3.4 Multiply and Divide Integers

Before you get started, take this readiness quiz.

Translate the quotient of $20$ and $13$ into an algebraic expression.
If you missed this problem, review the reference.

Add: $−5 + \left(−5\right) + \left(−5\right) .$
If you missed this problem, review the reference.

$\text{Evaluate} n + 4 \text{when} n = −7 .$
If you missed this problem, review the reference.

Multiply each of the following:

1. ⓐ $−9 \cdot 3$
2. ⓑ $−2 \left(−5\right)$
3. ⓒ $4 \left(−8\right)$
4. ⓓ $7 \cdot 6$

Multiply:

1. ⓐ $−6 \cdot 8$
2. ⓑ $−4 \left(−7\right)$
3. ⓒ $9 \left(−7\right)$
4. ⓓ $5 \cdot 12$

Multiply:

1. ⓐ $−8 \cdot 7$
2. ⓑ $−6 \left(−9\right)$
3. ⓒ $7 \left(−4\right)$
4. ⓓ $3 \cdot 13$

Multiply each of the following:

1. ⓐ $−1 \cdot 7$
2. ⓑ $−1 \left(−11\right)$

Multiply.

1. ⓐ $−1 \cdot 9$
2. ⓑ $−1 \cdot \left(−17\right)$

Multiply.

1. ⓐ $−1 \cdot 8$
2. ⓑ $−1 \cdot \left(−16\right)$

Divide each of the following:

1. ⓐ $−27 \div 3$
2. ⓑ $−100 \div \left(−4\right)$

Divide:

1. ⓐ $−42 \div 6$
2. ⓑ $−117 \div \left(−3\right)$

Divide:

1. ⓐ $−63 \div 7$
2. ⓑ $−115 \div \left(−5\right)$

Divide each of the following:

1. ⓐ $16 \div \left(−1\right)$
2. ⓑ $−20 \div \left(−1\right)$

Divide:

1. ⓐ $6 \div \left(−1\right)$
2. ⓑ $−36 \div \left(−1\right)$

Divide:

1. ⓐ $28 \div \left(−1\right)$
2. ⓑ $−52 \div \left(−1\right)$

$\text{Simplify}: 7 \left(−2\right) + 4 \left(−7\right) - 6 .$

Simplify:

$8 \left(−3\right) + 5 \left(−7\right) −4$

Simplify:

$9 \left(−3\right) + 7 \left(−8\right) - 1$

Simplify:

1. ⓐ $\left(−2\right)^{4}$
2. ⓑ $−2^{4}$

Simplify:

1. ⓐ $\left(−3\right)^{4}$
2. ⓑ $−3^{4}$

Simplify:

1. ⓐ $\left(−7\right)^{2}$
2. ⓑ $- 7^{2}$

$\text{Simplify}: 12 - 3 \left(9 - 12\right) .$

Simplify:

$17 - 4 \left(8 - 11\right)$

Simplify:

$16 - 6 \left(7 - 13\right)$

Simplify: $8 \left(−9\right) \div \left(−2\right)^{3} .$

Simplify:

$12 \left(−9\right) \div \left(−3\right)^{3}$

Simplify:

$18 \left(−4\right) \div \left(−2\right)^{3}$

$\text{Simplify}: −30 \div 2 + \left(−3\right) \left(−7\right) .$

Simplify:

$−27 \div 3 + \left(−5\right) \left(−6\right)$

Simplify:

$−32 \div 4 + \left(−2\right) \left(−7\right)$

Evaluate:

$3 x^{2} - 2 x + 6 \text{when} x = −3$

Evaluate:

$4 x^{2} - x - 5 \text{when} x = −2$

Evaluate:

$7 x + 6 y - 12 \text{when} x = −2 \text{and} y = 3$

Evaluate:

$8 x - 6 y + 13 \text{when} x = −3 \text{and} y = −5$

Translate to an algebraic expression and simplify if possible: the product of $−2$ and $14 .$

Translate to an algebraic expression and simplify if possible:

$\text{the product of }−\text{5 and 12}$

Translate to an algebraic expression and simplify if possible:

$\text{the product of 8 and }−\text{13}$

Translate to an algebraic expression and simplify if possible: the quotient of $−56$ and $−7 .$

Translate to an algebraic expression and simplify if possible:

$\text{the quotient of }−\text{63 and }−\text{9}$

Translate to an algebraic expression and simplify if possible:

$\text{the quotient of }−\text{72 and }−\text{9}$

Multiply each pair of integers.

$−4 \cdot 8$

Multiply each pair of integers.

$−5 \left(7\right)$

Multiply each pair of integers.

$−18 \left(−2\right)$

Multiply each pair of integers.

$9 \left(−7\right)$

Multiply each pair of integers.

$−1 \cdot 6$

Multiply each pair of integers.

$−1 \left(−14\right)$

Divide.

$−24 \div 6$

Divide.

$56 \div \left(−7\right)$

Divide.

$−52 \div \left(−4\right)$

Divide.

$−180 \div 15$

Divide.

$49 \div \left(−1\right)$

Simplify each expression.

$5 \left(−6\right) + 7 \left(−2\right) −3$

Simplify each expression.

$−8 \left(−2\right) −3 \left(−9\right)$

Simplify each expression.

$\left(−5\right)^{3}$

Simplify each expression.

$\left(−2\right)^{6}$

Simplify each expression.

$- 4^{2}$

Simplify each expression.

$−3 \left(−5\right) \left(6\right)$

Simplify each expression.

$−4 \cdot 2 \cdot 11$

Simplify each expression.

$\left(8 - 11\right) \left(9 - 12\right)$

Simplify each expression.

$26 - 3 \left(2 - 7\right)$

Simplify each expression.

$−10 \left(−4\right) \div \left(−8\right)$

Simplify each expression.

$65 \div \left(−5\right) + \left(−28\right) \div \left(−7\right)$

Simplify each expression.

$9 - 2 \left[3 - 8 \left(−2\right)\right]$

Simplify each expression.

$\left(−3\right)^{2} −24 \div \left(8 - 2\right)$

Evaluate each expression.

$−2 x + 17 \text{when}$

1. ⓐ $x = 8$
2. ⓑ $x = −8$

Evaluate each expression.

$10 - 3 m \text{when}$

1. ⓐ $m = 5$
2. ⓑ $m = −5$

Evaluate each expression.

$p^{2} - 5 p + 5 \text{when} p = −1$

Evaluate each expression.

$2 w^{2} - 3 w + 7$ when $w = −2$

Evaluate each expression.

$6 x - 5 y + 15$ when $x = 3$ and $y = −1$

Evaluate each expression.

$9 a - 2 b - 8$ when $a = −6$ and $b = −3$

Translate to an algebraic expression and simplify if possible.

The product of $−3$ and 15

Translate to an algebraic expression and simplify if possible.

The quotient of $−60$ and $−20$

Translate to an algebraic expression and simplify if possible.

The quotient of $−6$ and the sum of $a$ and $b$

Translate to an algebraic expression and simplify if possible.

The product of $−10$ and the difference of $p \text{and} q$

Stock market Javier owns $300$ shares of stock in one company. On Tuesday, the stock price dropped $\$\text{12}$ per share. What was the total effect on Javier’s portfolio?

In your own words, state the rules for multiplying two integers.

Why is $−2^{4} \neq \left(−2\right)^{4} ?$