Solve 1000/5:18/200*100:20/10+10/70

$$\frac { 1000 } { 5 } : \frac { 18 } { 200 } \cdot 100 : \frac { 20 } { 10 } + \frac { 10 } { 70 }$$

Evaluate

$$\frac{7000009}{63}\approx 111111.253968254$$

Solution Steps

Divide \frac{1000}{5} by \frac{18}{200} by multiplying \frac{1000}{5} by the reciprocal of \frac{18}{200}.

$$\frac{\frac{1000\times 200}{5\times 18}\times 100}{\frac{20}{10}}+\frac{10}{70}$$

Cancel out 2\times 5 in both numerator and denominator.

$$\frac{\frac{100\times 200}{9}\times 100}{\frac{20}{10}}+\frac{10}{70}$$

Multiply 100 and 200 to get 20000.

$$\frac{\frac{20000}{9}\times 100}{\frac{20}{10}}+\frac{10}{70}$$

Express \frac{20000}{9}\times 100 as a single fraction.

$$\frac{\frac{20000\times 100}{9}}{\frac{20}{10}}+\frac{10}{70}$$

Multiply 20000 and 100 to get 2000000.

$$\frac{\frac{2000000}{9}}{\frac{20}{10}}+\frac{10}{70}$$

Divide 20 by 10 to get 2.

$$\frac{\frac{2000000}{9}}{2}+\frac{10}{70}$$

Express \frac{\frac{2000000}{9}}{2} as a single fraction.

$$\frac{2000000}{9\times 2}+\frac{10}{70}$$

Multiply 9 and 2 to get 18.

$$\frac{2000000}{18}+\frac{10}{70}$$

Reduce the fraction \frac{2000000}{18} to lowest terms by extracting and canceling out 2.

$$\frac{1000000}{9}+\frac{10}{70}$$

Reduce the fraction \frac{10}{70} to lowest terms by extracting and canceling out 10.

$$\frac{1000000}{9}+\frac{1}{7}$$

Least common multiple of 9 and 7 is 63. Convert \frac{1000000}{9} and \frac{1}{7} to fractions with denominator 63.

$$\frac{7000000}{63}+\frac{9}{63}$$

Since \frac{7000000}{63} and \frac{9}{63} have the same denominator, add them by adding their numerators.

$$\frac{7000000+9}{63}$$

Add 7000000 and 9 to get 7000009.

$$\frac{7000009}{63}$$

Factor

$$\frac{7000009}{3 ^ {2} \cdot 7} = 111111\frac{16}{63} = 111111.25396825396$$