Solve 3/4+(-1/2)-11/5div11/2

$$\frac { 3 } { 4 } + ( - \frac { 1 } { 2 } ) - 1 \frac { 1 } { 5 } \div 1 \frac { 1 } { 2 }$$

Evaluate

$$-\frac{11}{20}=-0.55$$

Solution Steps

Least common multiple of 4 and 2 is 4. Convert \frac{3}{4} and \frac{1}{2} to fractions with denominator 4.

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

Since \frac{3}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 2 from 3 to get 1.

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

Divide \frac{1\times 5+1}{5} by \frac{1\times 2+1}{2} by multiplying \frac{1\times 5+1}{5} by the reciprocal of \frac{1\times 2+1}{2}.

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

Multiply 1 and 5 to get 5.

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

Add 5 and 1 to get 6.

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

Multiply 6 and 2 to get 12.

$$\frac{1}{4}-\frac{12}{5\left(1\times 2+1\right)}$$

Multiply 1 and 2 to get 2.

$$\frac{1}{4}-\frac{12}{5\left(2+1\right)}$$

Add 2 and 1 to get 3.

$$\frac{1}{4}-\frac{12}{5\times 3}$$

Multiply 5 and 3 to get 15.

$$\frac{1}{4}-\frac{12}{15}$$

Reduce the fraction \frac{12}{15} to lowest terms by extracting and canceling out 3.

$$\frac{1}{4}-\frac{4}{5}$$

Least common multiple of 4 and 5 is 20. Convert \frac{1}{4} and \frac{4}{5} to fractions with denominator 20.

$$\frac{5}{20}-\frac{16}{20}$$

Since \frac{5}{20} and \frac{16}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-16}{20}$$

Subtract 16 from 5 to get -11.

$$-\frac{11}{20}$$

Factor

$$-\frac{11}{20} = -0.55$$