Solve 3.5*((16.875-2/3*15/16)-(0.35+84/5))*100

$$3.5 \times ((16.875- \frac{ 2 }{ 3 } \times 1 \frac { 5 } { 16 } )-(0.35+ 8 \frac { 4 } { 5 } )) \times 100$$

Evaluate

$$2397.5$$

Solution Steps

Multiply 1 and 16 to get 16.

$$3.5\left(16.875-\frac{2}{3}\times \frac{16+5}{16}-\left(0.35+\frac{8\times 5+4}{5}\right)\right)\times 100$$

Add 16 and 5 to get 21.

$$3.5\left(16.875-\frac{2}{3}\times \frac{21}{16}-\left(0.35+\frac{8\times 5+4}{5}\right)\right)\times 100$$

Multiply \frac{2}{3} times \frac{21}{16} by multiplying numerator times numerator and denominator times denominator.

$$3.5\left(16.875-\frac{2\times 21}{3\times 16}-\left(0.35+\frac{8\times 5+4}{5}\right)\right)\times 100$$

Do the multiplications in the fraction \frac{2\times 21}{3\times 16}.

$$3.5\left(16.875-\frac{42}{48}-\left(0.35+\frac{8\times 5+4}{5}\right)\right)\times 100$$

Reduce the fraction \frac{42}{48} to lowest terms by extracting and canceling out 6.

$$3.5\left(16.875-\frac{7}{8}-\left(0.35+\frac{8\times 5+4}{5}\right)\right)\times 100$$

Convert decimal number 16.875 to fraction \frac{16875}{1000}. Reduce the fraction \frac{16875}{1000} to lowest terms by extracting and canceling out 125.

$$3.5\left(\frac{135}{8}-\frac{7}{8}-\left(0.35+\frac{8\times 5+4}{5}\right)\right)\times 100$$

Since \frac{135}{8} and \frac{7}{8} have the same denominator, subtract them by subtracting their numerators.

$$3.5\left(\frac{135-7}{8}-\left(0.35+\frac{8\times 5+4}{5}\right)\right)\times 100$$

Subtract 7 from 135 to get 128.

$$3.5\left(\frac{128}{8}-\left(0.35+\frac{8\times 5+4}{5}\right)\right)\times 100$$

Divide 128 by 8 to get 16.

$$3.5\left(16-\left(0.35+\frac{8\times 5+4}{5}\right)\right)\times 100$$

Multiply 8 and 5 to get 40.

$$3.5\left(16-\left(0.35+\frac{40+4}{5}\right)\right)\times 100$$

Add 40 and 4 to get 44.

$$3.5\left(16-\left(0.35+\frac{44}{5}\right)\right)\times 100$$

Convert decimal number 0.35 to fraction \frac{35}{100}. Reduce the fraction \frac{35}{100} to lowest terms by extracting and canceling out 5.

$$3.5\left(16-\left(\frac{7}{20}+\frac{44}{5}\right)\right)\times 100$$

Least common multiple of 20 and 5 is 20. Convert \frac{7}{20} and \frac{44}{5} to fractions with denominator 20.

$$3.5\left(16-\left(\frac{7}{20}+\frac{176}{20}\right)\right)\times 100$$

Since \frac{7}{20} and \frac{176}{20} have the same denominator, add them by adding their numerators.

$$3.5\left(16-\frac{7+176}{20}\right)\times 100$$

Add 7 and 176 to get 183.

$$3.5\left(16-\frac{183}{20}\right)\times 100$$

Convert 16 to fraction \frac{320}{20}.

$$3.5\left(\frac{320}{20}-\frac{183}{20}\right)\times 100$$

Since \frac{320}{20} and \frac{183}{20} have the same denominator, subtract them by subtracting their numerators.

$$3.5\times \frac{320-183}{20}\times 100$$

Subtract 183 from 320 to get 137.

$$3.5\times \frac{137}{20}\times 100$$

Convert decimal number 3.5 to fraction \frac{35}{10}. Reduce the fraction \frac{35}{10} to lowest terms by extracting and canceling out 5.

$$\frac{7}{2}\times \frac{137}{20}\times 100$$

Multiply \frac{7}{2} times \frac{137}{20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 137}{2\times 20}\times 100$$

Do the multiplications in the fraction \frac{7\times 137}{2\times 20}.

$$\frac{959}{40}\times 100$$

Express \frac{959}{40}\times 100 as a single fraction.

$$\frac{959\times 100}{40}$$

Multiply 959 and 100 to get 95900.

$$\frac{95900}{40}$$

Reduce the fraction \frac{95900}{40} to lowest terms by extracting and canceling out 20.

$$\frac{4795}{2}$$

Factor

$$\frac{5 \cdot 7 \cdot 137}{2} = 2397\frac{1}{2} = 2397.5$$