Solve 3/8(6.8)+(71/2)(-1/4)

$$\frac { 3 } { 8 } ( 6.8 ) + ( 7 \frac { 1 } { 2 } ) ( - \frac { 1 } { 4 } )$$

Evaluate

$$0.675$$

Solution Steps

Convert decimal number 6.8 to fraction \frac{68}{10}. Reduce the fraction \frac{68}{10} to lowest terms by extracting and canceling out 2.

$$\frac{3}{8}\times \frac{34}{5}+\frac{7\times 2+1}{2}\left(-\frac{1}{4}\right)$$

Multiply \frac{3}{8} times \frac{34}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 34}{8\times 5}+\frac{7\times 2+1}{2}\left(-\frac{1}{4}\right)$$

Do the multiplications in the fraction \frac{3\times 34}{8\times 5}.

$$\frac{102}{40}+\frac{7\times 2+1}{2}\left(-\frac{1}{4}\right)$$

Reduce the fraction \frac{102}{40} to lowest terms by extracting and canceling out 2.

$$\frac{51}{20}+\frac{7\times 2+1}{2}\left(-\frac{1}{4}\right)$$

Multiply 7 and 2 to get 14.

$$\frac{51}{20}+\frac{14+1}{2}\left(-\frac{1}{4}\right)$$

Add 14 and 1 to get 15.

$$\frac{51}{20}+\frac{15}{2}\left(-\frac{1}{4}\right)$$

Multiply \frac{15}{2} times -\frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{51}{20}+\frac{15\left(-1\right)}{2\times 4}$$

Do the multiplications in the fraction \frac{15\left(-1\right)}{2\times 4}.

$$\frac{51}{20}+\frac{-15}{8}$$

Fraction \frac{-15}{8} can be rewritten as -\frac{15}{8} by extracting the negative sign.

$$\frac{51}{20}-\frac{15}{8}$$

Least common multiple of 20 and 8 is 40. Convert \frac{51}{20} and \frac{15}{8} to fractions with denominator 40.

$$\frac{102}{40}-\frac{75}{40}$$

Since \frac{102}{40} and \frac{75}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{102-75}{40}$$

Subtract 75 from 102 to get 27.

$$\frac{27}{40}$$

Factor

$$\frac{3 ^ {3}}{5 \cdot 2 ^ {3}} = 0.675$$