Solve 3/4-[5/10*110/7-2/4]}

$$\frac { 3 } { 4 } - [ \frac { 5 } { 10 } \times 1 \frac { 10 } { 7 } - \frac { 2 } { 4 } ] \}$$

Evaluate

$$\frac{1}{28}\approx 0.035714286$$

Solution Steps

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{3}{4}-\left(\frac{1}{2}\times \frac{1\times 7+10}{7}-\frac{2}{4}\right)$$

Multiply 1 and 7 to get 7.

$$\frac{3}{4}-\left(\frac{1}{2}\times \frac{7+10}{7}-\frac{2}{4}\right)$$

Add 7 and 10 to get 17.

$$\frac{3}{4}-\left(\frac{1}{2}\times \frac{17}{7}-\frac{2}{4}\right)$$

Multiply \frac{1}{2} times \frac{17}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{4}-\left(\frac{1\times 17}{2\times 7}-\frac{2}{4}\right)$$

Do the multiplications in the fraction \frac{1\times 17}{2\times 7}.

$$\frac{3}{4}-\left(\frac{17}{14}-\frac{2}{4}\right)$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{3}{4}-\left(\frac{17}{14}-\frac{1}{2}\right)$$

Least common multiple of 14 and 2 is 14. Convert \frac{17}{14} and \frac{1}{2} to fractions with denominator 14.

$$\frac{3}{4}-\left(\frac{17}{14}-\frac{7}{14}\right)$$

Since \frac{17}{14} and \frac{7}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{4}-\frac{17-7}{14}$$

Subtract 7 from 17 to get 10.

$$\frac{3}{4}-\frac{10}{14}$$

Reduce the fraction \frac{10}{14} to lowest terms by extracting and canceling out 2.

$$\frac{3}{4}-\frac{5}{7}$$

Least common multiple of 4 and 7 is 28. Convert \frac{3}{4} and \frac{5}{7} to fractions with denominator 28.

$$\frac{21}{28}-\frac{20}{28}$$

Since \frac{21}{28} and \frac{20}{28} have the same denominator, subtract them by subtracting their numerators.

$$\frac{21-20}{28}$$

Subtract 20 from 21 to get 1.

$$\frac{1}{28}$$

Factor

$$\frac{1}{2 ^ {2} \cdot 7} = 0.03571428571428571$$