Multiplication and Division of Integers
Primary 6 · Mathematics
Multiplication and Division of Integers
Lesson 3 of 5
30 min
Let's begin
Keza's school has a water tank. When it rains, the water level rises 3 cm every hour. When the tap is open, it falls 3 cm every hour. Keza wants to know where the water level was, or will be, at different times. Her answers explain the sign rules better than any rule book!
Let a rising level be +3 cm per hour and a falling level be −3 cm per hour. Let time in the future be positive (+4 means “4 hours from now”) and time in the past be negative (−4 means “4 hours ago”).
| What happens | Multiplication | Change in level |
|---|---|---|
| Rising, 4 hours from now | (+3) × (+4) | +12: it will be 12 cm higher |
| Rising, 4 hours ago | (+3) × ( − 4) | −12: it was 12 cm lower |
| Falling, 4 hours from now | (−3) × (+4) | −12: it will be 12 cm lower |
| Falling, 4 hours ago | ( − 3) × ( − 4) | +12: it was 12 cm higher |
Think about the last row: if the water is going down now, then 4 hours ago it must have been higher. So negative × negative is positive.
Look at this list. The first number goes down by 1 each time:
Each answer goes up by 2. To keep the pattern going after 0, the answers must become positive: +2, +4, +6.
| Signs of the two numbers | Sign of the answer | Example |
|---|---|---|
| Same signs (+ and +, or − and −) | Positive | ( − 5) × ( − 6) = 30 |
| Different signs (+ and −, or − and +) | Negative | 5 × ( − 6) = −30 |
Worked example 1
( − 9) × 7
Worked example 2
( − 2) × ( − 3) × ( − 1)
When you multiply several integers, count the negative numbers. An even number of negatives gives a positive answer. An odd number of negatives gives a negative answer.
Tip
“Same signs, smile (+). Different signs, frown (−).” Work out the size first, then decide the sign.
Work each one in your exercise book first, then tap Show answer to check.
( − 8) × ( − 6)
Answer: 48. Same signs, so positive.
12 × ( − 4)
Answer: −48. Different signs, so negative.
( − 3) × ( − 2) × ( − 5)
Answer: −30. Three negatives is an odd number, so the answer is negative; 3 × 2 × 5 = 30.
( − 1) × 250
Answer: −250. Multiplying by −1 gives the opposite.
( − 6) × 0 × ( − 9)
Answer: 0. Anything multiplied by 0 is 0.
What you learned today
Sources and credits
The stories, Rwandan worked examples and practice questions were written by Ganzaa.
Quick check
(−7) × (−8) = ?
