This document contains a pre-algebra review created by Anna Wells for students at Mendez Fundamental Intermediate School. It includes over 60 mental math problems covering topics like properties of operations, solving equations, finding slopes of lines, calculating areas and perimeters of shapes, and more. The problems are followed by their answers to allow students to self-check their work.

1. Pre-Algebra
1/30/2015
Mental Math
Speed Review
With Answers
1

2. Created By: Anna Wells
Anna.wells@sausd.us
Mendez Fundamental Intermediate School
Santa Ana Unified School District
Santa Ana, California
Licensed under Creative Commons
1/30/2015 2

3. -2- 4
1/30/2015 3

4. -6
1/30/2015 4

5. -2 - 6
1/30/2015 5

6. -8
1/30/2015 6

7. -3 - 6
1/30/2015 7

8. -9
1/30/2015 8

9. - 4 + - 9
1/30/2015 9

10. -13
1/30/2015 10

11. -8 + - 2
1/30/2015 11

12. -10
1/30/2015 12

13. -2(6)
1/30/2015 13

14. -12
1/30/2015 14

15. -2 + -6
1/30/2015 15

16. -8
1/30/2015 16

17. -5(-3)
1/30/2015 17

18. 15
1/30/2015 18

19. -5 - 3
1/30/2015 19

20. -8
1/30/2015 20

21. -5 + 3
1/30/2015 21

22. -2
1/30/2015 22

23. -5 – 15 - 20
1/30/2015 23

24. -40
1/30/2015 24

25. -10 + -10 -10
1/30/2015 25

26. -30
1/30/2015 26

27. 50 – 25 – 25
1/30/2015 27

28. 0
1/30/2015 28

29. 30 – 20 – 5
1/30/2015 29

30. 5
1/30/2015 30

31. 1/30/2015 31

32. 1/30/2015 32

33. 1/30/2015 33

34. 12
1/30/2015 34

35. 1/30/2015 35

36. 2
1/30/2015 36

37. 122
1/30/2015 37

38. 144
1/30/2015 38

39. 121
1/30/2015 39

40. 12
1/30/2015 40

41. 120
1/30/2015 41

42. 1
1/30/2015 42

43. Name the Property
2 + (3 + 4) = (2 + 3) + 4
Commutative
Associative
Distributive
Identity
Inverse
1/30/2015 43

44. Assoc.
1/30/2015 44
Name the Property
2 + (3 + 4) = (2 + 3) + 4

45. Name the Property
5 + (-5) = 0
Commutative
Associative
Distributive
Identity
Inverse
1/30/2015 45

46. Inverse
1/30/2015 46
Name the Property
5 + (-5) = 0

47. Name the Property
Commutative
Associative
Distributive
Identity
Inverse
1/30/2015 47

48. Inverse
1/30/2015 48

49. Name the Property
2 + (3 + 4) = 2 + (4 + 3)
Commutative
Associative
Distributive
Identity
Inverse
1/30/2015 49

50. Commut.
1/30/2015 50
Name the Property
2 + (3 + 4) = 2 + (4 + 3)

51. Name the Property
1(p) = p
Commutative
Associative
Distributive
Identity
Inverse
1/30/2015 51

52. Identity
1/30/2015 52
Name the Property
1(p) = p

53. Name the Property
2(3a + 4b) = 6a + 8b
Commutative
Associative
Distributive
Identity
Inverse
1/30/2015 53

54. Distribut.
1/30/2015 54
Name the Property
2(3a + 4b) = 6a + 8b

55. Name the Property
a + (b + c) = (a + b) + c
Commutative
Associative
Distributive
Identity
Inverse
1/30/2015 55

56. Assoc.
1/30/2015 56
Name the Property
a + (b + c) = (a + b) + c

57. Name the Property
(a + b) + c = c + (a + b)
Commutative
Associative
Distributive
Identity
Inverse
1/30/2015 57

58. Commut
1/30/2015 58
Name the Property
(a + b) + c = c + (a + b)

59. Name the Property
5(a + 10) = 5a + 50
Commutative
Associative
Distributive
Identity
Inverse
1/30/2015 59

60. Distrib.
1/30/2015 60
Name the Property
5(a + 10) = 5a + 50

61. 1/30/2015 61

62. 1/30/2015 62

63. 1/30/2015 63

64. 7
1/30/2015 64

65. 1/30/2015 65

66. 1
1/30/2015 66

67. 1/30/2015 67

68. 0
1/30/2015 68

69. AREA = L x W
What is the area in the model above?
