Solve 105*99.81+77/35+3-8*1/5+(7/8)^2*-(3-5+10.25)

$$105 \times 99.81 + \frac { 77 } { 35 } + 3 - 8 \times \frac { 1 } { 5 } + ( \frac { 7 } { 8 } ) ^ { 2 } \times - ( 3 - 5 + 10.25 )$$

Evaluate

$$10477.33359375$$

Solution Steps

Multiply 105 and 99.81 to get 10480.05.

$$10480.05+\frac{77}{35}+3-8\times \frac{1}{5}+\left(\frac{7}{8}\right)^{2}\left(-\left(3-5+10.25\right)\right)$$

Reduce the fraction \frac{77}{35} to lowest terms by extracting and canceling out 7.

$$10480.05+\frac{11}{5}+3-8\times \frac{1}{5}+\left(\frac{7}{8}\right)^{2}\left(-\left(3-5+10.25\right)\right)$$

Convert decimal number 10480.05 to fraction \frac{1048005}{100}. Reduce the fraction \frac{1048005}{100} to lowest terms by extracting and canceling out 5.

$$\frac{209601}{20}+\frac{11}{5}+3-8\times \frac{1}{5}+\left(\frac{7}{8}\right)^{2}\left(-\left(3-5+10.25\right)\right)$$

Least common multiple of 20 and 5 is 20. Convert \frac{209601}{20} and \frac{11}{5} to fractions with denominator 20.

$$\frac{209601}{20}+\frac{44}{20}+3-8\times \frac{1}{5}+\left(\frac{7}{8}\right)^{2}\left(-\left(3-5+10.25\right)\right)$$

Since \frac{209601}{20} and \frac{44}{20} have the same denominator, add them by adding their numerators.

$$\frac{209601+44}{20}+3-8\times \frac{1}{5}+\left(\frac{7}{8}\right)^{2}\left(-\left(3-5+10.25\right)\right)$$

Add 209601 and 44 to get 209645.

$$\frac{209645}{20}+3-8\times \frac{1}{5}+\left(\frac{7}{8}\right)^{2}\left(-\left(3-5+10.25\right)\right)$$

Reduce the fraction \frac{209645}{20} to lowest terms by extracting and canceling out 5.

$$\frac{41929}{4}+3-8\times \frac{1}{5}+\left(\frac{7}{8}\right)^{2}\left(-\left(3-5+10.25\right)\right)$$

Convert 3 to fraction \frac{12}{4}.

$$\frac{41929}{4}+\frac{12}{4}-8\times \frac{1}{5}+\left(\frac{7}{8}\right)^{2}\left(-\left(3-5+10.25\right)\right)$$

Since \frac{41929}{4} and \frac{12}{4} have the same denominator, add them by adding their numerators.

$$\frac{41929+12}{4}-8\times \frac{1}{5}+\left(\frac{7}{8}\right)^{2}\left(-\left(3-5+10.25\right)\right)$$

Add 41929 and 12 to get 41941.

$$\frac{41941}{4}-8\times \frac{1}{5}+\left(\frac{7}{8}\right)^{2}\left(-\left(3-5+10.25\right)\right)$$

Multiply 8 and \frac{1}{5} to get \frac{8}{5}.

$$\frac{41941}{4}-\frac{8}{5}+\left(\frac{7}{8}\right)^{2}\left(-\left(3-5+10.25\right)\right)$$

Least common multiple of 4 and 5 is 20. Convert \frac{41941}{4} and \frac{8}{5} to fractions with denominator 20.

$$\frac{209705}{20}-\frac{32}{20}+\left(\frac{7}{8}\right)^{2}\left(-\left(3-5+10.25\right)\right)$$

Since \frac{209705}{20} and \frac{32}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{209705-32}{20}+\left(\frac{7}{8}\right)^{2}\left(-\left(3-5+10.25\right)\right)$$

Subtract 32 from 209705 to get 209673.

$$\frac{209673}{20}+\left(\frac{7}{8}\right)^{2}\left(-\left(3-5+10.25\right)\right)$$

Calculate \frac{7}{8} to the power of 2 and get \frac{49}{64}.

$$\frac{209673}{20}+\frac{49}{64}\left(-\left(3-5+10.25\right)\right)$$

Subtract 5 from 3 to get -2.

$$\frac{209673}{20}+\frac{49}{64}\left(-\left(-2+10.25\right)\right)$$

Add -2 and 10.25 to get 8.25.

$$\frac{209673}{20}+\frac{49}{64}\left(-8.25\right)$$

Convert decimal number -8.25 to fraction -\frac{825}{100}. Reduce the fraction -\frac{825}{100} to lowest terms by extracting and canceling out 25.

$$\frac{209673}{20}+\frac{49}{64}\left(-\frac{33}{4}\right)$$

Multiply \frac{49}{64} times -\frac{33}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{209673}{20}+\frac{49\left(-33\right)}{64\times 4}$$

Do the multiplications in the fraction \frac{49\left(-33\right)}{64\times 4}.

$$\frac{209673}{20}+\frac{-1617}{256}$$

Fraction \frac{-1617}{256} can be rewritten as -\frac{1617}{256} by extracting the negative sign.

$$\frac{209673}{20}-\frac{1617}{256}$$

Least common multiple of 20 and 256 is 1280. Convert \frac{209673}{20} and \frac{1617}{256} to fractions with denominator 1280.

$$\frac{13419072}{1280}-\frac{8085}{1280}$$

Since \frac{13419072}{1280} and \frac{8085}{1280} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13419072-8085}{1280}$$

Subtract 8085 from 13419072 to get 13410987.

$$\frac{13410987}{1280}$$

Factor

$$\frac{3 \cdot 4470329}{5 \cdot 2 ^ {8}} = 10477\frac{427}{1280} = 10477.33359375$$