Solve -(z-7)+[0.2*(1-1/2)]+5/4

$$- ( z - 7 ) + [ 0.2 \times ( 1 - \frac { 1 } { 2 } ) ] + \frac { 5 } { 4 }$$

Evaluate

$$8.35-z$$

Solution Steps

To find the opposite of z-7, find the opposite of each term.

$$-z-\left(-7\right)+0.2\left(1-\frac{1}{2}\right)+\frac{5}{4}$$

The opposite of -7 is 7.

$$-z+7+0.2\left(1-\frac{1}{2}\right)+\frac{5}{4}$$

Convert 1 to fraction \frac{2}{2}.

$$-z+7+0.2\left(\frac{2}{2}-\frac{1}{2}\right)+\frac{5}{4}$$

Since \frac{2}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$-z+7+0.2\times \frac{2-1}{2}+\frac{5}{4}$$

Subtract 1 from 2 to get 1.

$$-z+7+0.2\times \frac{1}{2}+\frac{5}{4}$$

Convert decimal number 0.2 to fraction \frac{2}{10}. Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$-z+7+\frac{1}{5}\times \frac{1}{2}+\frac{5}{4}$$

Multiply \frac{1}{5} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$-z+7+\frac{1\times 1}{5\times 2}+\frac{5}{4}$$

Do the multiplications in the fraction \frac{1\times 1}{5\times 2}.

$$-z+7+\frac{1}{10}+\frac{5}{4}$$

Convert 7 to fraction \frac{70}{10}.

$$-z+\frac{70}{10}+\frac{1}{10}+\frac{5}{4}$$

Since \frac{70}{10} and \frac{1}{10} have the same denominator, add them by adding their numerators.

$$-z+\frac{70+1}{10}+\frac{5}{4}$$

Add 70 and 1 to get 71.

$$-z+\frac{71}{10}+\frac{5}{4}$$

Least common multiple of 10 and 4 is 20. Convert \frac{71}{10} and \frac{5}{4} to fractions with denominator 20.

$$-z+\frac{142}{20}+\frac{25}{20}$$

Since \frac{142}{20} and \frac{25}{20} have the same denominator, add them by adding their numerators.

$$-z+\frac{142+25}{20}$$

Add 142 and 25 to get 167.

$$-z+\frac{167}{20}$$

Expand

$$8.35-z$$

Solution Steps

To find the opposite of z-7, find the opposite of each term.

$$-z-\left(-7\right)+0.2\left(1-\frac{1}{2}\right)+\frac{5}{4}$$

The opposite of -7 is 7.

$$-z+7+0.2\left(1-\frac{1}{2}\right)+\frac{5}{4}$$

Convert 1 to fraction \frac{2}{2}.

$$-z+7+0.2\left(\frac{2}{2}-\frac{1}{2}\right)+\frac{5}{4}$$

Since \frac{2}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$-z+7+0.2\times \frac{2-1}{2}+\frac{5}{4}$$

Subtract 1 from 2 to get 1.

$$-z+7+0.2\times \frac{1}{2}+\frac{5}{4}$$

Convert decimal number 0.2 to fraction \frac{2}{10}. Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$-z+7+\frac{1}{5}\times \frac{1}{2}+\frac{5}{4}$$

Multiply \frac{1}{5} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$-z+7+\frac{1\times 1}{5\times 2}+\frac{5}{4}$$

Do the multiplications in the fraction \frac{1\times 1}{5\times 2}.

$$-z+7+\frac{1}{10}+\frac{5}{4}$$

Convert 7 to fraction \frac{70}{10}.

$$-z+\frac{70}{10}+\frac{1}{10}+\frac{5}{4}$$

Since \frac{70}{10} and \frac{1}{10} have the same denominator, add them by adding their numerators.

$$-z+\frac{70+1}{10}+\frac{5}{4}$$

Add 70 and 1 to get 71.

$$-z+\frac{71}{10}+\frac{5}{4}$$

Least common multiple of 10 and 4 is 20. Convert \frac{71}{10} and \frac{5}{4} to fractions with denominator 20.

$$-z+\frac{142}{20}+\frac{25}{20}$$

Since \frac{142}{20} and \frac{25}{20} have the same denominator, add them by adding their numerators.

$$-z+\frac{142+25}{20}$$

Add 142 and 25 to get 167.

$$-z+\frac{167}{20}$$