Solve 6/5div5/6*7/16+2/3

$$\frac { 6 } { 5 } \div \frac { 5 } { 6 } \times \frac { 7 } { 16 } + \frac { 2 } { 3 }$$

Evaluate

$$\frac{389}{300}\approx 1.296666667$$

Solution Steps

Divide \frac{6}{5} by \frac{5}{6} by multiplying \frac{6}{5} by the reciprocal of \frac{5}{6}.

$$\frac{6}{5}\times \frac{6}{5}\times \frac{7}{16}+\frac{2}{3}$$

Multiply \frac{6}{5} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6\times 6}{5\times 5}\times \frac{7}{16}+\frac{2}{3}$$

Do the multiplications in the fraction \frac{6\times 6}{5\times 5}.

$$\frac{36}{25}\times \frac{7}{16}+\frac{2}{3}$$

Multiply \frac{36}{25} times \frac{7}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{36\times 7}{25\times 16}+\frac{2}{3}$$

Do the multiplications in the fraction \frac{36\times 7}{25\times 16}.

$$\frac{252}{400}+\frac{2}{3}$$

Reduce the fraction \frac{252}{400} to lowest terms by extracting and canceling out 4.

$$\frac{63}{100}+\frac{2}{3}$$

Least common multiple of 100 and 3 is 300. Convert \frac{63}{100} and \frac{2}{3} to fractions with denominator 300.

$$\frac{189}{300}+\frac{200}{300}$$

Since \frac{189}{300} and \frac{200}{300} have the same denominator, add them by adding their numerators.

$$\frac{189+200}{300}$$

Add 189 and 200 to get 389.

$$\frac{389}{300}$$

Factor

$$\frac{389}{2 ^ {2} \cdot 3 \cdot 5 ^ {2}} = 1\frac{89}{300} = 1.2966666666666666$$