Solve 7/10div5/6+2/3*2/5

$$\frac { 7 } { 10 } \div \frac { 5 } { 6 } + \frac { 2 } { 3 } \cdot \frac { 2 } { 5 }$$

Evaluate

$$\frac{83}{75}\approx 1.106666667$$

Solution Steps

Divide \frac{7}{10} by \frac{5}{6} by multiplying \frac{7}{10} by the reciprocal of \frac{5}{6}.

$$\frac{7}{10}\times \frac{6}{5}+\frac{2}{3}\times \frac{2}{5}$$

Multiply \frac{7}{10} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 6}{10\times 5}+\frac{2}{3}\times \frac{2}{5}$$

Do the multiplications in the fraction \frac{7\times 6}{10\times 5}.

$$\frac{42}{50}+\frac{2}{3}\times \frac{2}{5}$$

Reduce the fraction \frac{42}{50} to lowest terms by extracting and canceling out 2.

$$\frac{21}{25}+\frac{2}{3}\times \frac{2}{5}$$

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

$$\frac{21}{25}+\frac{2\times 2}{3\times 5}$$

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

$$\frac{21}{25}+\frac{4}{15}$$

Least common multiple of 25 and 15 is 75. Convert \frac{21}{25} and \frac{4}{15} to fractions with denominator 75.

$$\frac{63}{75}+\frac{20}{75}$$

Since \frac{63}{75} and \frac{20}{75} have the same denominator, add them by adding their numerators.

$$\frac{63+20}{75}$$

Add 63 and 20 to get 83.

$$\frac{83}{75}$$

Factor

$$\frac{83}{3 \cdot 5 ^ {2}} = 1\frac{8}{75} = 1.1066666666666667$$