Solve -51/4-22/7+-6/721/33frac{1}{4}

$$-5 \frac{ 1 }{ 4 } -2 \frac{ 2 }{ 7 } +- \frac{ 6 }{ 7 } 2 \frac{ 1 }{ 3 } 3 \frac{ 1 }{ 4 }$$

Evaluate

$$-\frac{393}{28}\approx -14.035714286$$

Solution Steps

Multiply 5 and 4 to get 20.

$$-\frac{20+1}{4}-\frac{2\times 7+2}{7}-\frac{6}{7}\times \frac{2\times 3+1}{3}\times \frac{3\times 4+1}{4}$$

Add 20 and 1 to get 21.

$$-\frac{21}{4}-\frac{2\times 7+2}{7}-\frac{6}{7}\times \frac{2\times 3+1}{3}\times \frac{3\times 4+1}{4}$$

Multiply 2 and 7 to get 14.

$$-\frac{21}{4}-\frac{14+2}{7}-\frac{6}{7}\times \frac{2\times 3+1}{3}\times \frac{3\times 4+1}{4}$$

Add 14 and 2 to get 16.

$$-\frac{21}{4}-\frac{16}{7}-\frac{6}{7}\times \frac{2\times 3+1}{3}\times \frac{3\times 4+1}{4}$$

Least common multiple of 4 and 7 is 28. Convert -\frac{21}{4} and \frac{16}{7} to fractions with denominator 28.

$$-\frac{147}{28}-\frac{64}{28}-\frac{6}{7}\times \frac{2\times 3+1}{3}\times \frac{3\times 4+1}{4}$$

Since -\frac{147}{28} and \frac{64}{28} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-147-64}{28}-\frac{6}{7}\times \frac{2\times 3+1}{3}\times \frac{3\times 4+1}{4}$$

Subtract 64 from -147 to get -211.

$$-\frac{211}{28}-\frac{6}{7}\times \frac{2\times 3+1}{3}\times \frac{3\times 4+1}{4}$$

Multiply 2 and 3 to get 6.

$$-\frac{211}{28}-\frac{6}{7}\times \frac{6+1}{3}\times \frac{3\times 4+1}{4}$$

Add 6 and 1 to get 7.

$$-\frac{211}{28}-\frac{6}{7}\times \frac{7}{3}\times \frac{3\times 4+1}{4}$$

Multiply -\frac{6}{7} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{211}{28}+\frac{-6\times 7}{7\times 3}\times \frac{3\times 4+1}{4}$$

Cancel out 7 in both numerator and denominator.

$$-\frac{211}{28}+\frac{-6}{3}\times \frac{3\times 4+1}{4}$$

Divide -6 by 3 to get -2.

$$-\frac{211}{28}-2\times \frac{3\times 4+1}{4}$$

Multiply 3 and 4 to get 12.

$$-\frac{211}{28}-2\times \frac{12+1}{4}$$

Add 12 and 1 to get 13.

$$-\frac{211}{28}-2\times \frac{13}{4}$$

Express -2\times \frac{13}{4} as a single fraction.

$$-\frac{211}{28}+\frac{-2\times 13}{4}$$

Multiply -2 and 13 to get -26.

$$-\frac{211}{28}+\frac{-26}{4}$$

Reduce the fraction \frac{-26}{4} to lowest terms by extracting and canceling out 2.

$$-\frac{211}{28}-\frac{13}{2}$$

Least common multiple of 28 and 2 is 28. Convert -\frac{211}{28} and \frac{13}{2} to fractions with denominator 28.

$$-\frac{211}{28}-\frac{182}{28}$$

Since -\frac{211}{28} and \frac{182}{28} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-211-182}{28}$$

Subtract 182 from -211 to get -393.

$$-\frac{393}{28}$$

Factor

$$-\frac{393}{28} = -14\frac{1}{28} = -14.035714285714286$$