tabe math refresher

1

Trigg County Adult Education

TABE Math Computation Refresher Course

Please return this workbook back to the Trigg County Adult Education Center. Do NOT write in this booklet. There are no example

problems for a reason- we want you to attend our refresher classes.

You should begin in the class you received the first minus (-) or progress (P) sign in. Ex: if you received a minus sign in the integer

section don’t start with algebra class!

In an effort to cut down on our supply usage, NO additional practice

pages will be handed out. If you need more practice you may go back

and rework these pages. Some other suggestions include coming into the center and write problems out of our classroom textbooks (NO

COPIES ARE MADE) or search the internet.

Clients will NOT be allowed to retest unless this

booklet is returned, along with the completion of two math refresher courses and additional

independent study hours.

TABLE OF CONTENTS

Decimals 2 - 5

Fractions 6 - 21

Percents 22 - 25

Integers 26 – 31

Exponents/Powers/Square Roots/Scientific Notation/Absolute Value 32 - 34

Order Of Operations 35-36

Combining Like Terms 37

Algebra 38-40

Distributing 41

2

Decimal-Addition

To add or subtract decimals, you must first line up your decimals.

Remember that if no decimal is visible it is understood that it is to the right

of the whole number. You may need to add zeros to serve as placeholders.

1a. 0.2 + 0.6 = 1b. 0 + 0.47 =

2a. 0.267 + 0.4 = 2b. 0.027 + 0.42=

3a. 0.985 + 0.44= 3b. 0.8 + 0.8 =

4a. 0.74 + 0.4 = 4b. 0.47 + 0.6=

5a. 0.62 + 0.6 = 5b. 0.7 + 0.76 =

Decimals - Subtraction

1a. 4 - 2.48 = 1b. 4 - 0.6 =

2a. 18 - 5.8 = 2b. 6 - 4.1 =

3a. 9.46 - 5 = 3b. 7 - 4 =

4a. 2 - 0.42 = 4b. 19 - 6.3 =

5a. 16 - 5.7 = 5b. 15 - 7.81=

3

Answers Decimals- Addition

1a. 0.8 1b. 0.47

2a. 0.667 2b. 0.447

3a. 1.425 3b. 1.6

4a. 1.14 4b. 1.07

5a. 1.22 5b. 1.46

Answers Decimals- Subtraction

1a. 1.52 1b. 3.4

2a. 12.2 2b. 1.9

3a. 4.46 3b. 3

4a. 1.58 4b. 12.7

5a. 10.3 5b. 7.19

Decimals - Multiplication

To multiply decimals, multiply the numbers as in a regular multiplication

problem. Remember with multiplication you can swap your numbers

around. It’s easier if you put the number with the most digits on top. Count

the number of decimal places in the problem, the answer is the same

number of decimal places.

1a. 0.7 X 0.07 = 1b. 0.6 X 0.1 =

2a. 0.01 X 0.1= 2b. 0.09 X 0.9 =

3a. 0.8 X 0.04 = 3b. 0.4 X 0.7 =

4a. 0.06 X 0.3 = 4b. 0.7 X 0.08 =

5a. 0.4 X 0.6 = 5b. 0.4 X 0.1 =

4

Answers Decimals- Multiplication

1a. 0.049 1b. 0.06

2a. 0.001 2b. 0.081

3a. 0.032 3b. 0.28

4a. 0.018 4b. 0.056

5a. 0.24 5b. 0.04

Decimals - Division

HINT: FIRST number (dividend) goes always goes IN your box.

To divide a decimal by a whole number, divide as normally would and

move your decimal straight up.

To divide a decimal by a decimal, first change the problem to a new

problem with a whole number divisor (number on the outside of the box).

To do this, move the decimal as far to the right as possible. Move the

decimal the same number of places on the inside of the box. If a decimal is

not already inside the box, it is understood that it is to the right of the last

number. You may have to add zero’s to your dividend in order to place the

zero in the correct spot. Then move your decimal straight up.

