Solve -53/7*4/6-3/7*4/5

$$- 5 \frac { 3 } { 7 } \cdot \frac { 4 } { 6 } - \frac { 3 } { 7 } \cdot \frac { 4 } { 5 }$$

Evaluate

$$-\frac{416}{105}\approx -3.961904762$$

Solution Steps

Multiply 5 and 7 to get 35.

$$\left(-\frac{35+3}{7}\right)\times \frac{4}{6}-\frac{3}{7}\times \frac{4}{5}$$

Add 35 and 3 to get 38.

$$-\frac{38}{7}\times \frac{4}{6}-\frac{3}{7}\times \frac{4}{5}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{38}{7}\times \frac{2}{3}-\frac{3}{7}\times \frac{4}{5}$$

Multiply -\frac{38}{7} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-38\times 2}{7\times 3}-\frac{3}{7}\times \frac{4}{5}$$

Do the multiplications in the fraction \frac{-38\times 2}{7\times 3}.

$$\frac{-76}{21}-\frac{3}{7}\times \frac{4}{5}$$

Fraction \frac{-76}{21} can be rewritten as -\frac{76}{21} by extracting the negative sign.

$$-\frac{76}{21}-\frac{3}{7}\times \frac{4}{5}$$

Multiply \frac{3}{7} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{76}{21}-\frac{3\times 4}{7\times 5}$$

Do the multiplications in the fraction \frac{3\times 4}{7\times 5}.

$$-\frac{76}{21}-\frac{12}{35}$$

Least common multiple of 21 and 35 is 105. Convert -\frac{76}{21} and \frac{12}{35} to fractions with denominator 105.

$$-\frac{380}{105}-\frac{36}{105}$$

Since -\frac{380}{105} and \frac{36}{105} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-380-36}{105}$$

Subtract 36 from -380 to get -416.

$$-\frac{416}{105}$$

Factor

$$-\frac{416}{105} = -3\frac{101}{105} = -3.961904761904762$$