Solve 7,5+21/2*(12/3:2,5-3

$$7,5 + 2 \frac { 1 } { 2 } \cdot ( 1 \frac { 2 } { 3 } : 2,5 - 3$$

Evaluate

$$\frac{5}{3}\approx 1,666666667$$

Solution Steps

Multiply 2 and 2 to get 4.

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

Add 4 and 1 to get 5.

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

Express \frac{\frac{1\times 3+2}{3}}{2,5} as a single fraction.

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

Multiply 1 and 3 to get 3.

$$7,5+\frac{5}{2}\left(\frac{3+2}{3\times 2,5}-3\right)$$

Add 3 and 2 to get 5.

$$7,5+\frac{5}{2}\left(\frac{5}{3\times 2,5}-3\right)$$

Multiply 3 and 2,5 to get 7,5.

$$7,5+\frac{5}{2}\left(\frac{5}{7,5}-3\right)$$

Expand \frac{5}{7,5} by multiplying both numerator and the denominator by 10.

$$7,5+\frac{5}{2}\left(\frac{50}{75}-3\right)$$

Reduce the fraction \frac{50}{75} to lowest terms by extracting and canceling out 25.

$$7,5+\frac{5}{2}\left(\frac{2}{3}-3\right)$$

Convert 3 to fraction \frac{9}{3}.

$$7,5+\frac{5}{2}\left(\frac{2}{3}-\frac{9}{3}\right)$$

Since \frac{2}{3} and \frac{9}{3} have the same denominator, subtract them by subtracting their numerators.

$$7,5+\frac{5}{2}\times \frac{2-9}{3}$$

Subtract 9 from 2 to get -7.

$$7,5+\frac{5}{2}\left(-\frac{7}{3}\right)$$

Multiply \frac{5}{2} times -\frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$7,5+\frac{5\left(-7\right)}{2\times 3}$$

Do the multiplications in the fraction \frac{5\left(-7\right)}{2\times 3}.

$$7,5+\frac{-35}{6}$$

Fraction \frac{-35}{6} can be rewritten as -\frac{35}{6} by extracting the negative sign.

$$7,5-\frac{35}{6}$$

Convert decimal number 7,5 to fraction \frac{75}{10}. Reduce the fraction \frac{75}{10} to lowest terms by extracting and canceling out 5.

$$\frac{15}{2}-\frac{35}{6}$$

Least common multiple of 2 and 6 is 6. Convert \frac{15}{2} and \frac{35}{6} to fractions with denominator 6.

$$\frac{45}{6}-\frac{35}{6}$$

Since \frac{45}{6} and \frac{35}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{45-35}{6}$$

Subtract 35 from 45 to get 10.

$$\frac{10}{6}$$

Reduce the fraction \frac{10}{6} to lowest terms by extracting and canceling out 2.

$$\frac{5}{3}$$

Factor

$$\frac{5}{3} = 1\frac{2}{3} = 1.6666666666666667$$