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04/08/2023 1
Pre-Algebra
Mental Math Speed ReviewWith Answers
04/08/2023 2
Created By: Anna [email protected]
Mendez Fundamental Intermediate SchoolSanta Ana Unified School District
Santa Ana, California
Licensed under Creative Commons
04/08/2023 3
-2- 4
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-6
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-2 - 6
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-8
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-3 - 6
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-9
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- 4 + - 9
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-13
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-8 + - 2
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-10
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-2(6)
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-12
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-2 + -6
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-8
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-5(-3)
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15
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-5 - 3
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-8
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-5 + 3
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-2
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-5 – 15 - 20
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-40
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-10 + -10 -10
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-30
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50 – 25 – 25
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0
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30 – 20 – 5
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5
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12
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2
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122
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144
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121
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12
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120
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1
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Name the Property
2 + (3 + 4) = (2 + 3) + 4Commutative
Associative Distributive
Identity Inverse
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Assoc.Name the Property
2 + (3 + 4) = (2 + 3) + 4
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Name the Property
5 + (-5) = 0Commutative
Associative Distributive
Identity Inverse
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InverseName the Property
5 + (-5) = 0
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Name the Property
Commutative Associative Distributive
Identity Inverse
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Inverse
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Name the Property
2 + (3 + 4) = 2 + (4 + 3)Commutative
Associative Distributive
Identity Inverse
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Commut.
Name the Property
2 + (3 + 4) = 2 + (4 + 3)
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Name the Property
1(p) = pCommutative
Associative Distributive
Identity Inverse
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Identity
Name the Property
1(p) = p
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Name the Property
2(3a + 4b) = 6a + 8bCommutative
Associative Distributive
Identity Inverse
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Distribut.
Name the Property
2(3a + 4b) = 6a + 8b
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Name the Property
a + (b + c) = (a + b) + cCommutative
Associative Distributive
Identity Inverse
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Assoc.
Name the Property
a + (b + c) = (a + b) + c
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Name the Property
(a + b) + c = c + (a + b)Commutative
Associative Distributive
Identity Inverse
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CommutName the Property
(a + b) + c = c + (a + b)
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Name the Property
5(a + 10) = 5a + 50Commutative
Associative Distributive
Identity Inverse
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Distrib.
Name the Property
5(a + 10) = 5a + 50
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7
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1
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0
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AREA = L x W
What is the area in the model above?
What is the perimeter in the model above?
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Area = (4 x 5) = 20 units2
Perimeter = (4 + 4 + 5 + 5) = 18 units
4
5
4
5
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What is the area?
What is the perimeter?
6
10
12
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Area = (6x10)÷2 = 30units2
Perimeter = 28 units = 6+12+10
6
10
12
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What is the area?
What is the perimeter?
3
4
5
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Area = 3 x 4 ÷2 = 6 units2
Perimeter = 12 units = 3 + 4 + 5
3
4
5
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This is a square. Each side measures 6 inches.What is the area? What is the perimeter?
6 inches
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Area = 36 in2
Perimeter = 24 in = 6 + 6 + 6 + 6
6 inchesThis is a square.
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This is a rectangle.What is the area? What is the perimeter?
2 inches
3 inches
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Area = 3 x 2 = 6 in2
Perimeter = 10 in 3+3+2+2
2 inches
3 inches
04/08/2023 79
Which of these numbers is irrational?
65
15
144
16
817.777…
9
15-64
3 15
16
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Which of these numbers is irrational?
65
15
144
16
817.777…
9
15-64
3 15
16
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Which of these numbers is irrational?
49
35100
49
121
1.2666…
7
3-35
0
28
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Which of these numbers is irrational?
49
35100
49
121
1.2666…
7
3-35
0
28
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Which of these numbers is irrational?
471
19
90
169
0.875
5
4-5
14
100
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Which of these numbers is irrational?
471
19
90
169
0.875
5
4-5
14
100
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53 xx
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€
x −3 • x 5
€
x 2
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28 xx
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€
x10
€
x 8 • x 2
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33 xx
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133 xx
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1885
x
Step 1: To solve this equation, what do you do first?
Step 2: What do you next?
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Subtract 8 from both sides.
Next, multiply both sides by -5.
1885
x
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2453
x
Step 1: To solve this equation, what do you do first?
Step 2: What do you next?
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Add 5 to both sides.
Next, multiply both sides by 3.
2453
x
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Step 1: To solve this equation, what do you do first?
244
3x
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Multiply both sidesby the reciprocal ( ).
244
3x
04/08/2023 99
Step 1: To solve this equation, what do you do first?
2411
6x
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Multiply both sidesby the reciprocal ( ).
2411
6x
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Step 1: To solve this equation, what do you do first?
Step 2: What do you do next?
3245
8x
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First, subtract 4 from each side.
Next, multiply both sidesby the reciprocal ( ).
