Solve 7.5*(3/8+0.7)-(5/2)^2=

$$7.5 \cdot ( \frac { 3 } { 8 } + 0.7 ) - ( \frac { 5 } { 2 } ) ^ { 2 } =$$

Evaluate

$$1.8125$$

Solution Steps

Convert decimal number 0.7 to fraction \frac{7}{10}.

$$7.5\left(\frac{3}{8}+\frac{7}{10}\right)-\left(\frac{5}{2}\right)^{2}$$

Least common multiple of 8 and 10 is 40. Convert \frac{3}{8} and \frac{7}{10} to fractions with denominator 40.

$$7.5\left(\frac{15}{40}+\frac{28}{40}\right)-\left(\frac{5}{2}\right)^{2}$$

Since \frac{15}{40} and \frac{28}{40} have the same denominator, add them by adding their numerators.

$$7.5\times \frac{15+28}{40}-\left(\frac{5}{2}\right)^{2}$$

Add 15 and 28 to get 43.

$$7.5\times \frac{43}{40}-\left(\frac{5}{2}\right)^{2}$$

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.

$$\frac{15}{2}\times \frac{43}{40}-\left(\frac{5}{2}\right)^{2}$$

Multiply \frac{15}{2} times \frac{43}{40} by multiplying numerator times numerator and denominator times denominator.

$$\frac{15\times 43}{2\times 40}-\left(\frac{5}{2}\right)^{2}$$

Do the multiplications in the fraction \frac{15\times 43}{2\times 40}.

$$\frac{645}{80}-\left(\frac{5}{2}\right)^{2}$$

Reduce the fraction \frac{645}{80} to lowest terms by extracting and canceling out 5.

$$\frac{129}{16}-\left(\frac{5}{2}\right)^{2}$$

Calculate \frac{5}{2} to the power of 2 and get \frac{25}{4}.

$$\frac{129}{16}-\frac{25}{4}$$

Least common multiple of 16 and 4 is 16. Convert \frac{129}{16} and \frac{25}{4} to fractions with denominator 16.

$$\frac{129}{16}-\frac{100}{16}$$

Since \frac{129}{16} and \frac{100}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{129-100}{16}$$

Subtract 100 from 129 to get 29.

$$\frac{29}{16}$$

Factor

$$\frac{29}{2 ^ {4}} = 1\frac{13}{16} = 1.8125$$