Multiplication and Division of Integers
Primary 6 · Mathematics
Multiplication and Division of Integers
Lesson 2 of 5
30 min
Let's begin
Gatete's phone takes 2 Frw from his balance every time he sends an SMS. He sends 3 messages. We can write the change in his balance as 3 × ( − 2). But what is 3 × ( − 2)? Let us find out with pictures.
3 × 4 means 3 groups of 4: 4 + 4 + 4 = 12. The same idea works when the number in each group is negative.
Worked example 1
3 × ( − 2) means 3 groups of −2:
( − 2) + ( − 2) + ( − 2) = −6. Gatete's balance goes down by 6 Frw.
Let ⊕ be a counter worth +1 and ⊖ be a counter worth −1. A pair ⊕⊖ is worth 0, because +1 and −1 cancel. We call it a zero pair.
3 × (+2): put in 3 groups of ⊕ ⊕. You have ⊕ ⊕ ⊕ ⊕ ⊕ ⊕, which is +6.
3 × ( − 2): put in 3 groups of ⊖ ⊖. You have ⊖ ⊖ ⊖ ⊖ ⊖ ⊖, which is −6.
(−3) × (+2): a negative number of groups means we take away 3 groups of ⊕ ⊕. Start with a pile worth 0 that has enough counters: 6 zero pairs. Take away 6 ⊕. What is left is ⊖ ⊖ ⊖ ⊖ ⊖ ⊖, which is −6.
( − 3) × ( − 2): take away 3 groups of ⊖ ⊖ from 6 zero pairs. What is left is ⊕ ⊕ ⊕ ⊕ ⊕ ⊕, which is +6.
Start at 0 and make equal jumps. The first number tells you how many jumps. The second tells you how big each jump is and which way it goes.
| Multiplication | Signs | Answer |
|---|---|---|
| 3 × 2 | positive × positive | +6 |
| 3 × ( − 2) | positive × negative | −6 |
| ( − 3) × 2 | negative × positive | −6 |
| ( − 3) × ( − 2) | negative × negative | +6 |
The size of the answer is always 3 × 2 = 6. Only the sign changes. In the next lesson you will learn the rule for the sign.
Tip
A minus sign in front means “turn around”. 4 × ( − 5) is 4 jumps to the left. ( − 4) × ( − 5) turns those jumps around, so they point right: +20.
Work each one in your exercise book first, then tap Show answer to check.
Write 5 × ( − 3) as a repeated addition and work it out.
Answer: ( − 3) + ( − 3) + ( − 3) + ( − 3) + ( − 3) = −15.
On a number line, what do 6 jumps of 2 to the left from 0 show?
Answer: 6 × ( − 2) = −12.
Use counters: take away 2 groups of 4 negative counters from 8 zero pairs. What is left, and which multiplication is it?
Answer: 8 positive counters: ( − 2) × ( − 4) = +8.
Work out ( − 5) × 4.
Answer: −20. The size is 5 × 4 = 20 and the signs are different.
What you learned today
Sources and credits
The stories, Rwandan worked examples and practice questions were written by Ganzaa.
Quick check
Which repeated addition shows 4 × (−3), that is, 4 groups of −3?
