1.4 Multiply and Divide Integers

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

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

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

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

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

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

Divide: ⓐ $−27 \div 3$ ⓑ $−100 \div \left(−4\right) .$

Divide: ⓐ $−42 \div 6$ ⓑ $−117 \div \left(−3\right) .$

Divide: ⓐ $−63 \div 7$ ⓑ $−115 \div \left(−5\right) .$

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

Simplify: ⓐ $\left(−3\right)^{4}$ ⓑ $− 3^{4} .$

Simplify: ⓐ $\left(−7\right)^{2}$ ⓑ $− 7^{2} .$

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

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

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

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

When $n = −8 ,$ evaluate ⓐ $n + 2$ ⓑ $− n + 2 .$

When $y = −9 ,$ evaluate ⓐ $y + 8$ ⓑ $− y + 8 .$

Evaluate $\left(x + y\right)^{2}$ when $x = −15$ and $y = 29 .$

Evaluate $\left(x + y\right)^{3}$ when $x = −8$ and $y = 10 .$

Evaluate: $17 - k$ when ⓐ $k = 19$ and ⓑ $k = −19 .$

Evaluate: $−5 - b$ when ⓐ $b = 14$ and ⓑ $b = −14 .$

Evaluate: $3 x^{2} - 2 x + 6$ when $x = −3 .$

Evaluate: $4 x^{2} - x - 5$ when $x = −2 .$

Translate and simplify: the sum of 8 and $−12 ,$ increased by 3.

Translate and simplify the sum of 9 and $−16 ,$ increased by 4.

Translate and simplify the sum of $−8$ and $−12 ,$ increased by 7.

Translate and then simplify ⓐ the difference of 13 and $−21$ ⓑ subtract 24 from $−19 .$

Translate and simplify ⓐ the difference of 14 and $−23$ ⓑ subtract 21 from $−17 .$

Translate and simplify ⓐ the difference of 11 and $−19$ ⓑ subtract 18 from $−11 .$

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

Translate to an algebraic expression and simplify if possible: the product of $−5$ and 12.

Translate to an algebraic expression and simplify if possible: the product of 8 and $−13 .$

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

Translate to an algebraic expression and simplify if possible: the quotient of $−63$ and $−9 .$

Translate to an algebraic expression and simplify if possible: the quotient of $−72$ and $−9 .$

In the morning, the temperature in Anchorage, Alaska was 15 degrees. By mid-afternoon the temperature had dropped to 30 degrees below zero. What was the difference in the morning and afternoon temperatures?

The temperature in Denver was $−6$ degrees at lunchtime. By sunset the temperature had dropped to $−15$ degrees. What was the difference in the lunchtime and sunset temperatures?

The Mustangs football team received three penalties in the third quarter. Each penalty gave them a loss of fifteen yards. What is the number of yards lost?

The Bears played poorly and had seven penalties in the game. Each penalty resulted in a loss of 15 yards. What is the number of yards lost due to penalties?

Bill uses the ATM on campus because it is convenient. However, each time he uses it he is charged a $2 fee. Last month he used the ATM eight times. How much was his total fee for using the ATM?

Multiply.

$−4 \cdot 8$

Multiply.

$9 \left(−7\right)$

Multiply.

$- 1 \cdot 6$

Multiply.

$−1 \left(−14\right)$

Divide.

$−24 \div 6$

Divide.

$−52 \div \left(−4\right)$

Divide.

$−180 \div 15$

Simplify each expression.

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

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.

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

Simplify each expression.

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

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.

$y + \left(−14\right)$ when ⓐ $y = −33$ ⓑ $y = 30$

Evaluate each expression.

1. ⓐ $a + 3$ when $a = −7$
2. ⓑ $− a + 3$ when $a = −7$

Evaluate each expression.

$m + n$ when
$m = −15 , n = 7$

Evaluate each expression.

$r + s$ when $r = −9 , s = −7$

Evaluate each expression.

$\left(x + y\right)^{2}$ when
$x = −3 , y = 14$

Evaluate each expression.

$−2 x + 17$ when

1. ⓐ $x = 8$
2. ⓑ $x = −8$

Evaluate each expression.

$10 - 3 m$ when
ⓐ $m = 5$
ⓑ $m = −5$

Evaluate each expression.

$2 w^{2} - 3 w + 7$ when
$w = −2$

Evaluate each expression.

$9 a - 2 b - 8$ when
$a = −6 \text{and} b = −3$

Translate to an algebraic expression and simplify if possible.

the sum of 3 and $−15 ,$ increased by 7

Translate to an algebraic expression and simplify if possible.

the difference of 10 and $−18$

Translate to an algebraic expression and simplify if possible.

the difference of $−5$ and $−30$

Translate to an algebraic expression and simplify if possible.

the product of $−\text{3 and 15}$

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 $p \text{and} q$

Solve.

Temperature On January $15 ,$ the high temperature in Anaheim, California, was $84 ° .$ That same day, the high temperature in Embarrass, Minnesota was $−12 ° .$ What was the difference between the temperature in Anaheim and the temperature in Embarrass?

Solve.

Football On the first down, the Chargers had the ball on their 25-yard line. They lost 6 yards on the first-down play, gained 10 yards on the second-down play, and lost 8 yards on the third-down play. What was the yard line at the end of the third-down play?

Solve.

Checking Account Mayra has $124 in her checking account. She writes a check for $152. What is the new balance in her checking account?

Solve.

Checking Account Diontre has a balance of $− $38$ in his checking account. He deposits $225 to the account. What is the new balance?

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

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

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