Lesson 4: Multiplying Integers

Property

For multiplication of two signed numbers:

• If the signs are the same, the product is positive.
• If the signs are different, the product is negative.

Same Signs (Product is Positive)

• Two positives: $7 \cdot 4 = 28$
• Two negatives: $-8(-6) = 48$

Different Signs (Product is Negative)

• Positive $\cdot$ negative: $7(-9) = -63$
• Negative $\cdot$ positive: $-5 \cdot 10 = -50$

Property

To model the product $a \times b$ on a number line, you start at 0 and make $a$ jumps of size $b$. The sign of $b$ determines the direction of the jumps (positive is right, negative is left).

Examples

• To model $3 \times (-4)$, start at 0 and make 3 jumps of size -4 (to the left). You land on -12. So, $3 \times (-4) = -12$.
• To model $2 \times 5$, start at 0 and make 2 jumps of size 5 (to the right). You land on 10. So, $2 \times 5 = 10$.

Explanation

Using a number line helps visualize multiplication as repeated addition or subtraction. The first factor tells you how many jumps to make, and the second factor tells you the size and direction of each jump. Always begin at 0, and your final position on the number line after completing all the jumps is the product of the two integers.