What is the perimeter in the model
above?
1/30/2015 69

70. Area = (4 x 5) = 20 units2
Perimeter = (4 + 4 + 5 + 5) = 18 units
1/30/2015 70
4
5
4
5

71. What is the
area?
What is the
perimeter?
6
10
12
1/30/2015 71

72. Area = (6x10)÷2 = 30units2
Perimeter = 28 units
= 6+12+10
1/30/2015 72
6
10
12

73. What is the
area?
What is the
perimeter?
3
4
5
1/30/2015 73

74. Area = 3 x 4 ÷2 = 6 units2
Perimeter = 12 units
= 3 + 4 + 5
1/30/2015 74
3
4
5

75. This is a square. Each
side measures 6 inches.
What is the area?
What is the perimeter?
6 inches
1/30/2015 75

76. Area = 36 in2
Perimeter = 24 in
= 6 + 6 + 6 + 6
1/30/2015 76
6 inchesThis is a square.

77. This is a rectangle.
What is the area?
What is the perimeter?
2 inches
3 inches
1/30/2015 77

78. Area = 3 x 2 =6 in2
Perimeter = 10 in
3+3+2+2
1/30/2015 78
2 inches
3 inches

79. Which of these
numbers is
irrational?
65
15
144
16
81
7.777…
9
15
-64 
3 15
16
1/30/2015 79

80. Which of these
numbers is
irrational?
65
15
144
16
81
7.777…
9
15
-64 
3 15
16
1/30/2015 80

81. Which of these
numbers is
irrational?
49
35
100
49
121
1.2666…
7
3
-35
0
28

1/30/2015 81

82. Which of these
numbers is
irrational?
49
35
100
49
121
1.2666…
7
3
-35
0
28

1/30/2015 82

83. Which of these
numbers is
irrational?
4
71
19
90
169
0.875
5
4
-5
14
100
1/30/2015 83

84. Which of these
numbers is
irrational?
4
71
19
90
169
0.875
5
4
-5
14
100
1/30/2015 84

85. 53
xx 
1/30/2015 85

86. 1/30/2015 86

87. 28
xx 
1/30/2015 87

88. 1/30/2015 88

89. 33 
 xx
1/30/2015 89

90. 1/30/2015
1
90
33 
 xx

91. 1/30/2015 91

92. 1/30/2015 92

93. 188
5


x
Step 1: To solve this equation, what
do you do first?
Step 2: What do you next?
1/30/2015 93

94. 1/30/2015
Subtract 8 from both sides.
Next, multiply both sides by -5.
94
188
5


x

95. 245
3

x
Step 1: To solve this equation, what
do you do first?
Step 2: What do you next?
1/30/2015 95

96. 1/30/2015
Add 5 to both sides.
Next, multiply both sides by 3.
96
245
3

x

97. Step 1: To solve this
equation, what do you do
first?
24
4
3
x
1/30/2015 97

98. 1/30/2015
Multiply both sides
by the reciprocal ( ).
98
24
4
3
x

99. Step 1: To solve this
equation, what do you do
first?
24
11
6
x
1/30/2015 99

100. 1/30/2015
Multiply both sides
by the reciprocal ( ).
100
24
11
6
x

101. Step 1: To solve this equation,
what do you do first?
Step 2: What do you do next?
324
5
8
x
1/30/2015 101

102. 1/30/2015
First, subtract 4 from each side.
Next, multiply both sides
by the reciprocal ( ).
102
324
5
8
x

103. 2
3
5
5
=
1/30/2015 103

104. 1/30/2015
5
104
2
3
5
5

105. 2
4
7
7
=
1/30/2015 105

106. 1/30/2015
49
106
2
4
7
7

107. 6
6
4
4
=
1/30/2015 107

108. 1/30/2015 108
6
6
4
4
= 1

109. 4
7
10
10
=
1/30/2015 109

110. =
1/30/2015 110
4
7
10
10
= 103 = 1000

111. 32 Is between _____ and _____
1/30/2015 111

112. 1/30/2015
5 and 6
112
32 Is between _____ and _____

113. 4
m
Can also be written as ____
1/30/2015 113

114. 1/30/2015
“ONE over M to the 4th Power”
4
1
m
114
4
m
Can also be written as ____

115. Can also be written as ____X-5
1/30/2015 115

116. 1/30/2015
“ONE over x to the 5th Power”
5
1
x
116
Can also be written as ____X-5

117. Can also be written as ____
y-2
1/30/2015 117

118. 1/30/2015
“ONE over Y to the 2nd Power
or
“ONE over Y squared”
2
1
y
118
Can also be written as ____y-2