1a. 0.45 ÷ 3 = 1b. 0.52 ÷ 2 =

2a. 0.00 ÷ 6 = 2b. 0.96 ÷ 2 =

3a. 0.78 ÷ 3 = 3b. 0.42 ÷ 6 =

4a. 1.47 ÷ 0.07 = 4b. 0.99 ÷ 0.09 =

5a. 1.72 ÷ 0.02 = 5b. 1.68 ÷ 0.04 =

6a. 1.76 ÷ 0.02 = 6b. 0.92 ÷ 0.04 =

7a. 1.86 ÷ 0.06 = 7a. 1.55 ÷ 0.05=

8a. 0.84 ÷ 0.06 = 8a. 1.18 ÷ 0.02 =

5

Answers Decimals- Division

1a. 0.15 1b. 0.26

2a. 0 2b. 0.48

3a. 0.26 3b. 0.07

4a. 21 4b. 11

5a. 86 5b. 42

6a. 22 6b. 23

7a. 31 7b. 31

8a. 14 8b. 59

Decimal Extra Practice

1a. 3.5 + 7.3 = 1b. 3.6 ÷ 0.04 =

2a. 26.73 + 13.05= 2b. 0.56 ÷ 0.007 =

3a. 90.47 + 14.3 = 3b. 14.3 X 7.8 =

4a. 47.7 - 39.09 = 4b. 5.2 X 2 =

5a. 0.593 - 0.3879 = 5b. 45 X 7.3 =

6a. 593.4 - 487.92 = 6b. 213 X 6.7 =

7a. 12.5 + 13.7 = 7b. 15.2 X 21.3 =

8a. 119 - 105.7 = 8b. 12.3 X 4.3 =

9a. 7.35 + 5.9 = 9b. 1.503 X 4 =

10a. 2.8 ÷ 7 = 10b. 7.82 X 6.8 =

11a. 0.128 ÷ 8 = 11b. 452.8 X 12 =

12a. 0.036 ÷ 6 = 12b. 54.02 X 0.2=

13a. 50 ÷ 2.5 = 13b. 21 X 0.5 =

14a. 0.0078 ÷ 0.003 14b. 1.327 X 91=

15a. 24 ÷ 0.3 = 15b. 5.42 X 0.63=

16a. 1.69 ÷ 1.3 16b. 4.85 X 5.6=

17a. 0.48 ÷ 0.2 17b. 4.20 X 4.5=

18a. 25 ÷ 0.05 18b. 5.04 X 6.1 =

6

Answers Decimal Extra Practice

1a. 10.8 1b. 90 10a. 0.4 10b. 53.176

2a. 39.78 2b. 80 11a. 0.016 11b. 5433.6

3a. 104.77 3b. 111.54 12a. 0.006 12b. 10.804

4a. 8.61 4b. 10.4 13a. 20 13b. 10.5

5a. 0.2051 5b. 328.5 14a. 2.6 14b. 120.757

6a. 105.48 6b. 1427.1 15a. 80 15b. 3.4146

7a. 26.2 7b. 323.76 16a. 1.3 16b. 27.16

8a. 13.3 8b. 52.89 17a. 2.4 17b. 18.9

9a. 13.25 9b. 6.012 18a. 500 18b. 30.744

Fraction Terminology

Fraction- part of a whole part numerator

_____ line represents division

Whol e denominator

proper fraction- numerator is smaller than denominator

improper fraction- numerator is larger than denominator

mixed number- whole number and fraction

Any time there is a whole number by itself, put it over the whole number 1

to make it into fraction form.

If there is a remainder make it into fraction form using the remainder as

your numerator and keep the same denominator

reduce/simplify/lowest terms- all fractions should be reduced

determine if there is a (same) number that will go into the numerator

and denominator both evenly

7

Simplify fractions

Ask- What is the largest number that will go EVENLY into both numbers?

Divide each number by that number to reduce the fraction down.

1a.

4

4

1b.

7

56

1c.

20

40

2a.

3

15

2b.

6

45

2c.

6

9

3a.

5

50

3b.

16

48

3c.

12

27

4a.

3

30

4b.

6

58

4c.

9

33

5a.

6

12

5b.

7

28

5c.

20

50

6a.

16

18

6b.

21

24

6c.

6

48

7a.

25

50

7b.

36

63

7c.

42

56

8a.

18

32

8b.

