{3}{6}+\frac{4}{6}+\left(1+\frac{1}{3}\right)g)$$

Since \frac{3}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$factor(\frac{3+4}{6}+\left(1+\frac{1}{3}\right)g)$$

Add 3 and 4 to get 7.

$$factor(\frac{7}{6}+\left(1+\frac{1}{3}\right)g)$$

Convert 1 to fraction \frac{3}{3}.

$$factor(\frac{7}{6}+\left(\frac{3}{3}+\frac{1}{3}\right)g)$$

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

$$factor(\frac{7}{6}+\frac{3+1}{3}g)$$

Add 3 and 1 to get 4.

$$factor(\frac{7}{6}+\frac{4}{3}g)$$

Factor out \frac{1}{6}.

$$\frac{7+8g}{6}$$