119. 1/30/2015 119

120. 1/30/2015 120

121. 1/30/2015 121

122. 1/30/2015
19
122

123. 1/30/2015 123

124. 1/30/2015
19
124

125. 1/30/2015 125

126. 1/30/2015
0
126

127. How do you get the slope?
What is the slope of the given line?
1/30/2015 127

128. How do you get the slope? Look at the
points. Write a fraction that shows:
The change in Y over the change in X.
What is the slope
of the given line?
3 over 4, 3/4
1/30/2015 128

129. How do you get the slope?
What is the slope of the given line?
1/30/2015 129

130. 1/30/2015
How do you get the slope? Look at the
points. Write a fraction that shows:
The change in Y over the change in X.
What is the slope of
the given line?
1 over 2, 1/2
130

131. How do you get the slope?
What is the slope of the given line?
Does it matter
which points
you use?
1/30/2015 131

132. 1/30/2015
How do you get the slope? Look at the
points. Write a fraction that shows:
The change in Y over the change in X.
What is the slope of
the given line?
*DOWN* 3 over 3, 3/3 = -1
Does it matter which points
you use? NO, you get the same slope (after
you simplify the fraction) no matter which
points you use!
132

133. How do you find the slope of
the line that passes through
any two points?
For example, how do you find
the slope of a line that passes
through (3,5) and (-1,-2)?
1/30/2015 133

134. 1/30/2015
You plot the two points on a graph, and
write a fraction that shows:
The change in Y over the change in X
134

135. How do you find the slope of
the line that passes through
any two points?
For example, how do you find
the slope of a line that passes
through (-3, 16) and (-4,-2)?
1/30/2015 135

136. 1/30/2015
You plot the two points on a graph, and
write a fraction that shows:
The change in Y over the change in X
136

137. A square has an area of 49
feet2. How long is each side?
1/30/2015 137

138. 1/30/2015
7 feet
138
A square has an area of 49 feet2. How long
is each side?

139. A square has an area of 64
square feet. How long is each
side?
1/30/2015 139

140. 1/30/2015 140
8 feet
A square has an area of 64 square feet. How
long is each side?

141. A square has an area of 169
square feet. How long is each
side?
1/30/2015 141

142. 1/30/2015 142
13 feet
A square has an area of 169 square feet.
How long is each side?

143. A square has an area of 30
square feet. About how long
is each side?
1/30/2015 143

144. 1/30/2015 144
Between 5
and 6 feet
A square has an area of 30 square feet.
About how long is each side?

145. A square has an area of 55
square feet. About how long
is each side?
1/30/2015 145

146. 1/30/2015 146
Between 7
and 8 feet

147. 1/30/2015 147

148. What is the slope?
y = -4x + 7
1/30/2015 148

149. What is the slope?
-4
y = -4x + 7
1/30/2015 149

150. What is the slope?
y = -x + 7
1/30/2015 150

151. What is the slope?
-1
y = -1x + 7
1/30/2015 151

152. What is the slope?
y = 5
1/30/2015 152

153. What is the slope?
0
y = 5
y = 0x + 5
1/30/2015 153

154. How do you find the length of x?
1/30/2015 154

155. How do you find the length of x?
1/30/2015 155
a2 + b2 = c2

156. How do you find the length of x?
1/30/2015 156

157. How do you find the length of x?
1/30/2015 157
c2 - a2 = b2

158. 1. A right triangle has legs that are 6 cm and
8 cm long. How do you find the length of
the hypotenuse?
2. In the problem above, if you found
the length of the hypotenuse but it
was way too big (it doesn’t make
sense) you probably forgot to do the
last calculation. What is the last
calculation in an a2 + b2 = c2 problem?
1/30/2015 158

159. 1. A right triangle has legs that are 6 cm and 8 cm
long. How do you find the length of the
hypotenuse?
2. In the problem above, if you found the length of
the hypotenuse but it was way too big (it doesn’t
make sense) you probably forgot to do the last
calculation. What is the last calculation in an a2 +
b2 = c2 problem?
Take the square root of
both sides!
1/30/2015 159
a2 + b2 = c2
2
225 c
c15

160. 6 m
5 m
How do you
find the length
of x?
1/30/2015 160

161. 6 m
5 m
How do you
find the length
of x?
1/30/2015 161
3
c2 - a2 = b2
52 - 32 = b2
Notice 3 not 6