6

48

8c.

35

49

8

Answers Simplifying Fractions

1a. 1 1b. 1/8 1c. 1/2

2a. 1/5 2b. 2/15 2c. 2/3

3a. 1/10 3b. 1/3 3c. 4/9

4a. 1/10 4b. 3/29 4c. 3/11

5a. ½ 5b. ¼ 5c. 2/5

6a. 8/9 6b. 7/8 6c. 1/8

7a. ½ 7b. 4/7 7c. 3/4

8a. 9/16 8b. 1/8 8c. 5/7

Improper Fractions to Mixed Numbers

improper fraction to a mixed number- divide your denominator into your

numerator

1a 14 1b 33 1c 45 1d 44 1e 11 1f 28 1g 50

8 6 9 16 2 10 4

2a 30 2b 26 2c 18 2d 36 2e 12 2f 30 2g 16 9 8 6 10 3 7 8

3a 22 3b 16 3c 40 3d 36 3e 45 3f 27 3g 18

7 3 9 11 6 3 6

4a 5 4b 56 4c 42 4d 15 4e 5 4f 9 4g 50

4 7 20 3 6 6 5

Answers Improper Fractions to Mixed Number 1a 1 3/4 1b 5 ½ 1c 5 1d 2 3/4 1e 5 1/2 1f 2 4/5 1g 12 1/2

2a 3 1/3 2b 3 ¼ 2c 3 2d 3 3/5 2e 4 2f 4 2/7 2g 2

3a 3 1/7 3b 5 1/3 3c 4 4/9 3d 3 3/11 3e 7 1/2 3f 9 3g 3

4a 1 1/4 4b 8 4c 2 1/10 4d 5 4e 2 1/2 4f 1 1/2 4g 10

9

Mixed Number to Improper Fraction

mixed number to an improper fraction- multiply the denominator times the

whole number, then add the product and numerator, that sum becomes the

numerator and the denominator stays the same

1a. 1 2/8 1b. 2 1/7 1c. 7 6/10

2a. 1 1/10 2b. 3 2/7 2c. 6 4/5

3a. 1 5/8 3b. 9 1/5 3c. 8 8/10

4a. 2 3/4 4b. 1 4/7 4c. 5 1/3

5a. 8 3/4 5b. 9 1/2 5c. 4 3/5

6a. 6 1/7 6b. 2 1/8 6c. 5 1/4

7a. 4 3/5 7a. 3 3/4 7c. 3 5/9

8a. 8 1/9 8a. 5 6/7 8c. 4 1/3

Answers Mixed Numbers to Improper Fractions

1a. 10/8 1b. 15/7 1c. 76/10

2a. 11/10 2b. 23/7 2c. 34/5

3a. 13/8

3b.

46/5 3c.