3245
8x
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2
3
5
5 =
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52
3
5
5
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2
4
7
7 =
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492
4
7
7
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6
6
4
4 =
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6
6
4
4= 1
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4
7
10
10 =
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=
4
7
10
10= 103 = 1000
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32 Is between _____ and _____
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5 and 632 Is between _____ and _____
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4mCan also be written as ____
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“ONE over M to the 4th Power”
4
1
m
4mCan also be written as ____
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Can also be written as ____X-5
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“ONE over x to the 5th Power”
5
1
x
Can also be written as ____X-5
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Can also be written as ____y-2
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“ONE over Y to the 2nd Power or
“ONE over Y squared”2
1
y
Can also be written as ____y-2
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19
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19
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0
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How do you get the slope? What is the slope of the given line?
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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
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How do you get the slope? What is the slope of the given line?
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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
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How do you get the slope? What is the slope of the given line?
Does it matter which points you use?
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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!
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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)?
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You plot the two points on a graph, and write a fraction that shows: The change in Y over the change in X
04/08/2023 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)?
04/08/2023 136
You plot the two points on a graph, and write a fraction that shows: The change in Y over the change in X
04/08/2023 137
A square has an area of 49 feet2. How long is each side?
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7 feet
A square has an area of 49 feet2. How long is each side?
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A square has an area of 64 square feet. How long is each side?
04/08/2023 140
8 feetA square has an area of 64 square feet. How long is each side?
04/08/2023 141
A square has an area of 169 square feet. How long is each side?
04/08/2023 142
13 feetA square has an area of 169 square feet. How long is each side?
04/08/2023 143
A square has an area of 30 square feet. About how long is each side?
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Between 5 and 6 feet
A square has an area of 30 square feet. About how long is each side?
04/08/2023 145
A square has an area of 55 square feet. About how long is each side?
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Between 7 and 8 feet
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What is the slope?
y = -4x + 7
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What is the slope? -4y = -4x + 7
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What is the slope?
y = -x + 7
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What is the slope? -1y = -1x + 7
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What is the slope?
y = 5
04/08/2023 153
What is the slope? 0y = 5y = 0x + 5
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How do you find the length of x?
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How do you find the length of x?
a2 + b2 = c2
04/08/2023 156
How do you find the length of x?
04/08/2023 157
How do you find the length of x?
c2 - a2 = b2
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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?
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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!
a2 + b2 = c2
2225 cc15
04/08/2023 160
6 m
5 m
How do you find the length of x?
04/08/2023 161
6 m
5 m
How do you find the length of x?
3
c2 - a2 = b2
52 - 32 = b2
Notice 3 not 6
04/08/2023 162
When would you use formula ?
04/08/2023 163
When would you use formula ?
To find the hypotenuse of a right triangle, or to find c.
04/08/2023 164
Distribute3(a + b + c)
04/08/2023 165
Distribute3(a + b + c)3a + 3b + 3c
04/08/2023 166
Distribute4(a -x)
04/08/2023 167
Distribute4(a – x)4a – 4x
04/08/2023 168
Distribute2(3f + 4g)
04/08/2023 169
Distribute2(3f + 4g) 6f + 8g
04/08/2023 170
Distribute-2(a + b)
04/08/2023 171
Distribute-2(a + b)-2a + -2b or-2a – 2b
04/08/2023 172
Distribute-3(x – y – z)
04/08/2023 173
Distribute-3(x – y – z)-3x - -3y - -3z or-3x + 3y + 3z
04/08/2023 174
04/08/2023 175
Simplify:
24x14 ÷ 12x2
04/08/2023 176
Simplify: 24x14 ÷ 12x2
2x12
04/08/2023 177
Simplify:
(ab)-4(ab) =
04/08/2023 178
Simplify:(ab)-4(ab)1 =(ab)(-4+1) =(ab)-3
04/08/2023 179
How do you simplify?:
04/08/2023 180
How do you simplify?:)56(88 188
82 = 64
04/08/2023 181
True or False: Slope can be described as steepness.
04/08/2023 182
True
04/08/2023 183
What is wrong with this sentence: Slope is the ratio (fraction) of the change in x to the change in y.
04/08/2023 184
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!
04/08/2023 185
How do you calculate the SLOPE of the hypotenuse? How do you calculate the LENGTHof the hypotenuse?
04/08/2023 186
How do you calculate the SLOPE of the hypotenuse? You write a FRACTION that shows: the CHANGE IN Y over theCHANGE IN X.How do you calculate the LENGTHof the hypotenuse?Use a2 + b2 = c2 (because it is a right triangle).
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How do you calculate the SLOPE of the hypotenuse? How do you calculate the LENGTHof the hypotenuse?
04/08/2023 188
How do you calculate the SLOPE of the hypotenuse? You write a FRACTION that shows: the CHANGE IN Y over theCHANGE IN X.How do you calculate the LENGTHof the hypotenuse?Use a2 + b2 = c2 (because it is a right triangle).