162. When would you use formula ?
1/30/2015 162

163. When would you use formula ?
1/30/2015 163
To find the hypotenuse of a
right triangle, or to find c.

164. Distribute
3(a + b + c)
1/30/2015 164

165. Distribute
3(a + b + c)
3a + 3b + 3c
1/30/2015 165

166. Distribute
4(a -x)
1/30/2015 166

167. Distribute
4(a – x)
4a – 4x
1/30/2015 167

168. Distribute
2(3f + 4g)
1/30/2015 168

169. Distribute
2(3f + 4g)
6f + 8g
1/30/2015 169

170. Distribute
-2(a + b)
1/30/2015 170

171. Distribute
-2(a + b)
-2a + -2b or
-2a – 2b
1/30/2015 171

172. Distribute
-3(x – y – z)
1/30/2015 172

173. Distribute
-3(x – y – z)
-3x - -3y - -3z or
-3x + 3y + 3z
1/30/2015 173

174. 1/30/2015 174

175. Simplify:
24x14 ÷ 12x2
1/30/2015 175

176. Simplify: 24x14 ÷ 12x2
1/30/2015 176
2x12

177. Simplify:
(ab)-4(ab) =
1/30/2015 177

178. Simplify:
(ab)-4(ab)1 =
1/30/2015 178
(ab)(-4+1) =
(ab)-3

179. How do you simplify?:
1/30/2015 179

180. How do you simplify?:
1/30/2015 180
)56(
88 

1
88
82 = 64

181. True or False: Slope
can be described as
steepness.
1/30/2015 181

182. 1/30/2015
True
182

183. What is wrong with this
sentence: Slope is the
ratio (fraction) of the
change in x to the change
in y.
1/30/2015 183

184. 1/30/2015
What is wrong with this sentence: Slope is
the ratio (fraction) of the change in x to the
change in y.
It is backwards, slope is the ratio
of the change in Y to X,
not X to Y.
21
21
xx
yy


Notice
y’s in the numerator,
x’s in the denominator!
184

185. How do you calculate the
SLOPE of the hypotenuse?
How do you
calculate the LENGTH
of the hypotenuse?
1/30/2015 185

186. How do you calculate the SLOPE of
the hypotenuse?
You write a FRACTION that shows:
the CHANGE IN Y over the
CHANGE IN X.
How do you
calculate the LENGTH
of the hypotenuse?
Use a2 + b2 = c2 (because
it is a right triangle).
1/30/2015 186

187. How do you calculate the
SLOPE of the hypotenuse?
How do you
calculate the LENGTH
of the hypotenuse?
1/30/2015 187

188. 1/30/2015 188
How do you calculate the SLOPE of
the hypotenuse?
You write a FRACTION that shows:
the CHANGE IN Y over the
CHANGE IN X.
How do you
calculate the LENGTH
of the hypotenuse?
Use a2 + b2 = c2 (because
it is a right triangle).

189. What is the unit rate shown in this chart?
1/30/2015 189

190. What is the unit rate shown in this chart?
1/30/2015
15
Find the rate for
ONE (1) hour!
= 15 miles per hour
30
2 Or find the slope,
change in Y over
change in X (30/2) and
simplify it (15/1),
= 15 miles per hour
190

191. What is the slope shown in this chart?
1/30/2015 191

192. What is the unit rate shown in this chart?
1/30/2015
15
Find the rate for
ONE (1) hour!
Slope = 15/1 = 15
30
2 Or find the slope,
change in Y over
change in X (30/2) and
simplify it (15/1),
Slope = 15
192

193. $-
$200
$400
$600
$800
$1,000
$1,200
$1,400
$1,600
$1,800
$2,000
0 2 4 6 8 10 12 14
Dollars
Months
What is the unit rate shown in this chart?
1/30/2015 193

194. $-
$200
$400
$600
$800
$1,000
$1,200
$1,400
$1,600
$1,800
$2,000
0 2 4 6 8 10 12 14
Dollars
Months
What is the unit rate shown in this chart?
1/30/2015 194
$150 per
month

195. What step(s) would you take to solve
this problem?
If Mary types 240 words in 6
minutes, how long will it take
her to type 440 words?
1/30/2015 195

196. What step(s) would you take to solve
this problem?
If Mary types 240 words in 6 minutes, how
long will it take her to type 440 words?
Set up a proportion,
then cross multiply (butterfly)
240 words 440 words
---------- = -------------
6 minutes x minutes
1/30/2015 196

197. Convert 6/7 into a
decimal or percent.
What is the first step?
1/30/2015 197

198. Convert 6/7 into a
decimal or percent.
Long Division!!!
1/30/2015 198

199. Convert 152/7 into a
decimal or percent.
What is the first step?
1/30/2015 199

200. Convert 152/7 into a
decimal or percent.
What is the first step?
Long division, 2 divided
by 7.
1/30/2015 200

201. Convert 43/8 into a
decimal or percent.
What is the first step?
1/30/2015 201

202. Convert 43/8 into a
decimal or percent.
What is the first step?
Long division, 3 divided
by 8.
1/30/2015 202

203. Convert 62/9 into a
decimal or percent.
What is the first step?
1/30/2015 203

204. Convert 62/9 into a
decimal or percent.
What is the first step?
Long Division, 2 divided
by 9.
1/30/2015 204

205. 1/30/2015 205

206. 1/30/2015 206

207. 1/30/2015
Read this decimal number:
0.56
Convert 0.56 into a fraction.
What are the two steps?
207

