1.3 Add and Subtract Integers

Order each of the following pairs of numbers, using $<$ or $> :$ ⓐ $15 ___ 7$ ⓑ $−2 ___ 5$ ⓒ $−3 ___ −7$
ⓓ $5 ___ −17 .$

Order each of the following pairs of numbers, using $<$ or $> :$ ⓐ $8 ___ 13$ ⓑ $3 ___ −4$ ⓒ $−5 ___ −2$
ⓓ $9 ___ −21 .$

Find: ⓐ the opposite of 4 ⓑ the opposite of $−3$ ⓒ $− \left(−1\right) .$

Find: ⓐ the opposite of 8 ⓑ the opposite of $−5$ ⓒ $− \left(−5\right) .$

Evaluate $− n ,$ when ⓐ $n = 4$ ⓑ $n = −4 .$

Evaluate $− m ,$ when ⓐ $m = 11$ ⓑ $m = −11 .$

Simplify: ⓐ $\left|3\right|$ ⓑ $\left|−44\right|$ ⓒ $\left|0\right|$.

Simplify: ⓐ $\left|4\right|$ ⓑ $\left|−28\right|$ ⓒ $\left|0\right| .$

Simplify: ⓐ $\left|−13\right|$ ⓑ $\left|47\right|$ ⓒ $\left|0\right| .$

Fill in $< , > , \text{or} =$ 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: ⓐ $\left|−9\right| ___ - \left|−9\right|$ ⓑ $2 ___ - \left|−2\right|$ ⓒ $−8 ___ \left|−8\right|$
ⓓ $− \left(−9\right) ___ - \left|−9\right| .$

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

Evaluate: ⓐ $\left|x\right| \text{when} x = −17$ ⓑ $\left|− y\right| \text{when} y = −39$ ⓒ $− \left|m\right| \text{when} m = 22$ ⓓ $− \left|p\right| \text{when} p = −11 .$

Evaluate: ⓐ $\left|y\right| \text{when} y = −23$ ⓑ $\left|− y\right| \text{when} y = −21$ ⓒ $− \left|n\right| \text{when} n = 37$ ⓓ $− \left|q\right| \text{when} q = −49 .$

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

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

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

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

Simplify: ⓐ $19 + \left(−47\right)$ ⓑ $−14 + \left(−36\right) .$

Simplify: ⓐ $−31 + \left(−19\right)$ ⓑ $15 + \left(−32\right) .$

Simplify: ⓐ $−42 + \left(−28\right)$ ⓑ $25 + \left(−61\right) .$

Simplify: $−5 + 3 \left(−2 + 7\right) .$

Simplify: $−2 + 5 \left(−4 + 7\right) .$

Simplify: $−4 + 2 \left(−3 + 5\right) .$

Subtract: ⓐ $7 - 5$ ⓑ $−7 - \left(−5\right) .$

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

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

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

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

Simplify: ⓐ $13 - 8$ and $13 + \left(−8\right)$ ⓑ $−17 - 9$ and $−17 + \left(−9\right) .$

Simplify: ⓐ $21 - 13$ and $21 + \left(−13\right)$ ⓑ $−11 - 7$ and $−11 + \left(−7\right) .$

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

Simplify: ⓐ $9 - \left(−15\right)$ and $9 + 15$ ⓑ $−7 - \left(−4\right)$ and $−7 + 4 .$

Simplify: ⓐ $6 - \left(−13\right)$ and $6 + 13$ ⓑ $−5 - \left(−1\right)$ and $−5 + 1 .$

Simplify: ⓐ $4 - \left(−19\right)$ 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: $12 - \left(−9 - 6\right) - 14$.

Order each of the following pairs of numbers, using < or >.

ⓐ $9 ___ 4$
ⓑ $−3 ___ 6$
ⓒ $−8 ___ −2$
ⓓ $1 ___ −10$

Find the opposite of each number.

ⓐ 2 ⓑ $−6$

Simplify.

$− \left(−4\right)$

Simplify.

$− \left(−15\right)$

Evaluate.

$− c$ whenⓐ $c = 12$ⓑ $c = −12$

Simplify.

ⓐ $\left|−32\right|$ⓑ $\left|0\right|$ⓒ $\left|16\right|$

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

ⓐ $−6 ___ \left|−6\right|$ⓑ $− \left|−3\right| ___ −3$

Simplify.

$− \left(−5\right) \text{and} − \left|−5\right|$

Simplify.

$8 \left|−7\right|$

Simplify.

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

Simplify.

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

Evaluate.

ⓐ $− \left|p\right| \text{when} p = 19$
ⓑ $− \left|q\right| \text{when} q = −33$

Simplify each expression.

$−21 + \left(−59\right)$

Simplify each expression.

$48 + \left(−16\right)$

Simplify each expression.

$−14 + \left(−12\right) + 4$

Simplify each expression.

$135 + \left(−110\right) + 83$

Simplify each expression.

$19 + 2 \left(−3 + 8\right)$

Simplify.

$8 - 2$

Simplify.

$−5 - 4$

Simplify.

$8 - \left(−4\right)$

Simplify.

ⓐ $44 - 28$ⓑ $44 + \left(−28\right)$

Simplify.

ⓐ $27 - \left(−18\right)$ⓑ $27 + 18$

Simplify each expression.

$15 - \left(−12\right)$

Simplify each expression.

$48 - 87$

Simplify each expression.

$−17 - 42$

Simplify each expression.

$−103 - \left(−52\right)$

Simplify each expression.

$−45 - \left(–54\right)$

Simplify each expression.

$8 - 3 - 7$

Simplify each expression.

$−5 - 4 + 7$

Simplify each expression.

$−14 - \left(−27\right) + 9$

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.

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

Simplify each expression.

$6 \cdot 3 - 4 \cdot 3 - 7 \cdot 2$

Simplify each expression.

$5^{2} - 6^{2}$

Elevation The highest elevation in the United States is Mount McKinley, Alaska, at 20,320 feet above sea level. The lowest elevation is Death Valley, California, at 282 feet below sea level.

Use integers to write the elevation of:

ⓐ Mount McKinley. ⓑ Death Valley.

State budgets In June, 2011, the state of Pennsylvania estimated it would have a budget surplus of $540 million. That same month, Texas estimated it would have a budget deficit of $27 billion.

Use integers to write the budget of:

ⓐ Pennsylvania.
ⓑ Texas.

Stock Market The week of September 15, 2008 was one of the most volatile weeks ever for the US stock market. The closing numbers of the Dow Jones Industrial Average each day were:

What was the overall change for the week? Was it positive or negative?

Give an example of a negative number from your life experience.

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