Solve 1/3a-2/4ab+7/2b-3/4a+frac{5}{1}ab-frac{3}{6}b=

$$\frac { 1 } { 3 } a - \frac { 2 } { 4 } a b + \frac { 7 } { 2 } b - \frac { 3 } { 4 } a + \frac { 5 } { 1 } a b - \frac { 3 } { 6 } b =$$

Evaluate

$$\frac{9ab}{2}-\frac{5a}{12}+3b$$

Solution Steps

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

$$\frac{1}{3}a-\frac{1}{2}ab+\frac{7}{2}b-\frac{3}{4}a+\frac{5}{1}ab-\frac{3}{6}b$$

Combine \frac{1}{3}a and -\frac{3}{4}a to get -\frac{5}{12}a.

$$-\frac{5}{12}a-\frac{1}{2}ab+\frac{7}{2}b+\frac{5}{1}ab-\frac{3}{6}b$$

Anything divided by one gives itself.

$$-\frac{5}{12}a-\frac{1}{2}ab+\frac{7}{2}b+5ab-\frac{3}{6}b$$

Combine -\frac{1}{2}ab and 5ab to get \frac{9}{2}ab.

$$-\frac{5}{12}a+\frac{9}{2}ab+\frac{7}{2}b-\frac{3}{6}b$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$-\frac{5}{12}a+\frac{9}{2}ab+\frac{7}{2}b-\frac{1}{2}b$$

Combine \frac{7}{2}b and -\frac{1}{2}b to get 3b.

$$-\frac{5}{12}a+\frac{9}{2}ab+3b$$

Factor

$$\frac{54ab-5a+36b}{12}$$

Solution Steps

Factor out \frac{1}{12}.

$$\frac{4a-6ab+42b-9a+60ab-6b}{12}$$