Solve 1960^3/3960000-21960^2/1875+5243(1960)/4125+1096

$$\frac{ { 1960 }^{ 3 } }{ 3960000 } - \frac{ 2 { 1960 }^{ 2 } }{ 1875 } + \frac{ 5243(1960) }{ 4125 } +1096$$

Evaluate

$$\frac{3442504}{2475}\approx 1390.910707071$$

Solution Steps

Calculate 1960 to the power of 3 and get 7529536000.

$$\frac{7529536000}{3960000}-\frac{2\times 1960^{2}}{1875}+\frac{5243\times 1960}{4125}+1096$$

Reduce the fraction \frac{7529536000}{3960000} to lowest terms by extracting and canceling out 8000.

$$\frac{941192}{495}-\frac{2\times 1960^{2}}{1875}+\frac{5243\times 1960}{4125}+1096$$

Calculate 1960 to the power of 2 and get 3841600.

$$\frac{941192}{495}-\frac{2\times 3841600}{1875}+\frac{5243\times 1960}{4125}+1096$$

Multiply 2 and 3841600 to get 7683200.

$$\frac{941192}{495}-\frac{7683200}{1875}+\frac{5243\times 1960}{4125}+1096$$

Reduce the fraction \frac{7683200}{1875} to lowest terms by extracting and canceling out 25.

$$\frac{941192}{495}-\frac{307328}{75}+\frac{5243\times 1960}{4125}+1096$$

Least common multiple of 495 and 75 is 2475. Convert \frac{941192}{495} and \frac{307328}{75} to fractions with denominator 2475.

$$\frac{4705960}{2475}-\frac{10141824}{2475}+\frac{5243\times 1960}{4125}+1096$$

Since \frac{4705960}{2475} and \frac{10141824}{2475} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4705960-10141824}{2475}+\frac{5243\times 1960}{4125}+1096$$

Subtract 10141824 from 4705960 to get -5435864.

$$-\frac{5435864}{2475}+\frac{5243\times 1960}{4125}+1096$$

Multiply 5243 and 1960 to get 10276280.

$$-\frac{5435864}{2475}+\frac{10276280}{4125}+1096$$

Reduce the fraction \frac{10276280}{4125} to lowest terms by extracting and canceling out 5.

$$-\frac{5435864}{2475}+\frac{2055256}{825}+1096$$

Least common multiple of 2475 and 825 is 2475. Convert -\frac{5435864}{2475} and \frac{2055256}{825} to fractions with denominator 2475.

$$-\frac{5435864}{2475}+\frac{6165768}{2475}+1096$$

Since -\frac{5435864}{2475} and \frac{6165768}{2475} have the same denominator, add them by adding their numerators.

$$\frac{-5435864+6165768}{2475}+1096$$

Add -5435864 and 6165768 to get 729904.

$$\frac{729904}{2475}+1096$$

Convert 1096 to fraction \frac{2712600}{2475}.

$$\frac{729904}{2475}+\frac{2712600}{2475}$$

Since \frac{729904}{2475} and \frac{2712600}{2475} have the same denominator, add them by adding their numerators.

$$\frac{729904+2712600}{2475}$$

Add 729904 and 2712600 to get 3442504.

$$\frac{3442504}{2475}$$

Factor

$$\frac{2 ^ {3} \cdot 13 \cdot 79 \cdot 419}{3 ^ {2} \cdot 5 ^ {2} \cdot 11} = 1390\frac{2254}{2475} = 1390.910707070707$$