Solve 500^3/3315000-3500^2/2000+18109(500)/10625+992

$$\frac{ { 500 }^{ 3 } }{ 3315000 } - \frac{ 3 { 500 }^{ 2 } }{ 2000 } + \frac{ 18109(500) }{ 10625 } +992$$

Evaluate

$$\frac{4995359}{3315}\approx 1506.895625943$$

Solution Steps

Calculate 500 to the power of 3 and get 125000000.

$$\frac{125000000}{3315000}-\frac{3\times 500^{2}}{2000}+\frac{18109\times 500}{10625}+992$$

Reduce the fraction \frac{125000000}{3315000} to lowest terms by extracting and canceling out 5000.

$$\frac{25000}{663}-\frac{3\times 500^{2}}{2000}+\frac{18109\times 500}{10625}+992$$

Calculate 500 to the power of 2 and get 250000.

$$\frac{25000}{663}-\frac{3\times 250000}{2000}+\frac{18109\times 500}{10625}+992$$

Multiply 3 and 250000 to get 750000.

$$\frac{25000}{663}-\frac{750000}{2000}+\frac{18109\times 500}{10625}+992$$

Divide 750000 by 2000 to get 375.

$$\frac{25000}{663}-375+\frac{18109\times 500}{10625}+992$$

Convert 375 to fraction \frac{248625}{663}.

$$\frac{25000}{663}-\frac{248625}{663}+\frac{18109\times 500}{10625}+992$$

Since \frac{25000}{663} and \frac{248625}{663} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25000-248625}{663}+\frac{18109\times 500}{10625}+992$$

Subtract 248625 from 25000 to get -223625.

$$-\frac{223625}{663}+\frac{18109\times 500}{10625}+992$$

Multiply 18109 and 500 to get 9054500.

$$-\frac{223625}{663}+\frac{9054500}{10625}+992$$

Reduce the fraction \frac{9054500}{10625} to lowest terms by extracting and canceling out 125.

$$-\frac{223625}{663}+\frac{72436}{85}+992$$

Least common multiple of 663 and 85 is 3315. Convert -\frac{223625}{663} and \frac{72436}{85} to fractions with denominator 3315.

$$-\frac{1118125}{3315}+\frac{2825004}{3315}+992$$

Since -\frac{1118125}{3315} and \frac{2825004}{3315} have the same denominator, add them by adding their numerators.

$$\frac{-1118125+2825004}{3315}+992$$

Add -1118125 and 2825004 to get 1706879.

$$\frac{1706879}{3315}+992$$

Convert 992 to fraction \frac{3288480}{3315}.

$$\frac{1706879}{3315}+\frac{3288480}{3315}$$

Since \frac{1706879}{3315} and \frac{3288480}{3315} have the same denominator, add them by adding their numerators.

$$\frac{1706879+3288480}{3315}$$

Add 1706879 and 3288480 to get 4995359.

$$\frac{4995359}{3315}$$

Factor

$$\frac{101 \cdot 49459}{3 \cdot 5 \cdot 13 \cdot 17} = 1506\frac{2969}{3315} = 1506.8956259426848$$