Solve -53/4+23/7-11/4-(-4/7)

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

Evaluate

$$-4$$

Solution Steps

Multiply 5 and 4 to get 20.

$$-\frac{20+3}{4}+\frac{2\times 7+3}{7}-\frac{1\times 4+1}{4}-\left(-\frac{4}{7}\right)$$

Add 20 and 3 to get 23.

$$-\frac{23}{4}+\frac{2\times 7+3}{7}-\frac{1\times 4+1}{4}-\left(-\frac{4}{7}\right)$$

Multiply 2 and 7 to get 14.

$$-\frac{23}{4}+\frac{14+3}{7}-\frac{1\times 4+1}{4}-\left(-\frac{4}{7}\right)$$

Add 14 and 3 to get 17.

$$-\frac{23}{4}+\frac{17}{7}-\frac{1\times 4+1}{4}-\left(-\frac{4}{7}\right)$$

Least common multiple of 4 and 7 is 28. Convert -\frac{23}{4} and \frac{17}{7} to fractions with denominator 28.

$$-\frac{161}{28}+\frac{68}{28}-\frac{1\times 4+1}{4}-\left(-\frac{4}{7}\right)$$

Since -\frac{161}{28} and \frac{68}{28} have the same denominator, add them by adding their numerators.

$$\frac{-161+68}{28}-\frac{1\times 4+1}{4}-\left(-\frac{4}{7}\right)$$

Add -161 and 68 to get -93.

$$-\frac{93}{28}-\frac{1\times 4+1}{4}-\left(-\frac{4}{7}\right)$$

Multiply 1 and 4 to get 4.

$$-\frac{93}{28}-\frac{4+1}{4}-\left(-\frac{4}{7}\right)$$

Add 4 and 1 to get 5.

$$-\frac{93}{28}-\frac{5}{4}-\left(-\frac{4}{7}\right)$$

Least common multiple of 28 and 4 is 28. Convert -\frac{93}{28} and \frac{5}{4} to fractions with denominator 28.

$$-\frac{93}{28}-\frac{35}{28}-\left(-\frac{4}{7}\right)$$

Since -\frac{93}{28} and \frac{35}{28} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-93-35}{28}-\left(-\frac{4}{7}\right)$$

Subtract 35 from -93 to get -128.

$$\frac{-128}{28}-\left(-\frac{4}{7}\right)$$

Reduce the fraction \frac{-128}{28} to lowest terms by extracting and canceling out 4.

$$-\frac{32}{7}-\left(-\frac{4}{7}\right)$$

The opposite of -\frac{4}{7} is \frac{4}{7}.

$$-\frac{32}{7}+\frac{4}{7}$$

Since -\frac{32}{7} and \frac{4}{7} have the same denominator, add them by adding their numerators.

$$\frac{-32+4}{7}$$

Add -32 and 4 to get -28.

$$\frac{-28}{7}$$

Divide -28 by 7 to get -4.

$$-4$$

Factor

$$-4$$