1.2 Integers

Fill in $< , > ,$ or $=$ for each of the following pairs of numbers:

ⓐ $\left|−5\right| __ - \left|−5\right|$ ⓑ $8 __ - \left|−8\right|$ ⓒ $−9 __ - \left|−9\right|$ ⓓ $− \left(−16\right) __ \left|−16\right| .$

Fill in $< , > ,$ or $=$ for each of the following pairs of numbers:

ⓐ $−9 __ - \left|−9\right|$ ⓑ $2 __ - \left|−2\right|$ ⓒ $−8 __ \left|−8\right|$ ⓓ $− \left(−9\right) __ \left|−9\right| .$

Fill in $< , > ,$ or $=$ for each of the following pairs of numbers:

ⓐ $7 __ - \left|−7\right|$ ⓑ $− \left(−10\right) __ \left|−10\right|$ ⓒ $\left|−4\right| __ - \left|−4\right|$ ⓓ $−1 __ \left|−1\right| .$

Simplify: $24 - \left|19 - 3 \left(6 - 2\right)\right| .$

Simplify:$19 - \left|11 - 4 \left(3 - 1\right)\right| .$

Simplify: $9 - \left|8 - 4 \left(7 - 5\right)\right| .$

Add: ⓐ $−2 + \left(−4\right)$ ⓑ $−2 + 4$ ⓒ $2 + \left(−4\right) .$

Add: ⓐ $−2 + \left(−5\right)$ ⓑ $−2 + 5$ ⓒ $2 + \left(−5\right) .$

Subtract: ⓐ $6 - 4$ ⓑ $−6 - \left(−4\right)$ ⓒ $−6 - 4$ ⓓ $6 - \left(−4\right) .$

Subtract: ⓐ $7 - 4$ ⓑ $−7 - \left(−4\right)$ ⓒ $−7 - 4$ ⓓ $7 - \left(−4\right) .$

Simplify: ⓐ $13 - 8$ and $13 + \left(−8\right)$ ⓑ $−17 - 9$ and $−17 + \left(−9\right)$ ⓒ $9 - \left(−15\right)$ and $9 + 15$ ⓓ $−7 - \left(−4\right)$ and $−7 + 4 .$

Simplify: ⓐ $21 - 13$ and $21 + \left(−13\right)$ ⓑ $−11 - 7$ and $−11 + \left(−7\right)$ ⓒ $6 - \left(−13\right)$ and $6 + 13$ ⓓ $−5 - \left(−1\right)$ and $−5 + 1 .$

Simplify: ⓐ $15 - 7$ and $15 + \left(−7\right)$ ⓑ $−14 - 8$ and $−14 + \left(−8\right)$ ⓒ $4 - \left(−19\right)$ and $4 + 19$ ⓓ $−4 - \left(−7\right)$ and $−4 + 7 .$

Simplify: $7 - \left(−4 - 3\right) - 9 .$

Simplify: $8 - \left(−3 - 1\right) - 9 .$

Simplify: $12 - \left(−9 - 6\right) - 14 .$

Multiply or divide: ⓐ $−100 \div \left(−4\right)$ ⓑ $7 \cdot 6$ ⓒ $4 \left(−8\right)$ ⓓ $−27 \div 3 .$

Multiply or divide: ⓐ $−115 \div \left(−5\right)$ ⓑ $5 \cdot 12$ ⓒ $9 \left(−7\right)$ ⓓ $−63 \div 7 .$

Multiply or divide: ⓐ $−117 \div \left(−3\right)$ ⓑ $3 \cdot 13$ ⓒ $7 \left(−4\right)$ ⓓ $−42 \div 6 .$

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

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

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

Simplify: ⓐ $8 \left(−9\right) \div \left(−2\right)^{3}$ ⓑ $−30 \div 2 + \left(−3\right) \left(−7\right) .$

Simplify: ⓐ $12 \left(−9\right) \div \left(−3\right)^{3}$ ⓑ $−27 \div 3 + \left(−5\right) \left(−6\right) .$

Simplify: ⓐ $18 \left(−4\right) \div \left(−2\right)^{3}$ ⓑ $−32 \div 4 + \left(−2\right) \left(−7\right) .$

Evaluate: $3 x^{2} - 2 x y + 6 y^{2}$ when $x = 1 , y = −2 .$

Evaluate: $4 x^{2} - x y + 5 y^{2}$ when $x = −2 , y = 3 .$

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.

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?

Fill in $< , > ,$ or $=$ for each of the following pairs of numbers.

ⓐ $\left|−7\right| ___ - \left|−7\right|$
ⓑ $6 ___ - \left|−6\right|$
ⓒ $\left|−11\right| ___ - 11$
ⓓ $− \left(−13\right) ___ - \left|−13\right|$

Fill in $< , > ,$ or $=$ for each of the following pairs of numbers.

ⓐ $− \left|2\right| ___ - \left|−2\right|$
ⓑ $−12 ___ - \left|−12\right|$
ⓒ $\left|−3\right| ___ - 3$
ⓓ $\left|−19\right| ___ - \left(−19\right)$

Simplify.

$\left|15 - 7\right| - \left|14 - 6\right|$

Simplify.

$18 - \left|2 \left(8 - 3\right)\right|$

Simplify.

$18 - \left|12 - 4 \left(4 - 1\right) + 3\right|$

Simplify.

$10 - 3 \left|9 - 3 \left(3 - 1\right)\right|$

Simplify each expression.

ⓐ $−7 + \left(−4\right)$
ⓑ $−7 + 4$
ⓒ $7 + \left(−4\right) .$

Simplify each expression.

$48 + \left(−16\right)$

Simplify each expression.

$−14 + \left(−12\right) + 4$

Simplify each expression.

$19 + 2 \left(−3 + 8\right)$

Simplify each expression.

ⓐ $13 - 7$
ⓑ $−13 - \left(−7\right)$
ⓒ $−13 - 7$
ⓓ $13 - \left(−7\right)$

Simplify each expression.

$−17 - 42$

Simplify each expression.

$−14 - \left(−27\right) + 9$

Simplify each expression.

ⓐ $44 - 28$ ⓑ $44 + \left(−28\right)$

Simplify each expression.

ⓐ $27 - \left(−18\right)$ ⓑ $27 + 18$

Simplify each expression.

$\left(2 - 7\right) - \left(3 - 8\right)$

Simplify each expression.

$− \left(6 - 8\right) - \left(2 - 4\right)$

Simplify each expression.

$25 - \left[10 - \left(3 - 12\right)\right]$

Multiply or divide.

ⓐ $−4 \cdot 8$
ⓑ $13 \left(−5\right)$
ⓒ $−24 \div 6$
ⓓ $−52 \div \left(−4\right)$

Multiply or divide.

ⓐ $−28 \div 7$
ⓑ $−180 \div 15$
ⓒ $3 \left(−13\right)$
ⓓ $−1 \left(−14\right)$

Simplify each expression.

ⓐ $\left(−2\right)^{6}$ ⓑ $− 2^{6}$

Simplify each expression.

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

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.

$8 - \left|2 - 4 \left(4 - 1\right) + 3\right|$

Simplify each expression.

$9 - 3 \left|2 \left(2 - 6\right) - \left(3 - 7\right)\right|$

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.

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

Evaluate each expression.

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

Evaluate each expression.

$3 x^{2} - 4 x y + 2 y^{2}$ when
$x = −2 , y = −3$

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 $−18$
ⓑ subtract $11$ from $−25$

Translate to an algebraic expression and simplify if possible.

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

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?

Explain why the sum of $−8$ and 2 is negative, but the sum of 8 and $−2$ is positive.

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