Question

Using the distributive property simplify the expression$12\left(\frac{2}{3}b+\frac{5}{6}\right)$

Short answer

The simplified form of expression $12\left(\frac{2}{3}b+\frac{5}{6}\right)$is $8b+10$

Step-by-step solution

Step 1:Given information

Given expression in the form is $12\left(\frac{2}{3}b+\frac{5}{6}\right)$.

Simplify the expression using distributive property.

Step 2:Description of distributive property

Distributive property : If $a,b,c$are real numbers thenlocalid="1644429259082" $$\begin{gathered} a(b+c)=ab+ac \\ a(b-c)=ab-ac \end{gathered}$$

Step 3:Simplification of the expression 

Applying the distributive property ,expression becomes $$\begin{gathered} 12\left(\frac{2}{3}b+\frac{5}{6}\right)=12\times \frac{2}{3}b+12\times \frac{5}{6} \\ =4\times 2b+2\times 5 \\ =8b+10 \end{gathered}$$

Step 3

The expression is $12\left(\frac{2}{3}b+\frac{5}{6}\right)$, by using distributive property we can write expression in the form$$\begin{gathered} 12\times \frac{2}{3}b+12\times \frac{5}{6}=4\times 2b+2\times 5 \\ =8b+10 \end{gathered}$$