Solve 1/2(10z+9)-1/6

$$\frac{ 1 }{ 2 } (10z+9)- \frac{ 1 }{ 6 }$$

Evaluate

$$5z+\frac{13}{3}$$

Solution Steps

Use the distributive property to multiply \frac{1}{2} by 10z+9.

$$\frac{1}{2}\times 10z+\frac{1}{2}\times 9-\frac{1}{6}$$

Multiply \frac{1}{2} and 10 to get \frac{10}{2}.

$$\frac{10}{2}z+\frac{1}{2}\times 9-\frac{1}{6}$$

Divide 10 by 2 to get 5.

$$5z+\frac{1}{2}\times 9-\frac{1}{6}$$

Multiply \frac{1}{2} and 9 to get \frac{9}{2}.

$$5z+\frac{9}{2}-\frac{1}{6}$$

Least common multiple of 2 and 6 is 6. Convert \frac{9}{2} and \frac{1}{6} to fractions with denominator 6.

$$5z+\frac{27}{6}-\frac{1}{6}$$

Since \frac{27}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$5z+\frac{27-1}{6}$$

Subtract 1 from 27 to get 26.

$$5z+\frac{26}{6}$$

Reduce the fraction \frac{26}{6} to lowest terms by extracting and canceling out 2.

$$5z+\frac{13}{3}$$

Expand

$$5z+\frac{13}{3}$$

Solution Steps

Use the distributive property to multiply \frac{1}{2} by 10z+9.

$$\frac{1}{2}\times 10z+\frac{1}{2}\times 9-\frac{1}{6}$$

Multiply \frac{1}{2} and 10 to get \frac{10}{2}.

$$\frac{10}{2}z+\frac{1}{2}\times 9-\frac{1}{6}$$

Divide 10 by 2 to get 5.

$$5z+\frac{1}{2}\times 9-\frac{1}{6}$$

Multiply \frac{1}{2} and 9 to get \frac{9}{2}.

$$5z+\frac{9}{2}-\frac{1}{6}$$

Least common multiple of 2 and 6 is 6. Convert \frac{9}{2} and \frac{1}{6} to fractions with denominator 6.

$$5z+\frac{27}{6}-\frac{1}{6}$$

Since \frac{27}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$5z+\frac{27-1}{6}$$

Subtract 1 from 27 to get 26.

$$5z+\frac{26}{6}$$

Reduce the fraction \frac{26}{6} to lowest terms by extracting and canceling out 2.

$$5z+\frac{13}{3}$$