Solve 1.625-3^2div2^3+3/5-21/4

$$1.625- { 3 }^{ 2 } \div { 2 }^{ 3 } + \frac{ 3 }{ 5 } - 2 \frac { 1 } { 4 }$$

Evaluate

$$-1.15$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$1.625-\frac{9}{2^{3}}+\frac{3}{5}-\frac{2\times 4+1}{4}$$

Calculate 2 to the power of 3 and get 8.

$$1.625-\frac{9}{8}+\frac{3}{5}-\frac{2\times 4+1}{4}$$

Convert decimal number 1.625 to fraction \frac{1625}{1000}. Reduce the fraction \frac{1625}{1000} to lowest terms by extracting and canceling out 125.

$$\frac{13}{8}-\frac{9}{8}+\frac{3}{5}-\frac{2\times 4+1}{4}$$

Since \frac{13}{8} and \frac{9}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13-9}{8}+\frac{3}{5}-\frac{2\times 4+1}{4}$$

Subtract 9 from 13 to get 4.

$$\frac{4}{8}+\frac{3}{5}-\frac{2\times 4+1}{4}$$

Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.

$$\frac{1}{2}+\frac{3}{5}-\frac{2\times 4+1}{4}$$

Least common multiple of 2 and 5 is 10. Convert \frac{1}{2} and \frac{3}{5} to fractions with denominator 10.

$$\frac{5}{10}+\frac{6}{10}-\frac{2\times 4+1}{4}$$

Since \frac{5}{10} and \frac{6}{10} have the same denominator, add them by adding their numerators.

$$\frac{5+6}{10}-\frac{2\times 4+1}{4}$$

Add 5 and 6 to get 11.

$$\frac{11}{10}-\frac{2\times 4+1}{4}$$

Multiply 2 and 4 to get 8.

$$\frac{11}{10}-\frac{8+1}{4}$$

Add 8 and 1 to get 9.

$$\frac{11}{10}-\frac{9}{4}$$

Least common multiple of 10 and 4 is 20. Convert \frac{11}{10} and \frac{9}{4} to fractions with denominator 20.

$$\frac{22}{20}-\frac{45}{20}$$

Since \frac{22}{20} and \frac{45}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{22-45}{20}$$

Subtract 45 from 22 to get -23.

$$-\frac{23}{20}$$

Factor

$$-1.15$$