Multiplying and Dividing Integers: Practice

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

$(-8) \times 7 = -(8 \times 7) = -56$

Multiply the sizes, then attach the negative sign.

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

$(-12) \times (-3) = +(12 \times 3) = 36$

A negative times a negative is positive.

Multiply left to right. First $9 \times (-1) = -9$, then $(-9) \times (-2) = 18$.

$9 \times (-1) \times (-2) = 18$

There are two negative factors, an even count, so the product is positive.

Divide the top by the bottom. The signs match (both negative), so the quotient is positive.

$\frac{-72}{-8} = 9 \quad \text{because} \quad 9 \times (-8) = -72$

Divide the sizes ($72 \div 8 = 9$); same signs give a positive quotient.

Division undoes multiplication, so the missing dividend is $6 \times (-7)$.

$6 \times (-7) = -42$

Check: $(-42) \div (-7) = 6$, since same signs give a positive quotient. The dividend is $-42$.

Anything multiplied by zero is zero, no matter the sign.

$(-15) \times 0 = 0$

Multiplying by zero always gives zero. (It is dividing by zero, not multiplying by it, that is undefined.)

Divide the top by the bottom. The signs differ, so the quotient is negative.

$\frac{64}{-8} = -8 \quad \text{because} \quad (-8) \times (-8) = 64$

Divide the sizes ($64 \div 8 = 8$) and attach the negative sign.

Both factors are negative, so the product is positive.

$(-13) \times (-2) = +(13 \times 2) = 26$

The size is $13 \times 2 = 26$.

Ask what number times $25$ gives $-100$. The signs differ, so the quotient is negative.

$(-100) \div 25 = -4 \quad \text{because} \quad (-4) \times 25 = -100$

Divide the sizes ($100 \div 25 = 4$) and attach the negative sign.

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

$12 \times (-6) = -(12 \times 6) = -72$

The size is $12 \times 6 = 72$.

The product $-36$ is negative while $-9$ is negative, so the missing factor must be positive to make the signs differ. Divide the sizes.

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

Check: $(-9) \times 4 = -36$, so the missing factor is $4$.

Ask what number times $-12$ gives $-84$. The signs match (both negative), so the quotient is positive.

$(-84) \div (-12) = 7 \quad \text{because} \quad 7 \times (-12) = -84$

Same signs give a positive quotient.