Solve 1/4(3/4+11/2)-12/5(1-frac{2}{7})

$$\frac { 1 } { 4 } ( \frac { 3 } { 4 } + 1 \frac { 1 } { 2 } ) - 1 \frac { 2 } { 5 } ( 1 - \frac { 2 } { 7 } )$$

Evaluate

$$-\frac{7}{16}=-0.4375$$

Solution Steps

Multiply 1 and 2 to get 2.

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

Add 2 and 1 to get 3.

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

Least common multiple of 4 and 2 is 4. Convert \frac{3}{4} and \frac{3}{2} to fractions with denominator 4.

$$\frac{1}{4}\left(\frac{3}{4}+\frac{6}{4}\right)-\frac{1\times 5+2}{5}\left(1-\frac{2}{7}\right)$$

Since \frac{3}{4} and \frac{6}{4} have the same denominator, add them by adding their numerators.

$$\frac{1}{4}\times \frac{3+6}{4}-\frac{1\times 5+2}{5}\left(1-\frac{2}{7}\right)$$

Add 3 and 6 to get 9.

$$\frac{1}{4}\times \frac{9}{4}-\frac{1\times 5+2}{5}\left(1-\frac{2}{7}\right)$$

Multiply \frac{1}{4} times \frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 9}{4\times 4}-\frac{1\times 5+2}{5}\left(1-\frac{2}{7}\right)$$

Do the multiplications in the fraction \frac{1\times 9}{4\times 4}.

$$\frac{9}{16}-\frac{1\times 5+2}{5}\left(1-\frac{2}{7}\right)$$

Multiply 1 and 5 to get 5.

$$\frac{9}{16}-\frac{5+2}{5}\left(1-\frac{2}{7}\right)$$

Add 5 and 2 to get 7.

$$\frac{9}{16}-\frac{7}{5}\left(1-\frac{2}{7}\right)$$

Convert 1 to fraction \frac{7}{7}.

$$\frac{9}{16}-\frac{7}{5}\left(\frac{7}{7}-\frac{2}{7}\right)$$

Since \frac{7}{7} and \frac{2}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9}{16}-\frac{7}{5}\times \frac{7-2}{7}$$

Subtract 2 from 7 to get 5.

$$\frac{9}{16}-\frac{7}{5}\times \frac{5}{7}$$

Cancel out \frac{7}{5} and its reciprocal \frac{5}{7}.

$$\frac{9}{16}-1$$

Convert 1 to fraction \frac{16}{16}.

$$\frac{9}{16}-\frac{16}{16}$$

Since \frac{9}{16} and \frac{16}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-16}{16}$$

Subtract 16 from 9 to get -7.

$$-\frac{7}{16}$$

Factor

$$-\frac{7}{16} = -0.4375$$