Solve 3/5(21/3a-21/2)-1/2(2frac{1}{5}a+3frac{2}{3})

$$\frac { 3 } { 5 } ( 2 \frac { 1 } { 3 } a - 2 \frac { 1 } { 2 } ) - \frac { 1 } { 2 } ( 2 \frac { 1 } { 5 } a + 3 \frac { 2 } { 3 } )$$

Evaluate

$$\frac{3a}{10}-\frac{10}{3}$$

Solution Steps

Multiply 2 and 3 to get 6.

$$\frac{3}{5}\left(\frac{6+1}{3}a-\frac{2\times 2+1}{2}\right)-\frac{1}{2}\left(\frac{2\times 5+1}{5}a+\frac{3\times 3+2}{3}\right)$$

Add 6 and 1 to get 7.

$$\frac{3}{5}\left(\frac{7}{3}a-\frac{2\times 2+1}{2}\right)-\frac{1}{2}\left(\frac{2\times 5+1}{5}a+\frac{3\times 3+2}{3}\right)$$

Multiply 2 and 2 to get 4.

$$\frac{3}{5}\left(\frac{7}{3}a-\frac{4+1}{2}\right)-\frac{1}{2}\left(\frac{2\times 5+1}{5}a+\frac{3\times 3+2}{3}\right)$$

Add 4 and 1 to get 5.

$$\frac{3}{5}\left(\frac{7}{3}a-\frac{5}{2}\right)-\frac{1}{2}\left(\frac{2\times 5+1}{5}a+\frac{3\times 3+2}{3}\right)$$

Use the distributive property to multiply \frac{3}{5} by \frac{7}{3}a-\frac{5}{2}.

$$\frac{3}{5}\times \frac{7}{3}a+\frac{3}{5}\left(-\frac{5}{2}\right)-\frac{1}{2}\left(\frac{2\times 5+1}{5}a+\frac{3\times 3+2}{3}\right)$$

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

$$\frac{3\times 7}{5\times 3}a+\frac{3}{5}\left(-\frac{5}{2}\right)-\frac{1}{2}\left(\frac{2\times 5+1}{5}a+\frac{3\times 3+2}{3}\right)$$

Cancel out 3 in both numerator and denominator.

$$\frac{7}{5}a+\frac{3}{5}\left(-\frac{5}{2}\right)-\frac{1}{2}\left(\frac{2\times 5+1}{5}a+\frac{3\times 3+2}{3}\right)$$

Multiply \frac{3}{5} times -\frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{5}a+\frac{3\left(-5\right)}{5\times 2}-\frac{1}{2}\left(\frac{2\times 5+1}{5}a+\frac{3\times 3+2}{3}\right)$$

Do the multiplications in the fraction \frac{3\left(-5\right)}{5\times 2}.

$$\frac{7}{5}a+\frac{-15}{10}-\frac{1}{2}\left(\frac{2\times 5+1}{5}a+\frac{3\times 3+2}{3}\right)$$

Reduce the fraction \frac{-15}{10} to lowest terms by extracting and canceling out 5.

$$\frac{7}{5}a-\frac{3}{2}-\frac{1}{2}\left(\frac{2\times 5+1}{5}a+\frac{3\times 3+2}{3}\right)$$

Multiply 2 and 5 to get 10.

$$\frac{7}{5}a-\frac{3}{2}-\frac{1}{2}\left(\frac{10+1}{5}a+\frac{3\times 3+2}{3}\right)$$

Add 10 and 1 to get 11.

$$\frac{7}{5}a-\frac{3}{2}-\frac{1}{2}\left(\frac{11}{5}a+\frac{3\times 3+2}{3}\right)$$

Multiply 3 and 3 to get 9.

$$\frac{7}{5}a-\frac{3}{2}-\frac{1}{2}\left(\frac{11}{5}a+\frac{9+2}{3}\right)$$

Add 9 and 2 to get 11.

$$\frac{7}{5}a-\frac{3}{2}-\frac{1}{2}\left(\frac{11}{5}a+\frac{11}{3}\right)$$

Use the distributive property to multiply -\frac{1}{2} by \frac{11}{5}a+\frac{11}{3}.

