Question

In the following exercises,Perform the indicated operation,$a)\frac{-3y}{10}-\frac{5}{6}$localid="1644496378905" $b)\frac{-3y}{10}.\frac{5}{6}$

Short answer

The simplified value of the fraction is $\frac{-3y}{10}-\frac{5}{6}=\frac{-9y-25}{30}$and$\frac{-3y}{10}.\frac{5}{6}=\frac{-y}{4}$

Step-by-step solution

Step 1, Given information

a) The given fraction is $\frac{-3y}{10}-\frac{5}{6}$

b)The given fraction is $\frac{-3y}{10}.\frac{5}{6}$

Part (a) Step 1.  Perform subtraction operation

The given fraction is $\frac{-3y}{10}-\frac{5}{6}$

$LCD=30$

role="math" localid="1644061311853" $$\begin{gathered} \frac{-3y}{10}-\frac{5}{6} \\ =\frac{-3y\times 3-5\times 5}{30} \\ =\frac{-9y-25}{30} \end{gathered}$$

Part (a) Step 2. Conclusion  

Hence, the simplified value is$\frac{-9y-25}{30}$

Part (b) Step 1.  Perform multiplication operation 

The given expression is$$\begin{gathered} \frac{-3y}{10}.\frac{5}{6} \\ =\frac{-y.1}{2.2} \\ =\frac{-y}{4} \end{gathered}$$

Part (b) Step 2.conclusion

Hence the simplified value is $\frac{-3y}{10}.\frac{5}{6}=\frac{-y}{4}$