Solve -12(5/6a-7/8)+1/14(31/2a-1frac{2}{5})

$$- 12 ( \frac { 5 } { 6 } a - \frac { 7 } { 8 } ) + \frac { 1 } { 14 } ( 3 \frac { 1 } { 2 } a - 1 \frac { 2 } { 5 } )$$

Evaluate

$$-\frac{39a}{4}+\frac{52}{5}$$

Solution Steps

Use the distributive property to multiply -12 by \frac{5}{6}a-\frac{7}{8}.

$$-12\times \frac{5}{6}a-12\left(-\frac{7}{8}\right)+\frac{1}{14}\left(\frac{3\times 2+1}{2}a-\frac{1\times 5+2}{5}\right)$$

Express -12\times \frac{5}{6} as a single fraction.

$$\frac{-12\times 5}{6}a-12\left(-\frac{7}{8}\right)+\frac{1}{14}\left(\frac{3\times 2+1}{2}a-\frac{1\times 5+2}{5}\right)$$

Multiply -12 and 5 to get -60.

$$\frac{-60}{6}a-12\left(-\frac{7}{8}\right)+\frac{1}{14}\left(\frac{3\times 2+1}{2}a-\frac{1\times 5+2}{5}\right)$$

Divide -60 by 6 to get -10.

$$-10a-12\left(-\frac{7}{8}\right)+\frac{1}{14}\left(\frac{3\times 2+1}{2}a-\frac{1\times 5+2}{5}\right)$$

Express -12\left(-\frac{7}{8}\right) as a single fraction.

$$-10a+\frac{-12\left(-7\right)}{8}+\frac{1}{14}\left(\frac{3\times 2+1}{2}a-\frac{1\times 5+2}{5}\right)$$

Multiply -12 and -7 to get 84.

$$-10a+\frac{84}{8}+\frac{1}{14}\left(\frac{3\times 2+1}{2}a-\frac{1\times 5+2}{5}\right)$$

Reduce the fraction \frac{84}{8} to lowest terms by extracting and canceling out 4.

$$-10a+\frac{21}{2}+\frac{1}{14}\left(\frac{3\times 2+1}{2}a-\frac{1\times 5+2}{5}\right)$$

Multiply 3 and 2 to get 6.

$$-10a+\frac{21}{2}+\frac{1}{14}\left(\frac{6+1}{2}a-\frac{1\times 5+2}{5}\right)$$

Add 6 and 1 to get 7.

$$-10a+\frac{21}{2}+\frac{1}{14}\left(\frac{7}{2}a-\frac{1\times 5+2}{5}\right)$$

Multiply 1 and 5 to get 5.

$$-10a+\frac{21}{2}+\frac{1}{14}\left(\frac{7}{2}a-\frac{5+2}{5}\right)$$

Add 5 and 2 to get 7.

$$-10a+\frac{21}{2}+\frac{1}{14}\left(\frac{7}{2}a-\frac{7}{5}\right)$$

Use the distributive property to multiply \frac{1}{14} by \frac{7}{2}a-\frac{7}{5}.

$$-10a+\frac{21}{2}+\frac{1}{14}\times \frac{7}{2}a+\frac{1}{14}\left(-\frac{7}{5}\right)$$

Multiply \frac{1}{14} times \frac{7}{2} by multiplying numerator times numerator and denominator times denominator.

$$-10a+\frac{21}{2}+\frac{1\times 7}{14\times 2}a+\frac{1}{14}\left(-\frac{7}{5}\right)$$

Do the multiplications in the fraction \frac{1\times 7}{14\times 2}.

$$-10a+\frac{21}{2}+\frac{7}{28}a+\frac{1}{14}\left(-\frac{7}{5}\right)$$

Reduce the fraction \frac{7}{28} to lowest terms by extracting and canceling out 7.

$$-10a+\frac{21}{2}+\frac{1}{4}a+\frac{1}{14}\left(-\frac{7}{5}\right)$$

Multiply \frac{1}{14} times -\frac{7}{5} by multiplying numerator times numerator and denominator times denominator.

$$-10a+\frac{21}{2}+\frac{1}{4}a+\frac{1\left(-7\right)}{14\times 5}$$

Do the multiplications in the fraction \frac{1\left(-7\right)}{14\times 5}.

$$-10a+\frac{21}{2}+\frac{1}{4}a+\frac{-7}{70}$$

Reduce the fraction \frac{-7}{70} to lowest terms by extracting and canceling out 7.

$$-10a+\frac{21}{2}+\frac{1}{4}a-\frac{1}{10}$$

Combine -10a and \frac{1}{4}a to get -\frac{39}{4}a.

$$-\frac{39}{4}a+\frac{21}{2}-\frac{1}{10}$$

Least common multiple of 2 and 10 is 10. Convert \frac{21}{2} and \frac{1}{10} to fractions with denominator 10.

$$-\frac{39}{4}a+\frac{105}{10}-\frac{1}{10}$$

Since \frac{105}{10} and \frac{1}{10} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{39}{4}a+\frac{105-1}{10}$$

Subtract 1 from 105 to get 104.

