Solve 0,4*5/4+3/2*(4/3)^2-2,76

$$0,4 \cdot \frac { 5 } { 4 } + \frac { 3 } { 2 } \cdot ( \frac { 4 } { 3 } ) ^ { 2 } - 2,76$$

Evaluate

$$\frac{61}{150}\approx 0,406666667$$

Solution Steps

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.

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

Multiply \frac{2}{5} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 5 in both numerator and denominator.

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

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

$$\frac{1}{2}+\frac{3}{2}\times \left(\frac{4}{3}\right)^{2}-2,76$$

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

$$\frac{1}{2}+\frac{3}{2}\times \frac{16}{9}-2,76$$

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

$$\frac{1}{2}+\frac{3\times 16}{2\times 9}-2,76$$

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

$$\frac{1}{2}+\frac{48}{18}-2,76$$

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

$$\frac{1}{2}+\frac{8}{3}-2,76$$

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{8}{3} to fractions with denominator 6.

$$\frac{3}{6}+\frac{16}{6}-2,76$$

Since \frac{3}{6} and \frac{16}{6} have the same denominator, add them by adding their numerators.

$$\frac{3+16}{6}-2,76$$

Add 3 and 16 to get 19.

$$\frac{19}{6}-2,76$$

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.

$$\frac{19}{6}-\frac{69}{25}$$

Least common multiple of 6 and 25 is 150. Convert \frac{19}{6} and \frac{69}{25} to fractions with denominator 150.

$$\frac{475}{150}-\frac{414}{150}$$

Since \frac{475}{150} and \frac{414}{150} have the same denominator, subtract them by subtracting their numerators.

$$\frac{475-414}{150}$$

Subtract 414 from 475 to get 61.

$$\frac{61}{150}$$

Factor

$$\frac{61}{2 \cdot 3 \cdot 5 ^ {2}} = 0.4066666666666667$$