Multiplying and Dividing Integers: Additional Practice (Set 1)

Multiply the sizes and count the negatives. The sizes give $6 \times 2 \times 3 = 36$, and there are three negative factors, an odd count.

$(-6) \times (-2) \times (-3) = -36$

An odd number of negatives makes the product negative.

Evaluate the numerator first. The product $(-7) \times (-6) = 42$ is positive.

$\frac{42}{-3} = -14$

The top is positive and the bottom is negative, so the quotient is negative; $42 \div 3 = 14$.

Work left to right. First $(-100) \div (-4) = 25$, since the signs match. Then divide by $-5$; those signs differ, so the quotient is negative.

$25 \div (-5) = -5$

Evaluate each. The first is $20$, the second is $-21$, the third is $-24$, and the fourth is $-20$.

$6 \times (-4) = -24$

The smallest value is the most negative one, and $-24$ lies farther left than $-21$, $-20$, or $20$, so the third expression is smallest.

Substitute and work left to right. First $a \times b = (-5) \times 4 = -20$.

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

Dividing $-20$ by $-2$ gives a positive result because the signs match.

Multiply the sizes and count the negatives. The sizes give $1 \times 2 \times 3 \times 4 \times 1 = 24$, and there are three negative factors, an odd count.

$(-1) \times 2 \times (-3) \times 4 \times (-1) = -24$

An odd number of negatives makes the product negative.

Work left to right. First $\frac{-54}{6} = -9$, since the signs differ.

$(-9) \times (-3) = 27$

Then multiplying two negatives gives the positive result $27$.

Multiply before subtracting. The products are $8 \times (-3) = -24$ and $(-6) \times 4 = -24$.

$-24 - (-24) = -24 + 24 = 0$

Subtracting $-24$ adds $24$, which cancels the first term to give $0$.

Each negative factor flips the sign once, so a positive product needs an even count of negative factors. Two negatives flip the sign twice, which lands back where it started.

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

Three integers can carry $0$, $1$, $2$ or $3$ negatives, and only an even count gives a positive product. Of the choices, exactly $2$ is the even one, so two negative factors is possible.

Evaluate the numerator first. The product $(-8) \times (-9) = 72$ is positive.

$\frac{72}{-12} = -6$

The top is positive and the bottom is negative, so the quotient is negative; $72 \div 12 = 6$.

Evaluate the quotient and the product first. The quotient $\frac{-72}{-9} = 8$ and the product $3 \times (-4) = -12$.

$8 - (-12) = 8 + 12 = 20$

Subtracting the negative $-12$ adds $12$, giving $20$.

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

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

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