Name _______________________________________________ Date __________________ Period _________
Unit 1: Integers
Study Guide
Comparing, Ordering and Absolute Value
1. Put the following numbers in order from least to greatest:
{ -6,
-8,
|-9|,
6,
2. Put the following numbers in order from least to greatest:
{ 16, -(-7), -4, -|-10|,
Compare the following using <. > or =.
3. -|14| ____ |-14|
4. -(9) ____ -|9|
5. -18 ____ -16
6. 6(6) ____ -6(-6)
Adding Integers
7. -8 + 20
8. -6 + (-8)
9. |-12| + (-5)
10. -|10| + 7 + (-8)
11. -4 + (-12) + (-8)
12. |-22| + (-49) + (-15) + 2
13. -|9| + |-9 + 9| + (-9) + 9
14. 9 + (-8) + |-2 + 8|
-|-4|,
-(-2) }
|-12|, -5 }
Subtracting Integers
15. -13 - 22
16. -3 - (-11)
17. |-15| - (-4)
18. -|17| - 5 - (-12)
19. -7 - (-16) - (-2)
20. |-20| - (-14) - (-1) - 9
21. -|12| - |-5 + 8| - (-12)
22. 16 – (-4) - |-9 – 11|
Multiplying and Dividing Integers
23. -7(8)
25.
27.
24. -12(-3)
26. -50  (-2)(5)
−28
2
−3(8)
−2(−3)(−4)
29. −
18
3
+ 2(-3)
28. (-5)2
30. Find the mean of the integers:
11, -7, -14, 10, -5
Applying Integers
31. The elevation of Death Valley, California is -282 feet. The Mississippi River in Illinois has an elevation of
279 feet.
a. Which is closer to sea level?
b. Write and solve an expression to find the difference between the two elevations.
32. The table below shows the income and expenses for a school carnival. The school’s goal was to raise
$1100. Did the school reach its goal? Explain.
Games
$650
Concessions
$530
Donations
$52
Combining Like Terms
Simplify the following expressions by combining like terms:
33.
4x + 12 – 5x2 – x
34.
8y – 3x + 4 – 2y + 9 – 6x
35.
7x4 – x + 11 – 2x2 + 16 – 6x
Flyers
-$28
Decorations
-$75
The Distributive Property
Use the distributive property to simplify each expression. Then, if possible, combine like terms.
36. 4(x + 8)
37. 7(2x – 5)
38. -12(6 – a)
39. 7(4 + 3x) – 8
40. 2 + 3(4x – 2)
41. 2 - 7(6 – x) + 6
42. 5 – (2x + 3)
43. -3 – (6x – 6)
Name ___________________________________________ Date ______________________ Period _________
Unit 1 – Integers: Study Guide Answer Key
1. -8, -6, -|-4|, -(-2), 6, |-9|
25. -14
2. -|-10|, -5, -4, -(-7), |-12|, 16
26. 5
3. <
27. 1
4. =
28. 25
5. <
29. -12
6. =
30. -1
7. 12
31. a. The Mississippi River in Illinois
8. -14
b.
9. 7
32. Yes, the school reached its goal because it
279 – (-282) = 561 feet
10. -11
raised $1,232 and only spent $103. This means
11. -24
they had a total income of $1,129 which is
12. -40
more than $1,100.
13. -9
33. -5x2 + 3x + 12
14. 7
34. 6y – 9x + 13
15. -35
35. 7x4 - 2x2 – 7x + 27
16. 8
36. 4x + 32
17. 19
37. 14x – 35
18. -10
38. 12a – 72
19. 11
39. 21x + 20
20. 26
40. 12x – 4
21. -3
41. 7x – 34
22. 0
42. -2x + 2
23. -56
43. -6x + 3
24. 36