Solve 32000div30*13-840div30*13+32000div240div60(65+30+14+30+18)+1500

$$32000 \div 30 \times 13-840 \div 30 \times 13+32000 \div 240 \div 60(65+30+14+30+18)+1500$$

Evaluate

$$\frac{138164}{9}\approx 15351.555555556$$

Solution Steps

Reduce the fraction \frac{32000}{30} to lowest terms by extracting and canceling out 10.

$$\frac{3200}{3}\times 13-\frac{840}{30}\times 13+\frac{\frac{32000}{240}}{60}\left(65+30+14+30+18\right)+1500$$

Express \frac{3200}{3}\times 13 as a single fraction.

$$\frac{3200\times 13}{3}-\frac{840}{30}\times 13+\frac{\frac{32000}{240}}{60}\left(65+30+14+30+18\right)+1500$$

Multiply 3200 and 13 to get 41600.

$$\frac{41600}{3}-\frac{840}{30}\times 13+\frac{\frac{32000}{240}}{60}\left(65+30+14+30+18\right)+1500$$

Divide 840 by 30 to get 28.

$$\frac{41600}{3}-28\times 13+\frac{\frac{32000}{240}}{60}\left(65+30+14+30+18\right)+1500$$

Multiply 28 and 13 to get 364.

$$\frac{41600}{3}-364+\frac{\frac{32000}{240}}{60}\left(65+30+14+30+18\right)+1500$$

Convert 364 to fraction \frac{1092}{3}.

$$\frac{41600}{3}-\frac{1092}{3}+\frac{\frac{32000}{240}}{60}\left(65+30+14+30+18\right)+1500$$

Since \frac{41600}{3} and \frac{1092}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{41600-1092}{3}+\frac{\frac{32000}{240}}{60}\left(65+30+14+30+18\right)+1500$$

Subtract 1092 from 41600 to get 40508.

$$\frac{40508}{3}+\frac{\frac{32000}{240}}{60}\left(65+30+14+30+18\right)+1500$$

Express \frac{\frac{32000}{240}}{60} as a single fraction.

$$\frac{40508}{3}+\frac{32000}{240\times 60}\left(65+30+14+30+18\right)+1500$$

Multiply 240 and 60 to get 14400.

$$\frac{40508}{3}+\frac{32000}{14400}\left(65+30+14+30+18\right)+1500$$

Reduce the fraction \frac{32000}{14400} to lowest terms by extracting and canceling out 1600.

$$\frac{40508}{3}+\frac{20}{9}\left(65+30+14+30+18\right)+1500$$

Add 65 and 30 to get 95.

$$\frac{40508}{3}+\frac{20}{9}\left(95+14+30+18\right)+1500$$

Add 95 and 14 to get 109.

$$\frac{40508}{3}+\frac{20}{9}\left(109+30+18\right)+1500$$

Add 109 and 30 to get 139.

$$\frac{40508}{3}+\frac{20}{9}\left(139+18\right)+1500$$

Add 139 and 18 to get 157.

$$\frac{40508}{3}+\frac{20}{9}\times 157+1500$$

Express \frac{20}{9}\times 157 as a single fraction.

$$\frac{40508}{3}+\frac{20\times 157}{9}+1500$$

Multiply 20 and 157 to get 3140.

$$\frac{40508}{3}+\frac{3140}{9}+1500$$

Least common multiple of 3 and 9 is 9. Convert \frac{40508}{3} and \frac{3140}{9} to fractions with denominator 9.

$$\frac{121524}{9}+\frac{3140}{9}+1500$$

Since \frac{121524}{9} and \frac{3140}{9} have the same denominator, add them by adding their numerators.

$$\frac{121524+3140}{9}+1500$$

Add 121524 and 3140 to get 124664.

$$\frac{124664}{9}+1500$$

Convert 1500 to fraction \frac{13500}{9}.

$$\frac{124664}{9}+\frac{13500}{9}$$

Since \frac{124664}{9} and \frac{13500}{9} have the same denominator, add them by adding their numerators.

$$\frac{124664+13500}{9}$$

Add 124664 and 13500 to get 138164.

$$\frac{138164}{9}$$

Factor

$$\frac{2 ^ {2} \cdot 13 \cdot 2657}{3 ^ {2}} = 15351\frac{5}{9} = 15351.555555555555$$