88/10

4a. 11/4 4b. 11/7 4c. 16/3

5a. 35/4 5b. 19/2 5c. 23/5

6a. 43/7 6b. 17/8 6c. 21/4

7a. 23/5 7a. 15/4 7c. 32/9

8a. 73/9 8a. 41/7 8c. 13/3

10

Fraction to Decimal

fraction to a decimal- divide your numerator by your denominator

Answers Fractions to Decimals

1a. .33 1b. .25 1c. .50 1d. .75 1e. .88 1f. .55 1g. .2

2a. .4 2b. .6 2c. .8 2d. .16 2e. .83 2f. .14 2g. .29

3a. .43

3b. .57 3c. .71 3d. .86 3e. 1 3f. .22 3g. .11

4a. .44 4b. .66 4c. .77 4d. .1 4e. .3 4f. .6 4g. .7

Multiplying Fractions

Multiplying Proper & Improper Fractions-

1. multiply the numerators

2. multiply the denominators

3. reduce

Multiplying Mixed Numbers-

1. change mixed number to improper fraction

2. follow the multiplication rules for improper fraction

1a 1 1b 1 1c 1 1d 3 1e 7 1f 5 1g 1

3 4 2 4 8 9 5

2a 2 2b 3 2c 4 2d 1 2e 5 2f 1 2g 2

5 5 5 6 6 7 7

3a 3 3b 4 3c 5 3d 6 3e 7 3f 2 3g 1

7 7 7 7 7 9 9

4a 4 4b 6 4c 7 4d 1 4e 3 4f 6 4g 7

9 9 9 10 10 10 10

11

1a. 6 X

5 =

1b. 1 X

4 =

1c. 1 X

3 =

7 12 5 8 8 8

2a. 1 X

5 =

2b. 2 X

4 =

2c. 5 X

1 =

9 9 3 5 7 9

3a. 2 X

7 =

3b. 1 X

4 =

3c. 3 X

5 =

3 10 5 5 8 8

4a. 4 X

4 =

4b. 5 X

4 =

4c. 1 X

3 =

7 9 6 7 5 8

5a. 3 X

5 =

5b. 15 X

12 =

5c. 5 X

3 =

4 6 16 30 9 10

6a. 4 X

3 =

6b. 5 X

9 =

6c. 4 X

1 =

9 16 12 10 5 6

7a. 8 X

10 =

7b. 4 X

3 =

7c. 3 X

4 =

15 13 7 5

8a. 7 X 2

=

8b. 3 X 2

=

8c. 1 X

3 =

4 4 5

9a. 6

2 X

4 =

9b. 4

1 X

3 =

8 10 5 4

10a. 1

1 X 1

5 =

10b. 2

1 X 2

1 =

2 8 3 5

11a. 1

6 X 4

1 =

11b. 3

2 X 3

1 =

7 2 5 3

12

Answers Multiplication Fractions

1a.

5

1b.

1

1c.

3

14 10 64

2a.

5

2b.

8

2c.

5

81 15 63

3a.

7

3b.

4

3c.

15

15 25 64

4a.

16

4b.

10

4c.

3

63 21 40

5a.

5

5b.

3

5c.

1

8 8 6

6a.

1

6b.

3

6c.

2

12 8 15

7a.

16

7b. 1

5

7c. 2

2

39 7 5

8a. 3

1

8b. 1

1

8c.

3

2 2 5

9a. 2

5

9b. 3

3

1 20

10a.

7

10b. 2

2

2 16 15

11a. 8

5

11b. 11

1

14 3

13

Fractions - Division

KFC- Keep (1st number), Flip (2nd number) & Change (the sign to

multiplication)

Dividing Mixed Numbers-

1. change mixed number to improper fraction

2. follow proper & improper division rules

1a. 2 ÷

8 =

1b. 2 ÷

2 =

1c. 2 ÷

2 =

4 10 10 7 4 8

2a. 8 ÷

1 =

2b. 3 ÷

2 =

2c. 4 ÷

2 =

9 3 7 5 9 3

3a. 5 ÷

10 =

3b. 8 ÷

2 =

3c. 5 ÷

25 =

12 11 9 9 11 33

4a. 6 ÷

1 =

4b. 9 ÷

1 =

4c. 4 ÷

1 =

25 5 14 2 11 11

5a. 3 ÷

5 =

5b. 4 ÷

1 =

5c. 5 ÷

3 =

4 6 5 6 9 10

6a. 4 ÷

3 =

6b. 5 ÷

3 =

6c. 2 ÷

4 =

9 12 12 9 5 15

7a. 12 ÷

2 =

7b. 9 ÷

1 =

7c. 5 ÷

15 =

5 3 16

8a. 5 ÷ 3

= 8b. 3 ÷

3 =

8c. 2 ÷ 5

=

4 5 6

9a. 3

2 ÷

3 =

9b. 4

6 ÷

5 =

4 12 7 12

10a. 1

1 ÷ 3

3 =

10b. 5

1 ÷ 4

2 =

2 4 4 3

11a. 2

3 ÷ 1

7 =

11b. 6

1 ÷ 3

1 =

4 8 2 4

14

Answers Division Fractions

1a.

5

1b.

7

1c. 2

8 10

2a. 2

2

2b. 1

1

2c.

2

3 14 3

3a.

11

3b. 4

3c.

3

24 5

4a. 1

1

4b. 1

2

4c.

4

5 7

5a.

