Solve 40,4*5/4+3/2*(4/3)^2-2,76

$$40,4 \cdot \frac { 5 } { 4 } + \frac { 3 } { 2 } \cdot ( \frac { 4 } { 3 } ) ^ { 2 } - 2,76$$

Evaluate

$$\frac{7561}{150}\approx 50,406666667$$

Solution Steps

Convert decimal number 40,4 to fraction \frac{404}{10}. Reduce the fraction \frac{404}{10} to lowest terms by extracting and canceling out 2.

$$\frac{202}{5}\times \frac{5}{4}+\frac{3}{2}\times \left(\frac{4}{3}\right)^{2}-2,76$$

Multiply \frac{202}{5} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{202\times 5}{5\times 4}+\frac{3}{2}\times \left(\frac{4}{3}\right)^{2}-2,76$$

Cancel out 5 in both numerator and denominator.

$$\frac{202}{4}+\frac{3}{2}\times \left(\frac{4}{3}\right)^{2}-2,76$$

Reduce the fraction \frac{202}{4} to lowest terms by extracting and canceling out 2.

$$\frac{101}{2}+\frac{3}{2}\times \left(\frac{4}{3}\right)^{2}-2,76$$

Calculate \frac{4}{3} to the power of 2 and get \frac{16}{9}.

$$\frac{101}{2}+\frac{3}{2}\times \frac{16}{9}-2,76$$

Multiply \frac{3}{2} times \frac{16}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{101}{2}+\frac{3\times 16}{2\times 9}-2,76$$

Do the multiplications in the fraction \frac{3\times 16}{2\times 9}.

$$\frac{101}{2}+\frac{48}{18}-2,76$$

Reduce the fraction \frac{48}{18} to lowest terms by extracting and canceling out 6.

$$\frac{101}{2}+\frac{8}{3}-2,76$$

Least common multiple of 2 and 3 is 6. Convert \frac{101}{2} and \frac{8}{3} to fractions with denominator 6.

$$\frac{303}{6}+\frac{16}{6}-2,76$$

Since \frac{303}{6} and \frac{16}{6} have the same denominator, add them by adding their numerators.

$$\frac{303+16}{6}-2,76$$

Add 303 and 16 to get 319.

$$\frac{319}{6}-2,76$$

Convert decimal number 2,76 to fraction \frac{276}{100}. Reduce the fraction \frac{276}{100} to lowest terms by extracting and canceling out 4.

$$\frac{319}{6}-\frac{69}{25}$$

Least common multiple of 6 and 25 is 150. Convert \frac{319}{6} and \frac{69}{25} to fractions with denominator 150.

$$\frac{7975}{150}-\frac{414}{150}$$

Since \frac{7975}{150} and \frac{414}{150} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7975-414}{150}$$

Subtract 414 from 7975 to get 7561.

$$\frac{7561}{150}$$

Factor

$$\frac{7561}{2 \cdot 3 \cdot 5 ^ {2}} = 50\frac{61}{150} = 50.406666666666666$$