Solve 13/7*6(-14-7/9y+21/3)=

$$1 \frac { 3 } { 7 } \cdot 6 ( - 14 - \frac { 7 } { 9 } y + 2 \frac { 1 } { 3 } ) =$$

Evaluate

$$-\frac{20y}{3}-100$$

Solution Steps

Multiply 1 and 7 to get 7.

$$\frac{7+3}{7}\times 6\left(-14-\frac{7}{9}y+\frac{2\times 3+1}{3}\right)$$

Add 7 and 3 to get 10.

$$\frac{10}{7}\times 6\left(-14-\frac{7}{9}y+\frac{2\times 3+1}{3}\right)$$

Express \frac{10}{7}\times 6 as a single fraction.

$$\frac{10\times 6}{7}\left(-14-\frac{7}{9}y+\frac{2\times 3+1}{3}\right)$$

Multiply 10 and 6 to get 60.

$$\frac{60}{7}\left(-14-\frac{7}{9}y+\frac{2\times 3+1}{3}\right)$$

Multiply 2 and 3 to get 6.

$$\frac{60}{7}\left(-14-\frac{7}{9}y+\frac{6+1}{3}\right)$$

Add 6 and 1 to get 7.

$$\frac{60}{7}\left(-14-\frac{7}{9}y+\frac{7}{3}\right)$$

Convert -14 to fraction -\frac{42}{3}.

$$\frac{60}{7}\left(-\frac{42}{3}-\frac{7}{9}y+\frac{7}{3}\right)$$

Since -\frac{42}{3} and \frac{7}{3} have the same denominator, add them by adding their numerators.

$$\frac{60}{7}\left(\frac{-42+7}{3}-\frac{7}{9}y\right)$$

Add -42 and 7 to get -35.

$$\frac{60}{7}\left(-\frac{35}{3}-\frac{7}{9}y\right)$$

Use the distributive property to multiply \frac{60}{7} by -\frac{35}{3}-\frac{7}{9}y.

$$\frac{60}{7}\left(-\frac{35}{3}\right)+\frac{60}{7}\left(-\frac{7}{9}\right)y$$

Multiply \frac{60}{7} times -\frac{35}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{60\left(-35\right)}{7\times 3}+\frac{60}{7}\left(-\frac{7}{9}\right)y$$

Do the multiplications in the fraction \frac{60\left(-35\right)}{7\times 3}.

$$\frac{-2100}{21}+\frac{60}{7}\left(-\frac{7}{9}\right)y$$

Divide -2100 by 21 to get -100.

$$-100+\frac{60}{7}\left(-\frac{7}{9}\right)y$$

Multiply \frac{60}{7} times -\frac{7}{9} by multiplying numerator times numerator and denominator times denominator.

$$-100+\frac{60\left(-7\right)}{7\times 9}y$$

Do the multiplications in the fraction \frac{60\left(-7\right)}{7\times 9}.

$$-100+\frac{-420}{63}y$$

Reduce the fraction \frac{-420}{63} to lowest terms by extracting and canceling out 21.

$$-100-\frac{20}{3}y$$

Expand

$$-\frac{20y}{3}-100$$

Solution Steps

Multiply 1 and 7 to get 7.

$$\frac{7+3}{7}\times 6\left(-14-\frac{7}{9}y+\frac{2\times 3+1}{3}\right)$$

Add 7 and 3 to get 10.

$$\frac{10}{7}\times 6\left(-14-\frac{7}{9}y+\frac{2\times 3+1}{3}\right)$$

Express \frac{10}{7}\times 6 as a single fraction.

$$\frac{10\times 6}{7}\left(-14-\frac{7}{9}y+\frac{2\times 3+1}{3}\right)$$

Multiply 10 and 6 to get 60.

$$\frac{60}{7}\left(-14-\frac{7}{9}y+\frac{2\times 3+1}{3}\right)$$

Multiply 2 and 3 to get 6.

$$\frac{60}{7}\left(-14-\frac{7}{9}y+\frac{6+1}{3}\right)$$

Add 6 and 1 to get 7.

$$\frac{60}{7}\left(-14-\frac{7}{9}y+\frac{7}{3}\right)$$

Convert -14 to fraction -\frac{42}{3}.

$$\frac{60}{7}\left(-\frac{42}{3}-\frac{7}{9}y+\frac{7}{3}\right)$$

Since -\frac{42}{3} and \frac{7}{3} have the same denominator, add them by adding their numerators.

$$\frac{60}{7}\left(\frac{-42+7}{3}-\frac{7}{9}y\right)$$

Add -42 and 7 to get -35.

$$\frac{60}{7}\left(-\frac{35}{3}-\frac{7}{9}y\right)$$

Use the distributive property to multiply \frac{60}{7} by -\frac{35}{3}-\frac{7}{9}y.

$$\frac{60}{7}\left(-\frac{35}{3}\right)+\frac{60}{7}\left(-\frac{7}{9}\right)y$$

Multiply \frac{60}{7} times -\frac{35}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{60\left(-35\right)}{7\times 3}+\frac{60}{7}\left(-\frac{7}{9}\right)y$$

Do the multiplications in the fraction \frac{60\left(-35\right)}{7\times 3}.

$$\frac{-2100}{21}+\frac{60}{7}\left(-\frac{7}{9}\right)y$$

Divide -2100 by 21 to get -100.

$$-100+\frac{60}{7}\left(-\frac{7}{9}\right)y$$

Multiply \frac{60}{7} times -\frac{7}{9} by multiplying numerator times numerator and denominator times denominator.

$$-100+\frac{60\left(-7\right)}{7\times 9}y$$

Do the multiplications in the fraction \frac{60\left(-7\right)}{7\times 9}.

$$-100+\frac{-420}{63}y$$

Reduce the fraction \frac{-420}{63} to lowest terms by extracting and canceling out 21.

$$-100-\frac{20}{3}y$$