5.3 Multiplication and Division with Negative Numbers

Multiplying and dividing with negative numbers is an important skill to possess. Let’s go through a calculator exploration to investigate what happens when you multiply by negative numbers.

Calculator Exploration—Multiplication with Negative Numbers

Calculator symbolThe calculator can be accessed on the left-hand side bar under Toolkit.

Activity symbol Activity: Multiplying Negative Numbers

Copy the following tables into your notebook. Then use the calculator to find the answers and see if you can spot any patterns that emerge.

CalculationAnswerCalculationAnswer
two multiplication four
two multiplication left parenthesis super minus times four right parenthesis
one multiplication four
one multiplication left parenthesis super minus times four right parenthesis
zero multiplication four
zero multiplication left parenthesis super minus times four right parenthesis
left parenthesis super minus times one right parenthesis prefix multiplication of four
left parenthesis super minus times one right parenthesis prefix multiplication of left parenthesis super minus times four right parenthesis
left parenthesis super minus times two right parenthesis prefix multiplication of four
left parenthesis super minus times two right parenthesis prefix multiplication of left parenthesis super minus times four right parenthesis
left parenthesis super minus times three right parenthesis prefix multiplication of four
left parenthesis super minus times three right parenthesis prefix multiplication of left parenthesis super minus times four right parenthesis
Hint symbol

Discussion

Take your time, and remember to enclose each negative number in parentheses.

Solution symbol

Answer

CalculationAnswerCalculationAnswer
two multiplication four
8
two multiplication left parenthesis super minus times four right parenthesis
8
one multiplication four
4
one multiplication left parenthesis super minus times four right parenthesis
4
zero multiplication four
0
zero multiplication left parenthesis super minus times four right parenthesis
0
left parenthesis super minus times one right parenthesis prefix multiplication of four
4
left parenthesis super minus times one right parenthesis prefix multiplication of left parenthesis super minus times four right parenthesis
4
left parenthesis super minus times two right parenthesis prefix multiplication of four
8
left parenthesis super minus times two right parenthesis prefix multiplication of left parenthesis super minus times four right parenthesis
8
left parenthesis super minus times three right parenthesis prefix multiplication of four
12
left parenthesis super minus times three right parenthesis prefix multiplication of left parenthesis super minus times four right parenthesis
12

In the first solutions column, the numbers are going down by four each time, and in the second solutions column, the numbers are increasing by four each time.

Activity symbol Activity: What Happens Next?

Use the patterns in the tables to predict the answer to the next calculation in each sequence. Then, check your predictions using the calculator.

(a) left parenthesis super minus times four right parenthesis prefix multiplication of four

Hint symbol

Discussion

What number comes next in the sequence of answers?

Solution symbol

Answer

(a) The next number in the sequence 4, 8, 12 is 16 and on the calculator left parenthesis super minus times four right parenthesis prefix multiplication of four times equals super minus times 16.

(b) left parenthesis super minus times four right parenthesis prefix multiplication of left parenthesis super minus times four right parenthesis

Solution symbol

Answer

(b) The next number in the sequence 4, 8, 12 is 16 and left parenthesis super minus times four right parenthesis prefix multiplication of left parenthesis super minus times four right parenthesis equals 16.

Now we’ll see if we can write some rules to help us remember this pattern.

5.2.9 Calculator Exploration—Negative Numbers

5.3.1 Investigating Multiplication by a Negative Number