9

5b. 4

4

5c. 1

23

10 5 27

6a. 1

7

6b. 1

1

6c. 1

1

9 4 2

7a. 30

7b. 27

7c. 5

1

3

8a. 6

2

8b. 5

8c. 2

2

3 5

9a. 14

9b. 11

23

35

10a.

2

10b. 1

1

5 8

11a. 1

7

11b. 2

15

15

Fractions – Adding Common Denominator

Adding/Subtracting with Common (same) Denominators-

1. bring denominator down

2. perform the operation(add/subtract) for numerators

3. reduce

1a.

4

11

+

2

11

=

1b.

7

10

+

3

10

=

2a.

1

12

+

10

12

=

2b.

6

8

+

2

8

=

3a.

6

12

+

1

12

=

3b.

4

11

+

6

11

=

Fractions - Adding Common Denominators

1a. 6/11 1b. 1

2a. 11/12 2b. 1

3a. 7/12

3b.

10/11

Fractions – Subtraction Common Denominator

1a.

10

12

−

9

12

=

1b.

9

10

−

1

10

=

2a.

3

9

−

2

9

=

2b.

5

12

−

2

12

=

Fractions - Subtraction Common Denominator

1a. 1/12 1b. 4/5

2a. 1/9 2b. 1/4

16

Fractions – Adding/Subtracting Unlike Denominator & Mixed Numbers

Adding/Subtracting with Unlike Denominators-

1. find common denominator

a. find a multiple of both denominators

b. look at your largest denominator, will your smallest denominator go

evenly into your larger denominator

c. if all else fails multiply your denominators by each other

2. multiply your numerator by the same number as you multiplied the

denominator by in that fraction

3. follow adding/subtracting with common denominator rules

Adding/Subtracting with Mixed Numbers-

1. follow adding/subtracting fraction rules

2. simply perform the operation on your whole numbers

Borrowing and Subtracting Fractions

1. When you do not have a fraction to subtract from you have to borrow from

your whole number.

2. When borrowing if no fraction is available take the denominator of the

mixed number and put it over itself.

3. If a fraction is available but you still must borrow, then borrow from your

whole number and change your numerator by adding your denominator to

your numerator for your new numerator and your denominator stays the

same.

17

1a. 4 +

1 =

1b. 4 +

7 =

1c. 7 +

3 =

9 8 6 8 10 5

2a. 5 +

3 =

2b. 3 +

9 =

2c. 3 +

2 =

9 48 4 11 8 3

3a. 1 +

4 =

3b. 8 +

3 =

3c. 1 +

6 =

3 9 10 8 6 10

4a. 1 +

2 =

4b. 8 +

8 =

4c. 3 +

4 =

6 8 10 12 4 12

5a. 3 +

5 =

5b. 4 +

1 =

5c. 5 +

3 =

4 6 5 6 9 10

6a. 4 +

3 =

6b. 5 +

3 =

6c. 2 +

4 =

9 12 12 9 5 15

7a. 12

+

2 =

7b. 9

+

1 =

7c. 5

+

15 =

5 3 16

8a. 5

+

3 =

8b. 3

+

3 =

8c. 2

+

5 =

4 5 6

9a. 3

2 +

3 =

9b. 4

6 +

5 =

4 12 7 12

10a. 1

1 + 3

3 =

10b. 5

1 +

4 2

=

2 4 4 3

11a. 2

3 + 1

7 =

11b. 6

1 +

3 1

=

4 8 2 4

18

1a. 41 1b.

1

13 1c.

1

3

72 24 10

2a. 89 2b.

1

25 2c.

1

1

144 44 24

3a. 7 3b.

1

7 3c. 23

9 40 30

4a.

5 4b.

1

7 4c.

1

1

12 15 12

5a.

1

7 5b. 29

5c.

77

12 30 90

6a. 3 6b. 3 6c. 2

4 4 3

7a.

12

2 7b.

9

1 7c.

5

15

5 3 16

8a.

5

3 8b.

3

3 8c.

2

5

4 5 6

9a.

3

3 9b.

5

23

4 84

10a.

5

1 10b.

9

11

4 12

11a.

4

5 11b.

