Solve (4/5+1/4)div7/3+7/10

$$( \frac{ 4 }{ 5 } + \frac{ 1 }{ 4 } ) \div \frac{ 7 }{ 3 } + \frac{ 7 }{ 10 }$$

Evaluate

$$\frac{23}{20}=1.15$$

Solution Steps

Least common multiple of 5 and 4 is 20. Convert \frac{4}{5} and \frac{1}{4} to fractions with denominator 20.

$$\frac{\frac{16}{20}+\frac{5}{20}}{\frac{7}{3}}+\frac{7}{10}$$

Since \frac{16}{20} and \frac{5}{20} have the same denominator, add them by adding their numerators.

$$\frac{\frac{16+5}{20}}{\frac{7}{3}}+\frac{7}{10}$$

Add 16 and 5 to get 21.

$$\frac{\frac{21}{20}}{\frac{7}{3}}+\frac{7}{10}$$

Divide \frac{21}{20} by \frac{7}{3} by multiplying \frac{21}{20} by the reciprocal of \frac{7}{3}.

$$\frac{21}{20}\times \frac{3}{7}+\frac{7}{10}$$

Multiply \frac{21}{20} times \frac{3}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{21\times 3}{20\times 7}+\frac{7}{10}$$

Do the multiplications in the fraction \frac{21\times 3}{20\times 7}.

$$\frac{63}{140}+\frac{7}{10}$$

Reduce the fraction \frac{63}{140} to lowest terms by extracting and canceling out 7.

$$\frac{9}{20}+\frac{7}{10}$$

Least common multiple of 20 and 10 is 20. Convert \frac{9}{20} and \frac{7}{10} to fractions with denominator 20.

$$\frac{9}{20}+\frac{14}{20}$$

Since \frac{9}{20} and \frac{14}{20} have the same denominator, add them by adding their numerators.

$$\frac{9+14}{20}$$

Add 9 and 14 to get 23.

$$\frac{23}{20}$$

Factor

$$\frac{23}{2 ^ {2} \cdot 5} = 1\frac{3}{20} = 1.15$$