Multiplying and Dividing Integers: Practice

Read this as four groups of $-3$, which is repeated addition of a negative. Exactly one factor is negative, so the product is negative.

$4 \times (-3) = -(4 \times 3) = -12$

Multiply the sizes, then attach the negative sign.

Both factors are negative, so the two sign flips cancel and the product is positive.

$(-5) \times (-2) = +(5 \times 2) = 10$

A negative times a negative is positive; the size is $5 \times 2 = 10$.

Exactly one factor is negative, so the product is negative.

$(-6) \times 3 = -(6 \times 3) = -18$

The size is $6 \times 3 = 18$, and the single negative makes it negative.

Division asks for the missing factor: what number times $4$ gives $-12$? The signs differ, so the quotient is negative.

$(-12) \div 4 = -3 \quad \text{because} \quad (-3) \times 4 = -12$

Divide the sizes ($12 \div 4 = 3$) and attach the negative sign.

Ask what number times $-5$ gives $-20$. The signs match (both negative), so the quotient is positive.

$(-20) \div (-5) = 4 \quad \text{because} \quad 4 \times (-5) = -20$

Same signs give a positive quotient.

Multiplying by $-1$ keeps the size and flips the sign once.

$8 \times (-1) = -8$

Exactly one factor is negative, so the product is negative.

Both factors are negative, so the product is positive. This is multiplication, not addition.

$(-3) \times (-3) = +(3 \times 3) = 9$

The size is $3 \times 3 = 9$, and two negatives make it positive.

Both factors are negative, so the two sign flips cancel and the product is positive.

$(-4) \times (-5) = +(4 \times 5) = 20$

A negative times a negative is positive.

Ask what number times $-2$ gives $-16$. The signs match (both negative), so the quotient is positive.

$(-16) \div (-2) = 8 \quad \text{because} \quad 8 \times (-2) = -16$

Divide the sizes ($16 \div 2 = 8$); same signs give a positive quotient.

Exactly one factor is negative, so the product is negative.

$(-7) \times 2 = -(7 \times 2) = -14$

The size is $7 \times 2 = 14$.

Both factors are negative, so the product is positive. Multiplying by $-1$ keeps the size and flips the sign.

$(-8) \times (-1) = 8$

The two negatives cancel, leaving a positive.

Exactly one factor is negative, so the product is negative.

$(-9) \times 4 = -(9 \times 4) = -36$

The size is $9 \times 4 = 36$.