Multiplying and Dividing Integers: Practice

Multiply the sizes and count the negative factors. The sizes give $2 \times 3 \times 1 \times 5 = 30$, and there are four negative factors, an even count.

$(-2) \times (-3) \times (-1) \times (-5) = +30$

An even number of negatives makes the product positive.

Evaluate the numerator first, then divide. The numerator $(-6) \times 4 = -24$.

$\frac{-24}{-3} = 8$

The top and bottom are both negative, so the quotient is positive; $24 \div 3 = 8$.

Evaluate each. In order they are $-20$, then $20$, then $18$, then $-24$.

$(-2) \times (-10) = 20$

The two positive results are $20$ and $18$, and $20$ is the larger, so the second expression is greatest.

Order of operations says multiply before adding. The two products are $(-3) \times 4 = -12$ and $(-2) \times (-5) = 10$.

$-12 + 10 = -2$

Adding a smaller positive to a larger negative leaves a negative result.

Dividing by zero asks for a number that, times $0$, gives $-8$. No number times zero equals $-8$, so the quotient cannot exist.

$\frac{-8}{0} \;\text{is undefined}$

The others all have values: $\frac{-8}{-8} = 1$, $\frac{0}{-8} = 0$, and $(-8) \times 0 = 0$.

Division undoes multiplication, so the missing dividend is $(-9) \times (-4)$.

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

Check: $\frac{36}{-4} = -9$, since the signs differ. The dividend is $36$.

Multiply the sizes and count the negatives. The sizes give $2 \times 2 \times 2 \times 2 = 16$, and there are four negative factors, an even count.

$(-2) \times (-2) \times (-2) \times (-2) = 16$

An even number of negatives makes the product positive.

A total change of $-32$ dollars spread evenly over $4$ days is a division.

$(-32) \div 4 = -8$

The signs differ, so the quotient is negative: the stock changed by $-8$ dollars, a drop of $8$ dollars, each day.

Evaluate the numerator first. The three factors give $(-3) \times (-4) = 12$, then $12 \times (-2) = -24$.

$\frac{-24}{-6} = 4$

The numerator and denominator are both negative, so the quotient is positive; $24 \div 6 = 4$.

Evaluate each. The first is $12$, the second is $-12$, the third is $12$, and the fourth is $12$.

$(-48) \div 4 = -12$

Only the second, with one negative and one positive, gives the negative result $-12$.

Each factor has size $1$, so the size of the product is $1$. Count the negative factors: there are six, an even count.

$(-1)\;\text{multiplied six times} = 1$

An even number of negatives makes the product positive, so the answer is $1$.

Evaluate the fraction first. The numerator $(-5) \times 8 = -40$, then $\frac{-40}{-2} = 20$.

$20 - 6 = 14$

The quotient is positive because top and bottom are both negative; subtracting $6$ leaves $14$.