9

3

8 4

19

1a. 8 -

3 =

1b. 5 -

2 =

1c. 1 -

1 =

9 8 6 9 2 8

2a. 2 -

7 =

2b. 3 -

7 =

2c. 9 -

2 =

3 11 5 12 10 11

3a. 2 -

1 =

3b. 8 -

1 =

3c. 4 -

4 =

5 6 10 7 5 8

4a. 7 -

5 =

4b. 11 -

5 =

4c. 3 -

3 =

8 10 24 12 4 16

5a. 5 -

1 =

5b. 5 -

1 =

5c. 4 -

1 =

6 3 9 6 5 3

6a. 5 -

3 =

6b. 4 -

1 =

6c. 3 -

2 =

6 5 9 6 4 7

7a. 7 -

2 =

7b. 7

-

3 =

7c. 1

-

2 =

7 9 4

8a. 12 - 4

=

8b. 8 -

5 =

8c. 4 -

3 =

11 6 7

9a. 6

6 -

2 =

9b. 17

7 -

6 =

11 3 11 8

10a. 7

1 - 4

11 =

10b. 5

2 -

2 3

=

3 12 3 4

11a. 10

2 - 5

7 =

11b. 12

4 -

5 2

=

5 10 5 9

20

1a. 37 1b.

11 1c.

3

72 18 8

2a. 1 2b.

1 2c.

79

33 60 110

3a. 7 3b.

23 3c. 3

30 35 10

4a.

3 4b.

1 4c.

9

8 24 16

5a.

1 5b. 7

5c.

7

2 18 15

6a. 7 6b. 5 6c. 13

30 18 28

7a.

6

5 7b.

6

2 7c.

1

7 3 2

8a.

11

7 8b.

7

1 8c.

3

4

11 6 7

9a.

5

29 9b.

16

39

33 144

10a.

2

5 10b.

2

11

12 12

11a.

4

7 11b.

7

26

10 45

21

Fractions Extra Practice

1a. 7/9 + 1/9 = 1b. 6/28 X 14/36 =

2a. 12/13 - 10/13 = 2b. 4 X 5 1/3=

3a. 30/12 - 14/12 = 3b. 4 4/5 X 3 1/8=

4a. 32/18 - 7/18 = 4b. 6 1/2 X 3

5a. 25/30 + 2/30 = 5b. 1/3 ÷ 5/9 =

6a. 6/7 + 11/14 = 6b. 17/9 ÷ 8/9 =

7a. 7/8 - 3/10 = 7b. 3/12 ÷ 6/36 =

8a. 28/32 - 7/8 = 8b. 6/54 ÷ 3/9 =

9a. 7/10 + 5/12 = 9b. 3 ÷ 2/3 =

10a. 5/12 - 3/15 = 10b. 3 1/2 ÷ 4 6/8 =

11a. 13/36 + 5/12= 11b. 7 1/3 ÷ 4/12 =

12a. 3 5/8 + 5 4/8= 12b. 3 1/2 ÷ 9/18 =

13a. 2 5/7 + 3 2/7= 13b. 5 1/2 ÷ 1 2/3 =

14a. 3 8/11 - 2 10/11= 14b. 1 7/9 ÷ 4 2/9 =

15a. 1/2 X 5/6 = 15b. 1/2 ÷ 1/3 =

16a. 8/12 X 4/6 = 16b. 12 ÷ 3/15 =

17a. 5/6 x 2 = 17b. 5 ÷ 4 2/9 =

18a. 2 3/4 X 4/5= 18b. 2 1/4 ÷ 2 1/4 =

Answers Fractions Extra Practice

1a. 8/9 1b. 1/12 10a. 13/60 10b. 14/19

2a. 2/13 2b. 21 1/3 11a. 7/9 11b. 22

3a. 1 1/3 3b. 15 12a. 9 1/8 12b. 7

4a. 1 7/18 4b. 19 1/2 13a. 6 13b. 3 3/10

5a. 9/10 5b. 3/5 14a. 9/11 14b. 8/19

6a. 1 9/14 6b. 2 1/8 15a. 5/12 15b. 1 1/2

7a. 23/40 7b. 1 1/2 16a. 4/9 16b. 60

8a. 0 8b. 1/3 17a. 1 2/3 17b. 1 7/38

9a. 1 7/60 9b. 4 1/2 18a. 2 1/5 18b. 1

22

Percents

To change a percent to a decimal, move the decimal to the left 2 places. If no decimal is

visible it is understood that it is to the right of the digits.