208. 1/30/2015
0.56 Fifty-six hundredths.
Convert 0.56 into a fraction.
What are the two steps?
Write the 56 over 100
(56/100)
then simplify.
208

209. 1/30/2015
Read this number:
0.375
Convert 0.375 into a fraction.
What are the two steps?
209

210. 1/30/2015
0.375 Three hundred seventy-
Five thousandths.
Convert 0.375 into a fraction.
What are the two steps?
Write 375 over 1000 (375/1000),
then simplify.
210

211. 1/30/2015
Convert 3.4 into a mixed
number.
What are the two steps?
211

212. 1/30/2015
Convert 3.4 into a mixed
number.
What are the two steps?
212
Write 4 over 10 (4/10),
then simplify (2/5), then write the
3 alongside the fraction:
5
2
3

213. 1/30/2015
How do you solve
this problem?
“What is 7/8 of
3/4?”
213

214. 1/30/2015
How do you solve this
problem?
“What is 7/8 of 3/4?”
Multiply them together!
When used with fractions
or percents, “of” means
multiply!
214

215. 1/30/2015
How do you solve
this problem?
“What is two-thirds
of five eighths?”
215

216. 1/30/2015
How do you solve this
problem?
“What is two-thirds of
five eighths?” Multiply
them together! When
used with fractions or
percents, “of” means
multiply!
216

217. 1/30/2015
How do you solve
this problem?
“What is six-fifths of
nine-tenths?”
217

218. 1/30/2015
How do you solve this
problem?
“What is six-fifths of
nine-tenths?” Multiply
them together! When
used with fractions or
percents, “of” means
multiply!
218

219. 1/30/2015
What does “OF”
represent or indicate in
a fraction (or percent)
word problem?
219

220. 1/30/2015
What does “OF” represent or
indicate in a fraction (or
percent) word problem?
Multiply!
220

221. 1/30/2015
How do you solve
this problem?
“What is 40% of
350?”
221

222. 1/30/2015
How do you solve this
problem?
“What is 40% of 350?”
Multiply .40 times 350
Or
Multiply 40/100 times 350
222

223. 1/30/2015
2
5
6
How do you solve?
223

224. 1/30/2015
2
5
6
How do you solve?
224
Change 6 to improper fraction
then pre-simplify, then
multiply across.
1
6

225. 1/30/2015 225
6
2
1
4 
How do you solve?

226. 1/30/2015 226
6
2
1
4 
How do you solve?
Change BOTH to improper
fractions, then pre-simplify,
then multiply.

227. 1/30/2015 227
4
3
28
How do you solve?

228. 1/30/2015 228
4
3
28
How do you solve?
Change BOTH to improper
fractions, then pre-simplify,
then multiply.

229. 1/30/2015 229
2
1
6
3
2
3 
How do you solve?

230. 1/30/2015 230
2
1
6
3
2
3 
How do you solve?
Change BOTH to improper
fractions, then pre-simplify,
then multiply.

231. 1/30/2015
5 students work 6
hours on a project.
How many person-
hours is this?
231

232. 1/30/2015
30 person -hours
232

233. 1/30/2015
10 students work 5
hours at the carwash.
How many person-
hours is this?
233

234. 1/30/2015
50 hours
234

235. 1/30/2015
It took the contractor 33
person-hours to paint the
house. There were 3 workers
on the job. How long did the
job take? Include units with
your answer.
235

236. 1/30/2015
11 hours
236

237. 1/30/2015 237
What is the
equation for this set
of points?
Choose one:
y = x2
y = -x2
y = x3
y = -x3

238. 1/30/2015 238
y = x2

239. 1/30/2015 239
What is the
equation for this
set of points?
Choose one:
y = x2
y = -x2
y = x3
y = -x3

240. 1/30/2015 240
y = -x2

241. 1/30/2015 241
What is the
equation for this
set of points?
Choose one:
y = x2
y = -x2
y = x3
y = -x3

242. 1/30/2015 242
y = x3

243. 1/30/2015 243
What is the
equation for this
set of points?
Choose one:
y = x2
y = -x2
y = x3
y = -x3

244. 1/30/2015 244
y = -x3