Solve 41/2-0,5:(23/5-3/4)

$$4 \frac { 1 } { 2 } - 0,5 : ( 2 \frac { 3 } { 5 } - \frac { 3 } { 4 } )$$

Evaluate

$$\frac{313}{74}\approx 4,22972973$$

Solution Steps

Multiply 4 and 2 to get 8.

$$\frac{8+1}{2}-\frac{0,5}{\frac{2\times 5+3}{5}-\frac{3}{4}}$$

Add 8 and 1 to get 9.

$$\frac{9}{2}-\frac{0,5}{\frac{2\times 5+3}{5}-\frac{3}{4}}$$

Multiply 2 and 5 to get 10.

$$\frac{9}{2}-\frac{0,5}{\frac{10+3}{5}-\frac{3}{4}}$$

Add 10 and 3 to get 13.

$$\frac{9}{2}-\frac{0,5}{\frac{13}{5}-\frac{3}{4}}$$

Least common multiple of 5 and 4 is 20. Convert \frac{13}{5} and \frac{3}{4} to fractions with denominator 20.

$$\frac{9}{2}-\frac{0,5}{\frac{52}{20}-\frac{15}{20}}$$

Since \frac{52}{20} and \frac{15}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9}{2}-\frac{0,5}{\frac{52-15}{20}}$$

Subtract 15 from 52 to get 37.

$$\frac{9}{2}-\frac{0,5}{\frac{37}{20}}$$

Divide 0,5 by \frac{37}{20} by multiplying 0,5 by the reciprocal of \frac{37}{20}.

$$\frac{9}{2}-0,5\times \frac{20}{37}$$

Convert decimal number 0,5 to fraction \frac{5}{10}. Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{9}{2}-\frac{1}{2}\times \frac{20}{37}$$

Multiply \frac{1}{2} times \frac{20}{37} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9}{2}-\frac{1\times 20}{2\times 37}$$

Do the multiplications in the fraction \frac{1\times 20}{2\times 37}.

$$\frac{9}{2}-\frac{20}{74}$$

Reduce the fraction \frac{20}{74} to lowest terms by extracting and canceling out 2.

$$\frac{9}{2}-\frac{10}{37}$$

Least common multiple of 2 and 37 is 74. Convert \frac{9}{2} and \frac{10}{37} to fractions with denominator 74.

$$\frac{333}{74}-\frac{20}{74}$$

Since \frac{333}{74} and \frac{20}{74} have the same denominator, subtract them by subtracting their numerators.

$$\frac{333-20}{74}$$

Subtract 20 from 333 to get 313.

$$\frac{313}{74}$$

Factor

$$\frac{313}{2 \cdot 37} = 4\frac{17}{74} = 4.22972972972973$$