Percent to Decimals

1a. 91.50% 1b. 91.10% 1c. 21%

2a. 58.70% 2b. 15.70% 2c. 16%

3a. 5% 3b. 7% 3c. 12.30%

4a. 1.25% 4b. 23% 4c. 12.50%

5a. 1.37% 5b. 23.25%

5c.

2%

Answers Percents to Decimals

1a. 0.915 1b. 0.911 1c. 0.21

2a. 0.587 2b. 0.157 2c. 0.16

3a. 0.05 3b. 0.07 3c. 0.1230

4a. 0.0125 4b. 0.23

4c.

0.1250

5a. 0.0137 5b. 0.2325 5c. 0.02

To change a decimal to a percent, move the decimal to the right 2 places.

Decimals to Percents

1a. 0.206 1b. 0.163 1c. 0.125

2a. 0.7 2b. 0.141 2c. 23.5

3a. 0.547 3b. 0.05 3c. 15.75

4a. 0.3 4b. 0.22 4c. 1.25

5a. 0.24 5b. 0.3

5c.

502.5

23

Answers Percents to Decimals

1a. 20.6% 1b. 16.3% 1c. 12.5%

2a. 70% 2b. 14.1% 2c. 2350%

3a. 54.7% 3b. 5% 3c. 1575%

4a. 30% 4b. 22%

4c. 125%

5a. 24% 5b. 30% 5c. 50250%

Percentage problems are set up in this format:

_____ % of _____ is _____

1st X 2nd = 3rd

If you have the 1st & 2nd numbers, then you multiply to find the 3rd number.

Calculate the percentages.

1a. 15% of 50 = 1b. What is 30% of 90? 1c. 6 2/3% of 45 =

2a. What is 25% of 80 ? 2b. 20% of 360 = 2c. 8 1/3% of 36 =

3a. 40% of 60 = 3b. What is 75% of 120? 3c. What is 1 1/2% of 200?

4a. What is 20% of 80? 4b. 50% of 50= 4c. What is 12 1/2% of 40?

5a. 37 1/2% of 64 = 5b. 30 1/4% of 400 =

5c.

What is 75% of 24?

If you have the 2nd & 3rd or 1st & 3rd numbers, then you divide to find the 1st or 2nd number . (3rd number always goes in your box.

1a. 25% of what number is 8?

1b. 50% of what number is 45?

2a. 60 is 40% of what number?

2b. 10% of what number is 6.3?

3a. 7 1/2% of what number is 3.75?

3b. 27 is 67.5% of what number?

4a. 37 1/2% of what number is 24?


5a. 80% of what number is 20?

5b. 2 1/2% of what number is 25?

6a. 230 is 50% of what number ?


24

Solve the percent problems.

1a. 15 is what percent of 60?

1b. 45 is what percent of 50?

2a. What percent of 20 is 16?





4b. What percent of 0.92 is 0.23?





Answers Calculate the Percentages

1a. 7.5 1b. 27 1c. 3

2a. 20 2b. 72 2c. 3

3a. 24 3b. 90 3c. 3

4a. 16 4b. 25

4c.

5

5a. 24 5b. 121 5c. 18

1a. 32 1b. 90 Answers Solve the Percent Problems

2a. 150 2b. 63

1a. 25% 1b. 90%

2a. 80% 2b. 10%

3a. 50 3b. 40

3a. 35% 3b. 7%

4a. 64 4b. 610

4a. 20% 4b. 25%

5a. 25 5b. 1000

5a. 20% 5b. 13%

6a. 460 6b. 120 6a. 30% 6b. 75%

25

Percent Extra Practice

1a.

75% of 8 = ___

2a.

30% of 80 = __

3a.

35% of 18 = __

4a.

25% of 96 = __

5a.

12 ½% of 84= ___

6a.

15% of what number is 3?

7a.


8a.


9a.


10a.







