1.4 Multiply and divide integers  (Page 2/4)

Solution

1. ⓐ
   $\begin{array}{cccccc}& & & & & \hfill -27÷3\hfill \\ \begin{array}{c}\text{Divide, with different signs, the quotient is}\hfill \\ \text{negative.}\hfill \end{array}\hfill & & & & & \hfill -9\hfill \end{array}$
   
   
2. ⓑ
   $\begin{array}{cccccc}& & & & & \hfill -100÷\left(\mathrm{-4}\right)\hfill \\ \begin{array}{c}\text{Divide, with signs that are the same the}\hfill \\ \text{quotient is positive.}\hfill \end{array}\hfill & & & & & \hfill 25\hfill \end{array}$

Solution

$\begin{array}{cccccc}& & & & & \hfill 7\left(\mathrm{-2}\right)+4\left(\mathrm{-7}\right)-6\hfill \\ \text{Multiply first.}\hfill & & & & & \hfill \mathrm{-14}+\left(\mathrm{-28}\right)-6\hfill \\ \text{Add.}\hfill & & & & & \hfill \mathrm{-42}-6\hfill \\ \text{Subtract.}\hfill & & & & & \hfill \mathrm{-48}\hfill \end{array}$

Solution

1. ⓐ
   $\begin{array}{cccccc}& & & & & \hfill {\left(\mathrm{-2}\right)}^4\hfill \\ \text{Write in expanded form.}\hfill & & & & & \hfill \left(\mathrm{-2}\right)\left(\mathrm{-2}\right)\left(\mathrm{-2}\right)\left(\mathrm{-2}\right)\hfill \\ \text{Multiply.}\hfill & & & & & \hfill 4\left(\mathrm{-2}\right)\left(\mathrm{-2}\right)\hfill \\ \text{Multiply.}\hfill & & & & & \hfill \mathrm{-8}\left(\mathrm{-2}\right)\hfill \\ \text{Multiply.}\hfill & & & & & \hfill 16\hfill \end{array}$
   
   
2. ⓑ
   $\begin{array}{cccccc}& & & & & \hfill \text{−}{2}^4\hfill \\ \begin{array}{c}\text{Write in expanded form. We are asked}\hfill \\ \text{to find the opposite of}{2}^4.\hfill \end{array}\hfill & & & & & \hfill \text{−}\left(2·2·2·2\right)\hfill \\ \text{Multiply.}\hfill & & & & & \hfill \text{−}\left(4·2·2\right)\hfill \\ \text{Multiply.}\hfill & & & & & \hfill \text{−}\left(8·2\right)\hfill \\ \text{Multiply.}\hfill & & & & & \hfill \mathrm{-16}\hfill \end{array}$

Notice the difference in parts ⓐ and ⓑ . In part ⓐ , the exponent means to raise what is in the parentheses, the $\left(\mathrm{-2}\right)$ to the $4^{\text{th}}$ power. In part ⓑ , the exponent means to raise just the 2 to the $4^{\text{th}}$ power and then take the opposite.

Solution

$\begin{array}{cccccc}& & & & & \hfill 12-3\left(9-12\right)\hfill \\ \text{Subtract in parentheses first.}\hfill & & & & & \hfill 12-3\left(\mathrm{-3}\right)\hfill \\ \text{Multiply.}\hfill & & & & & \hfill 12-\left(\mathrm{-9}\right)\hfill \\ \text{Subtract.}\hfill & & & & & \hfill 21\hfill \end{array}$

Solution

$\begin{array}{cccccc}& & & & & \hfill 8\left(\mathrm{-9}\right)÷{\left(\mathrm{-2}\right)}^3\hfill \\ \text{Exponents first.}\hfill & & & & & \hfill 8\left(\mathrm{-9}\right)÷\left(\mathrm{-8}\right)\hfill \\ \text{Multiply.}\hfill & & & & & \hfill \mathrm{-72}÷\left(\mathrm{-8}\right)\hfill \\ \text{Divide.}\hfill & & & & & \hfill 9\hfill \end{array}$

Solution

$\begin{array}{cccccc}& & & & & \hfill \mathrm{-30}÷2+\left(\mathrm{-3}\right)\left(\mathrm{-7}\right)\hfill \\ \text{Multiply and divide left to right, so divide first.}\hfill & & & & & \hfill \mathrm{-15}+\left(\mathrm{-3}\right)\left(\mathrm{-7}\right)\hfill \\ \text{Multiply.}\hfill & & & & & \hfill \mathrm{-15}+21\hfill \\ \text{Add.}\hfill & & & & & \hfill 6\hfill \end{array}$

Solution

ⓐ

Simplify.	−4

ⓑ

Simplify.
Add.	6

Solution

Add inside parenthesis.	(6) 2
Simplify.	36

Solution

ⓐ

Subtract.	8

Subtract.	32