Find each of the following products or quotients without using a calculator. Draw a diagram or use words to explain how you know your product makes sense.  

1. $6 ( - 3 )$ 

   Hint (a):

   By definition, multiplication is a shortcut for repeated addition. Now think of what it's like to multiply negative numbers. Can you put this in your own words?

   Answer (a):

   The product is $-18$. Don't forget to explain why this makes sense.

2. $- 6 ( 3 )$ 

   Hint (b):

   It may help to think of multiplying a positive and negative number as removing groups of a positive number. For example, here you are removing groups of three, six times. Can you represent this in a diagram?

3. $- 8 ( - 3 )$ 

   Hint (c):

   Claire found the product of this expression and then explained that multiplying two negative numbers is like removing groups of negatives. Can you think of another way to explain this? Try drawing a diagram or putting Claire's idea into your own words.

4. $- 8 ( 0 )$ 

   Hint (d):

   Zero multiplied by any number will always be zero. Can you explain why?

5. $- 20 \div 5$ 

   Hint (e):

   How many groups of $5$ are there in $20$?

   More Help (e):

   If there are $4$ groups of $5$ in $20$, how many groups of $5$ do you think there would be in $−20$?

   Answer (e):

   $-20\div5=-4$

6. $- 36 \div ( - 9 )$ 

   Hint (f):

   How many groups of $-9$ are there in $-36$?