$$\frac{7}{5}a-\frac{3}{2}-\frac{1}{2}\times \frac{11}{5}a-\frac{1}{2}\times \frac{11}{3}$$

Multiply -\frac{1}{2} times \frac{11}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{5}a-\frac{3}{2}+\frac{-11}{2\times 5}a-\frac{1}{2}\times \frac{11}{3}$$

Do the multiplications in the fraction \frac{-11}{2\times 5}.

$$\frac{7}{5}a-\frac{3}{2}+\frac{-11}{10}a-\frac{1}{2}\times \frac{11}{3}$$

Fraction \frac{-11}{10} can be rewritten as -\frac{11}{10} by extracting the negative sign.

$$\frac{7}{5}a-\frac{3}{2}-\frac{11}{10}a-\frac{1}{2}\times \frac{11}{3}$$

Multiply -\frac{1}{2} times \frac{11}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{5}a-\frac{3}{2}-\frac{11}{10}a+\frac{-11}{2\times 3}$$

Do the multiplications in the fraction \frac{-11}{2\times 3}.

$$\frac{7}{5}a-\frac{3}{2}-\frac{11}{10}a+\frac{-11}{6}$$

Fraction \frac{-11}{6} can be rewritten as -\frac{11}{6} by extracting the negative sign.

$$\frac{7}{5}a-\frac{3}{2}-\frac{11}{10}a-\frac{11}{6}$$

Combine \frac{7}{5}a and -\frac{11}{10}a to get \frac{3}{10}a.

$$\frac{3}{10}a-\frac{3}{2}-\frac{11}{6}$$

Least common multiple of 2 and 6 is 6. Convert -\frac{3}{2} and \frac{11}{6} to fractions with denominator 6.

$$\frac{3}{10}a-\frac{9}{6}-\frac{11}{6}$$

Since -\frac{9}{6} and \frac{11}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{10}a+\frac{-9-11}{6}$$

Subtract 11 from -9 to get -20.

$$\frac{3}{10}a+\frac{-20}{6}$$

Reduce the fraction \frac{-20}{6} to lowest terms by extracting and canceling out 2.

$$\frac{3}{10}a-\frac{10}{3}$$

Expand

$$\frac{3a}{10}-\frac{10}{3}$$

Solution Steps

Multiply 2 and 3 to get 6.

$$\frac{3}{5}\left(\frac{6+1}{3}a-\frac{2\times 2+1}{2}\right)-\frac{1}{2}\left(\frac{2\times 5+1}{5}a+\frac{3\times 3+2}{3}\right)$$

Add 6 and 1 to get 7.

$$\frac{3}{5}\left(\frac{7}{3}a-\frac{2\times 2+1}{2}\right)-\frac{1}{2}\left(\frac{2\times 5+1}{5}a+\frac{3\times 3+2}{3}\right)$$

Multiply 2 and 2 to get 4.

$$\frac{3}{5}\left(\frac{7}{3}a-\frac{4+1}{2}\right)-\frac{1}{2}\left(\frac{2\times 5+1}{5}a+\frac{3\times 3+2}{3}\right)$$

Add 4 and 1 to get 5.

$$\frac{3}{5}\left(\frac{7}{3}a-\frac{5}{2}\right)-\frac{1}{2}\left(\frac{2\times 5+1}{5}a+\frac{3\times 3+2}{3}\right)$$

Use the distributive property to multiply \frac{3}{5} by \frac{7}{3}a-\frac{5}{2}.

$$\frac{3}{5}\times \frac{7}{3}a+\frac{3}{5}\left(-\frac{5}{2}\right)-\frac{1}{2}\left(\frac{2\times 5+1}{5}a+\frac{3\times 3+2}{3}\right)$$

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

$$\frac{3\times 7}{5\times 3}a+\frac{3}{5}\left(-\frac{5}{2}\right)-\frac{1}{2}\left(\frac{2\times 5+1}{5}a+\frac{3\times 3+2}{3}\right)$$

Cancel out 3 in both numerator and denominator.

