Solve 53/7+(-27/4)-(-33/28)=

$$5 \frac { 3 } { 7 } + ( - 2 \frac { 7 } { 4 } ) - ( - 3 \frac { 3 } { 28 } ) =$$

Evaluate

$$\frac{67}{14}\approx 4.785714286$$

Solution Steps

Multiply 5 and 7 to get 35.

$$\frac{35+3}{7}-\frac{2\times 4+7}{4}-\left(-\frac{3\times 28+3}{28}\right)$$

Add 35 and 3 to get 38.

$$\frac{38}{7}-\frac{2\times 4+7}{4}-\left(-\frac{3\times 28+3}{28}\right)$$

Multiply 2 and 4 to get 8.

$$\frac{38}{7}-\frac{8+7}{4}-\left(-\frac{3\times 28+3}{28}\right)$$

Add 8 and 7 to get 15.

$$\frac{38}{7}-\frac{15}{4}-\left(-\frac{3\times 28+3}{28}\right)$$

Least common multiple of 7 and 4 is 28. Convert \frac{38}{7} and \frac{15}{4} to fractions with denominator 28.

$$\frac{152}{28}-\frac{105}{28}-\left(-\frac{3\times 28+3}{28}\right)$$

Since \frac{152}{28} and \frac{105}{28} have the same denominator, subtract them by subtracting their numerators.

$$\frac{152-105}{28}-\left(-\frac{3\times 28+3}{28}\right)$$

Subtract 105 from 152 to get 47.

$$\frac{47}{28}-\left(-\frac{3\times 28+3}{28}\right)$$

Multiply 3 and 28 to get 84.

$$\frac{47}{28}-\left(-\frac{84+3}{28}\right)$$

Add 84 and 3 to get 87.

$$\frac{47}{28}-\left(-\frac{87}{28}\right)$$

The opposite of -\frac{87}{28} is \frac{87}{28}.

$$\frac{47}{28}+\frac{87}{28}$$

Since \frac{47}{28} and \frac{87}{28} have the same denominator, add them by adding their numerators.

$$\frac{47+87}{28}$$

Add 47 and 87 to get 134.

$$\frac{134}{28}$$

Reduce the fraction \frac{134}{28} to lowest terms by extracting and canceling out 2.

$$\frac{67}{14}$$

Factor

$$\frac{67}{2 \cdot 7} = 4\frac{11}{14} = 4.785714285714286$$