Solve 3/5+25/7(-3/12)+(-5/12)=?

$$\frac { 3 } { 5 } + \frac { 25 } { 7 } ( - \frac { 3 } { 12 } ) + ( - \frac { 5 } { 12 } ) = ?$$

Evaluate

$$-\frac{149}{210}\approx -0.70952381$$

Solution Steps

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

$$\frac{3}{5}+\frac{25}{7}\left(-\frac{1}{4}\right)-\frac{5}{12}$$

Multiply \frac{25}{7} times -\frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{5}+\frac{25\left(-1\right)}{7\times 4}-\frac{5}{12}$$

Do the multiplications in the fraction \frac{25\left(-1\right)}{7\times 4}.

$$\frac{3}{5}+\frac{-25}{28}-\frac{5}{12}$$

Fraction \frac{-25}{28} can be rewritten as -\frac{25}{28} by extracting the negative sign.

$$\frac{3}{5}-\frac{25}{28}-\frac{5}{12}$$

Least common multiple of 5 and 28 is 140. Convert \frac{3}{5} and \frac{25}{28} to fractions with denominator 140.

$$\frac{84}{140}-\frac{125}{140}-\frac{5}{12}$$

Since \frac{84}{140} and \frac{125}{140} have the same denominator, subtract them by subtracting their numerators.

$$\frac{84-125}{140}-\frac{5}{12}$$

Subtract 125 from 84 to get -41.

$$-\frac{41}{140}-\frac{5}{12}$$

Least common multiple of 140 and 12 is 420. Convert -\frac{41}{140} and \frac{5}{12} to fractions with denominator 420.

$$-\frac{123}{420}-\frac{175}{420}$$

Since -\frac{123}{420} and \frac{175}{420} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-123-175}{420}$$

Subtract 175 from -123 to get -298.

$$\frac{-298}{420}$$

Reduce the fraction \frac{-298}{420} to lowest terms by extracting and canceling out 2.

$$-\frac{149}{210}$$

Factor

$$-\frac{149}{210} = -0.7095238095238096$$