$$\frac{7}{5}a+\frac{3}{5}\left(-\frac{5}{2}\right)-\frac{1}{2}\left(\frac{2\times 5+1}{5}a+\frac{3\times 3+2}{3}\right)$$

Multiply \frac{3}{5} times -\frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{5}a+\frac{3\left(-5\right)}{5\times 2}-\frac{1}{2}\left(\frac{2\times 5+1}{5}a+\frac{3\times 3+2}{3}\right)$$

Do the multiplications in the fraction \frac{3\left(-5\right)}{5\times 2}.

$$\frac{7}{5}a+\frac{-15}{10}-\frac{1}{2}\left(\frac{2\times 5+1}{5}a+\frac{3\times 3+2}{3}\right)$$

Reduce the fraction \frac{-15}{10} to lowest terms by extracting and canceling out 5.

$$\frac{7}{5}a-\frac{3}{2}-\frac{1}{2}\left(\frac{2\times 5+1}{5}a+\frac{3\times 3+2}{3}\right)$$

Multiply 2 and 5 to get 10.

$$\frac{7}{5}a-\frac{3}{2}-\frac{1}{2}\left(\frac{10+1}{5}a+\frac{3\times 3+2}{3}\right)$$

Add 10 and 1 to get 11.

$$\frac{7}{5}a-\frac{3}{2}-\frac{1}{2}\left(\frac{11}{5}a+\frac{3\times 3+2}{3}\right)$$

Multiply 3 and 3 to get 9.

$$\frac{7}{5}a-\frac{3}{2}-\frac{1}{2}\left(\frac{11}{5}a+\frac{9+2}{3}\right)$$

Add 9 and 2 to get 11.

$$\frac{7}{5}a-\frac{3}{2}-\frac{1}{2}\left(\frac{11}{5}a+\frac{11}{3}\right)$$

Use the distributive property to multiply -\frac{1}{2} by \frac{11}{5}a+\frac{11}{3}.

$$\frac{7}{5}a-\frac{3}{2}-\frac{1}{2}\times \frac{11}{5}a-\frac{1}{2}\times \frac{11}{3}$$

Multiply -\frac{1}{2} times \frac{11}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{5}a-\frac{3}{2}+\frac{-11}{2\times 5}a-\frac{1}{2}\times \frac{11}{3}$$

Do the multiplications in the fraction \frac{-11}{2\times 5}.

$$\frac{7}{5}a-\frac{3}{2}+\frac{-11}{10}a-\frac{1}{2}\times \frac{11}{3}$$

Fraction \frac{-11}{10} can be rewritten as -\frac{11}{10} by extracting the negative sign.

$$\frac{7}{5}a-\frac{3}{2}-\frac{11}{10}a-\frac{1}{2}\times \frac{11}{3}$$

Multiply -\frac{1}{2} times \frac{11}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{5}a-\frac{3}{2}-\frac{11}{10}a+\frac{-11}{2\times 3}$$

Do the multiplications in the fraction \frac{-11}{2\times 3}.

$$\frac{7}{5}a-\frac{3}{2}-\frac{11}{10}a+\frac{-11}{6}$$

Fraction \frac{-11}{6} can be rewritten as -\frac{11}{6} by extracting the negative sign.

$$\frac{7}{5}a-\frac{3}{2}-\frac{11}{10}a-\frac{11}{6}$$

Combine \frac{7}{5}a and -\frac{11}{10}a to get \frac{3}{10}a.

$$\frac{3}{10}a-\frac{3}{2}-\frac{11}{6}$$

Least common multiple of 2 and 6 is 6. Convert -\frac{3}{2} and \frac{11}{6} to fractions with denominator 6.

$$\frac{3}{10}a-\frac{9}{6}-\frac{11}{6}$$

Since -\frac{9}{6} and \frac{11}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{10}a+\frac{-9-11}{6}$$

Subtract 11 from -9 to get -20.

$$\frac{3}{10}a+\frac{-20}{6}$$

Reduce the fraction \frac{-20}{6} to lowest terms by extracting and canceling out 2.

$$\frac{3}{10}a-\frac{10}{3}$$