04/08/2023 189
What is the unit rate shown in this chart?
04/08/2023 190
What is the unit rate shown in this chart?
15
Find the rate for ONE (1) hour!= 15 miles per hour
302 Or find the slope,
change in Y overchange in X (30/2) and simplify it (15/1), = 15 miles per hour
04/08/2023 191
What is the slope shown in this chart?
04/08/2023 192
What is the unit rate shown in this chart?
15
Find the rate for ONE (1) hour!Slope = 15/1 = 15
302 Or find the slope,
change in Y overchange in X (30/2) and simplify it (15/1), Slope = 15
04/08/2023 193
0 2 4 6 8 10 12 14 $-
$200
$400
$600
$800
$1,000
$1,200
$1,400
$1,600
$1,800
$2,000
Dollars
Months
What is the unit rate shown in this chart?
04/08/2023 194
0 2 4 6 8 10 12 14 $-
$200
$400
$600
$800
$1,000
$1,200
$1,400
$1,600
$1,800
$2,000
Dollars
Months
What is the unit rate shown in this chart?
$150 per month
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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?
04/08/2023 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
04/08/2023 197
Convert 6/7 into a decimal or percent.
What is the first step?
04/08/2023 198
Convert 6/7 into a decimal or percent.
Long Division!!!
04/08/2023 199
Convert 152/7 into a decimal or percent.
What is the first step?
04/08/2023 200
Convert 152/7 into a decimal or percent. What is the first step?Long division, 2 divided by 7.
04/08/2023 201
Convert 43/8 into a decimal or percent.
What is the first step?
04/08/2023 202
Convert 43/8 into a decimal or percent. What is the first step? Long division, 3 divided by 8.
04/08/2023 203
Convert 62/9 into a decimal or percent.
What is the first step?
04/08/2023 204
Convert 62/9 into a decimal or percent. What is the first step?Long Division, 2 divided by 9.
04/08/2023 205
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Read this decimal number: 0.56Convert 0.56 into a fraction. What are the two steps?
04/08/2023 208
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.
04/08/2023 209
Read this number: 0.375Convert 0.375 into a fraction.What are the two steps?
04/08/2023 210
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.
04/08/2023 211
Convert 3.4 into a mixed number. What are the two steps?
04/08/2023 212
Convert 3.4 into a mixed number. What are the two steps? Write 4 over 10 (4/10), then simplify (2/5), then write the 3 alongside the fraction:
5
23
04/08/2023 213
How do you solve this problem?
“What is 7/8 of 3/4?”
04/08/2023 214
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!
04/08/2023 215
How do you solve this problem?
“What is two-thirds of five eighths?”
04/08/2023 216
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!
04/08/2023 217
How do you solve this problem?
“What is six-fifths of nine-tenths?”
04/08/2023 218
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!
04/08/2023 219
What does “OF” represent or indicate in a fraction (or percent) word problem?
04/08/2023 220
What does “OF” represent or indicate in a fraction (or percent) word problem? Multiply!
04/08/2023 221
How do you solve this problem?
“What is 40% of 350?”
04/08/2023 222
How do you solve this problem? “What is 40% of 350?”
Multiply .40 times 350Or
Multiply 40/100 times 350
04/08/2023 223
2
56
How do you solve?
04/08/2023 224
2
56
How do you solve?
Change 6 to improper fraction then pre-simplify, then multiply across.
1
6
04/08/2023 225
62
14
How do you solve?
04/08/2023 226
62
14
How do you solve?
Change BOTH to improper fractions, then pre-simplify, then multiply.
04/08/2023 227
4
328
How do you solve?
04/08/2023 228
4
328
How do you solve?
Change BOTH to improper fractions, then pre-simplify, then multiply.
04/08/2023 229
2
16
3
23
How do you solve?
04/08/2023 230
2
16
3
23
How do you solve?
Change BOTH to improper fractions, then pre-simplify, then multiply.
04/08/2023 231
5 students work 6 hours on a project. How many person-hours is this?
04/08/2023 232
30 person -hours
04/08/2023 233
10 students work 5 hours at the carwash. How many person-hours is this?
04/08/2023 234
50 hours
04/08/2023 235
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.
04/08/2023 236
11 hours
04/08/2023 237
What is the equation for this set of points?Choose one: y = x2
y = -x2
y = x3
y = -x3
04/08/2023 238
y = x2
04/08/2023 239
What is the equation for this set of points?Choose one: y = x2
y = -x2
y = x3
y = -x3
04/08/2023 240
y = -x2
04/08/2023 241
What is the equation for this set of points?Choose one: y = x2
y = -x2
y = x3
y = -x3
04/08/2023 242
y = x3
04/08/2023 243
What is the equation for this set of points?Choose one: y = x2
y = -x2
y = x3
y = -x3
04/08/2023 244
y = -x3