$$-\frac{39}{4}a+\frac{104}{10}$$

Reduce the fraction \frac{104}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{39}{4}a+\frac{52}{5}$$

Expand

$$-\frac{39a}{4}+\frac{52}{5}$$

Solution Steps

Use the distributive property to multiply -12 by \frac{5}{6}a-\frac{7}{8}.

$$-12\times \frac{5}{6}a-12\left(-\frac{7}{8}\right)+\frac{1}{14}\left(\frac{3\times 2+1}{2}a-\frac{1\times 5+2}{5}\right)$$

Express -12\times \frac{5}{6} as a single fraction.

$$\frac{-12\times 5}{6}a-12\left(-\frac{7}{8}\right)+\frac{1}{14}\left(\frac{3\times 2+1}{2}a-\frac{1\times 5+2}{5}\right)$$

Multiply -12 and 5 to get -60.

$$\frac{-60}{6}a-12\left(-\frac{7}{8}\right)+\frac{1}{14}\left(\frac{3\times 2+1}{2}a-\frac{1\times 5+2}{5}\right)$$

Divide -60 by 6 to get -10.

$$-10a-12\left(-\frac{7}{8}\right)+\frac{1}{14}\left(\frac{3\times 2+1}{2}a-\frac{1\times 5+2}{5}\right)$$

Express -12\left(-\frac{7}{8}\right) as a single fraction.

$$-10a+\frac{-12\left(-7\right)}{8}+\frac{1}{14}\left(\frac{3\times 2+1}{2}a-\frac{1\times 5+2}{5}\right)$$

Multiply -12 and -7 to get 84.

$$-10a+\frac{84}{8}+\frac{1}{14}\left(\frac{3\times 2+1}{2}a-\frac{1\times 5+2}{5}\right)$$

Reduce the fraction \frac{84}{8} to lowest terms by extracting and canceling out 4.

$$-10a+\frac{21}{2}+\frac{1}{14}\left(\frac{3\times 2+1}{2}a-\frac{1\times 5+2}{5}\right)$$

Multiply 3 and 2 to get 6.

$$-10a+\frac{21}{2}+\frac{1}{14}\left(\frac{6+1}{2}a-\frac{1\times 5+2}{5}\right)$$

Add 6 and 1 to get 7.

$$-10a+\frac{21}{2}+\frac{1}{14}\left(\frac{7}{2}a-\frac{1\times 5+2}{5}\right)$$

Multiply 1 and 5 to get 5.

$$-10a+\frac{21}{2}+\frac{1}{14}\left(\frac{7}{2}a-\frac{5+2}{5}\right)$$

Add 5 and 2 to get 7.

$$-10a+\frac{21}{2}+\frac{1}{14}\left(\frac{7}{2}a-\frac{7}{5}\right)$$

Use the distributive property to multiply \frac{1}{14} by \frac{7}{2}a-\frac{7}{5}.

$$-10a+\frac{21}{2}+\frac{1}{14}\times \frac{7}{2}a+\frac{1}{14}\left(-\frac{7}{5}\right)$$

Multiply \frac{1}{14} times \frac{7}{2} by multiplying numerator times numerator and denominator times denominator.

$$-10a+\frac{21}{2}+\frac{1\times 7}{14\times 2}a+\frac{1}{14}\left(-\frac{7}{5}\right)$$

Do the multiplications in the fraction \frac{1\times 7}{14\times 2}.

$$-10a+\frac{21}{2}+\frac{7}{28}a+\frac{1}{14}\left(-\frac{7}{5}\right)$$

Reduce the fraction \frac{7}{28} to lowest terms by extracting and canceling out 7.

$$-10a+\frac{21}{2}+\frac{1}{4}a+\frac{1}{14}\left(-\frac{7}{5}\right)$$

Multiply \frac{1}{14} times -\frac{7}{5} by multiplying numerator times numerator and denominator times denominator.

$$-10a+\frac{21}{2}+\frac{1}{4}a+\frac{1\left(-7\right)}{14\times 5}$$

Do the multiplications in the fraction \frac{1\left(-7\right)}{14\times 5}.

$$-10a+\frac{21}{2}+\frac{1}{4}a+\frac{-7}{70}$$

Reduce the fraction \frac{-7}{70} to lowest terms by extracting and canceling out 7.

$$-10a+\frac{21}{2}+\frac{1}{4}a-\frac{1}{10}$$

Combine -10a and \frac{1}{4}a to get -\frac{39}{4}a.

$$-\frac{39}{4}a+\frac{21}{2}-\frac{1}{10}$$

Least common multiple of 2 and 10 is 10. Convert \frac{21}{2} and \frac{1}{10} to fractions with denominator 10.

$$-\frac{39}{4}a+\frac{105}{10}-\frac{1}{10}$$

Since \frac{105}{10} and \frac{1}{10} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{39}{4}a+\frac{105-1}{10}$$

Subtract 1 from 105 to get 104.

$$-\frac{39}{4}a+\frac{104}{10}$$

Reduce the fraction \frac{104}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{39}{4}a+\frac{52}{5}$$