Solve 15/-4-1/3div71/3/(frac{1{10})^2}-3divfrac{1}{100}

$$\frac { \frac { 15 } { - 4 } - \frac { 1 } { 3 } \div \frac { 71 } { 3 } } { ( \frac { 1 } { 10 } ) ^ { 2 } } - 3 \div \frac { 1 } { 100 }$$

Evaluate

$$-\frac{48025}{71}\approx -676.408450704$$

Solution Steps

Fraction \frac{15}{-4} can be rewritten as -\frac{15}{4} by extracting the negative sign.

$$\frac{-\frac{15}{4}-\frac{\frac{1}{3}}{\frac{71}{3}}}{\left(\frac{1}{10}\right)^{2}}-\frac{3}{\frac{1}{100}}$$

Divide \frac{1}{3} by \frac{71}{3} by multiplying \frac{1}{3} by the reciprocal of \frac{71}{3}.

$$\frac{-\frac{15}{4}-\frac{1}{3}\times \frac{3}{71}}{\left(\frac{1}{10}\right)^{2}}-\frac{3}{\frac{1}{100}}$$

Multiply \frac{1}{3} times \frac{3}{71} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\frac{15}{4}-\frac{1\times 3}{3\times 71}}{\left(\frac{1}{10}\right)^{2}}-\frac{3}{\frac{1}{100}}$$

Cancel out 3 in both numerator and denominator.

$$\frac{-\frac{15}{4}-\frac{1}{71}}{\left(\frac{1}{10}\right)^{2}}-\frac{3}{\frac{1}{100}}$$

Least common multiple of 4 and 71 is 284. Convert -\frac{15}{4} and \frac{1}{71} to fractions with denominator 284.

$$\frac{-\frac{1065}{284}-\frac{4}{284}}{\left(\frac{1}{10}\right)^{2}}-\frac{3}{\frac{1}{100}}$$

Since -\frac{1065}{284} and \frac{4}{284} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{-1065-4}{284}}{\left(\frac{1}{10}\right)^{2}}-\frac{3}{\frac{1}{100}}$$

Subtract 4 from -1065 to get -1069.

$$\frac{-\frac{1069}{284}}{\left(\frac{1}{10}\right)^{2}}-\frac{3}{\frac{1}{100}}$$

Calculate \frac{1}{10} to the power of 2 and get \frac{1}{100}.

$$\frac{-\frac{1069}{284}}{\frac{1}{100}}-\frac{3}{\frac{1}{100}}$$

Divide -\frac{1069}{284} by \frac{1}{100} by multiplying -\frac{1069}{284} by the reciprocal of \frac{1}{100}.

$$-\frac{1069}{284}\times 100-\frac{3}{\frac{1}{100}}$$

Express -\frac{1069}{284}\times 100 as a single fraction.

$$\frac{-1069\times 100}{284}-\frac{3}{\frac{1}{100}}$$

Multiply -1069 and 100 to get -106900.

$$\frac{-106900}{284}-\frac{3}{\frac{1}{100}}$$

Reduce the fraction \frac{-106900}{284} to lowest terms by extracting and canceling out 4.

$$-\frac{26725}{71}-\frac{3}{\frac{1}{100}}$$

Divide 3 by \frac{1}{100} by multiplying 3 by the reciprocal of \frac{1}{100}.

$$-\frac{26725}{71}-3\times 100$$

Multiply 3 and 100 to get 300.

$$-\frac{26725}{71}-300$$

Convert 300 to fraction \frac{21300}{71}.

$$-\frac{26725}{71}-\frac{21300}{71}$$

Since -\frac{26725}{71} and \frac{21300}{71} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-26725-21300}{71}$$

Subtract 21300 from -26725 to get -48025.

$$-\frac{48025}{71}$$

Factor

$$-\frac{48025}{71} = -676\frac{29}{71} = -676.4084507042254$$