pre algebra mental math speed review with answers

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Pre-Algebra

Mental Math Speed ReviewWith Answers

04/08/2023 2

Created By: Anna WellsAnna.wells@sausd.us

Mendez Fundamental Intermediate SchoolSanta Ana Unified School District

Santa Ana, California

Licensed under Creative Commons

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-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

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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?

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

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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

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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, 16) and (-4,-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

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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?

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8 feetA square has an area of 64 square feet. How long is each side?

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A square has an area of 169 square feet. How long is each side?

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13 feetA square has an area of 169 square feet. How long is each side?

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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?

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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

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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

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How do you find the length of x?

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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

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6 m

5 m

How do you find the length of x?

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6 m

5 m

How do you find the length of x?

3

c2 - a2 = b2

52 - 32 = b2

Notice 3 not 6

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When would you use formula ?

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When would you use formula ?

To find the hypotenuse of a right triangle, or to find c.

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Distribute3(a + b + c)

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Distribute3(a + b + c)3a + 3b + 3c

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Distribute4(a -x)

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Distribute4(a – x)4a – 4x

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Distribute2(3f + 4g)

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Distribute2(3f + 4g) 6f + 8g

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Distribute-2(a + b)

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Distribute-2(a + b)-2a + -2b or-2a – 2b

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Distribute-3(x – y – z)

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Distribute-3(x – y – z)-3x - -3y - -3z or-3x + 3y + 3z

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Simplify:

24x14 ÷ 12x2

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Simplify: 24x14 ÷ 12x2

2x12

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Simplify:

(ab)-4(ab) =

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Simplify:(ab)-4(ab)1 =(ab)(-4+1) =(ab)-3

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How do you simplify?:

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How do you simplify?:)56(88 188

82 = 64

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True or False: Slope can be described as steepness.

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True

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

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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!

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How do you calculate the SLOPE of the hypotenuse? How do you calculate the LENGTHof the hypotenuse?

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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?

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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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What is the unit rate shown in this chart?

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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

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What is the slope shown in this chart?

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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

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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?

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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?

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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?

Set up a proportion, then cross multiply (butterfly)

240 words 440 words ---------- = ------------- 6 minutes x minutes

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Convert 6/7 into a decimal or percent.

What is the first step?

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Convert 6/7 into a decimal or percent.

Long Division!!!

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Convert 152/7 into a decimal or percent.

What is the first step?

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

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Convert 43/8 into a decimal or percent.

What is the first step?

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

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Convert 62/9 into a decimal or percent.

What is the first step?

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

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Read this decimal number: 0.56Convert 0.56 into a fraction. What are the two steps?

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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.

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Read this number: 0.375Convert 0.375 into a fraction.What are the two steps?

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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.

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Convert 3.4 into a mixed number. What are the two steps?

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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

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How do you solve this problem?

“What is 7/8 of 3/4?”

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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!

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How do you solve this problem?

“What is two-thirds of five eighths?”

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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!

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How do you solve this problem?

“What is six-fifths of nine-tenths?”

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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!

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What does “OF” represent or indicate in a fraction (or percent) word problem?

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What does “OF” represent or indicate in a fraction (or percent) word problem? Multiply!

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How do you solve this problem?

“What is 40% of 350?”

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How do you solve this problem? “What is 40% of 350?”

Multiply .40 times 350Or

Multiply 40/100 times 350

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2

56

How do you solve?

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2

56

How do you solve?

Change 6 to improper fraction then pre-simplify, then multiply across.

1

6

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62

14

How do you solve?

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62

14

How do you solve?

Change BOTH to improper fractions, then pre-simplify, then multiply.

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4

328

How do you solve?

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4

328

How do you solve?

Change BOTH to improper fractions, then pre-simplify, then multiply.

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2

16

3

23

How do you solve?

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2

16

3

23

How do you solve?

Change BOTH to improper fractions, then pre-simplify, then multiply.

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5 students work 6 hours on a project. How many person-hours is this?

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30 person -hours

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10 students work 5 hours at the carwash. How many person-hours is this?

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50 hours

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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.

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11 hours

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What is the equation for this set of points?Choose one: y = x2

y = -x2

y = x3

y = -x3

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y = x2

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What is the equation for this set of points?Choose one: y = x2

y = -x2

y = x3

y = -x3

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y = -x2

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What is the equation for this set of points?Choose one: y = x2

y = -x2

y = x3

y = -x3

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y = x3

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What is the equation for this set of points?Choose one: y = x2

y = -x2

y = x3

y = -x3

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y = -x3