Solve [31/2-(0.4-1/3)*4.5]div(3.25-11/4)

$$[ 3 \frac { 1 } { 2 } - ( 0.4 - \frac { 1 } { 3 } ) \times 4.5 ] \div ( 3.25 - 1 \frac { 1 } { 4 } )$$

Evaluate

$$1.6$$

Solution Steps

Multiply 3 and 2 to get 6.

$$\frac{\frac{6+1}{2}-\left(0.4-\frac{1}{3}\right)\times 4.5}{3.25-\frac{1\times 4+1}{4}}$$

Add 6 and 1 to get 7.

$$\frac{\frac{7}{2}-\left(0.4-\frac{1}{3}\right)\times 4.5}{3.25-\frac{1\times 4+1}{4}}$$

Convert decimal number 0.4 to fraction \frac{4}{10}. Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{7}{2}-\left(\frac{2}{5}-\frac{1}{3}\right)\times 4.5}{3.25-\frac{1\times 4+1}{4}}$$

Least common multiple of 5 and 3 is 15. Convert \frac{2}{5} and \frac{1}{3} to fractions with denominator 15.

$$\frac{\frac{7}{2}-\left(\frac{6}{15}-\frac{5}{15}\right)\times 4.5}{3.25-\frac{1\times 4+1}{4}}$$

Since \frac{6}{15} and \frac{5}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7}{2}-\frac{6-5}{15}\times 4.5}{3.25-\frac{1\times 4+1}{4}}$$

Subtract 5 from 6 to get 1.

$$\frac{\frac{7}{2}-\frac{1}{15}\times 4.5}{3.25-\frac{1\times 4+1}{4}}$$

Convert decimal number 4.5 to fraction \frac{45}{10}. Reduce the fraction \frac{45}{10} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{7}{2}-\frac{1}{15}\times \frac{9}{2}}{3.25-\frac{1\times 4+1}{4}}$$

Multiply \frac{1}{15} times \frac{9}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{7}{2}-\frac{1\times 9}{15\times 2}}{3.25-\frac{1\times 4+1}{4}}$$

Do the multiplications in the fraction \frac{1\times 9}{15\times 2}.

$$\frac{\frac{7}{2}-\frac{9}{30}}{3.25-\frac{1\times 4+1}{4}}$$

Reduce the fraction \frac{9}{30} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{7}{2}-\frac{3}{10}}{3.25-\frac{1\times 4+1}{4}}$$

Least common multiple of 2 and 10 is 10. Convert \frac{7}{2} and \frac{3}{10} to fractions with denominator 10.

$$\frac{\frac{35}{10}-\frac{3}{10}}{3.25-\frac{1\times 4+1}{4}}$$

Since \frac{35}{10} and \frac{3}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{35-3}{10}}{3.25-\frac{1\times 4+1}{4}}$$

Subtract 3 from 35 to get 32.

$$\frac{\frac{32}{10}}{3.25-\frac{1\times 4+1}{4}}$$

Reduce the fraction \frac{32}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{16}{5}}{3.25-\frac{1\times 4+1}{4}}$$

Multiply 1 and 4 to get 4.

$$\frac{\frac{16}{5}}{3.25-\frac{4+1}{4}}$$

Add 4 and 1 to get 5.

$$\frac{\frac{16}{5}}{3.25-\frac{5}{4}}$$

Convert decimal number 3.25 to fraction \frac{325}{100}. Reduce the fraction \frac{325}{100} to lowest terms by extracting and canceling out 25.

$$\frac{\frac{16}{5}}{\frac{13}{4}-\frac{5}{4}}$$

Since \frac{13}{4} and \frac{5}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{16}{5}}{\frac{13-5}{4}}$$

Subtract 5 from 13 to get 8.

$$\frac{\frac{16}{5}}{\frac{8}{4}}$$

Divide 8 by 4 to get 2.

$$\frac{\frac{16}{5}}{2}$$

Express \frac{\frac{16}{5}}{2} as a single fraction.

$$\frac{16}{5\times 2}$$

Multiply 5 and 2 to get 10.

$$\frac{16}{10}$$

Reduce the fraction \frac{16}{10} to lowest terms by extracting and canceling out 2.

$$\frac{8}{5}$$

Factor

$$\frac{2 ^ {3}}{5} = 1\frac{3}{5} = 1.6$$