Answers Percent Extra Practice

1a. 6 6a. 20 11a. 25%

2a. 24 7a. 38 12a. 114%

3a. 6.3 8a. 100 13a. 120%

4a. 24 9a. 80 14a. 200%

5a. 10.5 10a. 5 15a. 66%

26

Signed Numbers/Integers Positive Numbers – greater than zero (doesn’t have a sign)

Negative Numbers – are less than zero (always written with a negative

sign - )

Zero has no sign and is always written as 0

Adding Integers Same sign – add the number s & give that sign

o (+) + (+) = (+)

o (-) + (-) = (-)

1a. 5 + 6 = ____ 1b. 9 + 9 = ____

2a. -3 + -4 = ____ 2b. -3 + -5 = ____

3a. -12 + -9 = ____ 3b. 22 + 4 = ____

4a. 8 + 3 = ____ 4b. -5 + -4 = ____

5a. -5 + -2 = ____ 5b. -1 + -8 = ____

6a. -15 + -6 = ____ 6b. -25 + -10 = _____

7a. 12 + 7= ____ 7b. 5 + 12 = ____

8a. -6 + -1 = ____ 8b. -4 + -2 = ____

9a. -13 + -12 = ____ 9b. -10 + -15 = ____

10a. 9 + 7 = ____ 10b. 6 + 5= ____ opposite signs - subtract the two numbers, give the sign of the greater number

o (+ larger number) + (- smaller number) = (+) ex. 5 + -2 = 3

o (+ smaller number) + (-larger number) = (-) ex. 2 + -5 = -3

1a. 5 + -6 = ____ 1b. -9 + 7= ____

2a. -3 + 3= ____ 2b. -3 + 5= ____

3a. 12 + -9 = ____ 3b. -22 + 4= ____

4a. 8 + -3 = ____ 4b. 5 + -4= ____

5a. -5 + 6= ____ 5b. -1 + 8= ____

6a. 15 + -6 = ____ 6b. 25 + -10 = _____

7a. -12 + 7 = ____ 7b. 5 + -12= ____

8a. -6 + 1= ____ 8b. 4 + -2= ____

9a. 13 + -12 = ____ 9b. 10 + -15= ____

10a. 9 + -7 = ____ 10b. 6 + -5= ____

27

Answers

Adding Integers Same Signs Adding Integers Different Signs

1a. 11 1b. 18 1a. -1 1b. -2

2a. -7 2b. -8 2a. 0 2b. 2

3a. -21 3b. 26 3a. 3 3b. -18

4a. 11 4b. -9 4a. 5 4b. 1

5a. -7 5b. -9 5a. 1 5b. 7

6a. -21 6b. -35 6a. 9 6b. 15

7a. 19 7b. 17 7a. -5 7b. -7

8a. -7 8b. -6 8a. -5 8b. 2

9a. -25 9b. -25 9a. 1 9b. -5

10a. 16 10b. 11 10a. 2 10b. 1

Subtracting Integers Change the sign of the second number, change the subtraction sign to addition then follow your

addition rules

1a. 5 - (-6) = ____ 1b. -9 - 7= ____

2a. -3 - 5= ____ 2b. -3 - 9= ____

3a. 12 – (-9) = ____ 3b. -22 - 4= ____

4a. 8 – (-3) = ____ 4b. 5 - 4= ____

5a. -5 - 6= ____ 5b. -1 - 8= ____

6a. 15 - (-6) = ____ 6b. 25 – (-10) = _____

7a. -12 - 7= ____ 7b. 5 - 12= ____

8a. -6 - 1= ____ 8b. 4 - 2= ____

9a. 13 – (-12) = ____ 9b. 10 – (-15)= ____

10a. 9 – (-7) = ____ 10b. 6 – (-5)= ____

28

Answers Subtracting Integers

1a. 11 1b. -16

2a. -8 2b. -12

3a. 21 3b. -26

4a. 11 4b. 1

5a. -11 5b. -9

6a. 21 6b. 35

7a. -19 7b. -7

8a. -7 8b. 2

9a. 25 9b. 25

10a. 16 10b. 11

Multiplying Integers Same signs = positive Opposite signs = negative

Same sign – multiply numbers and make a positive o (+) X (+) = (+) o (-) X (-) = (+)

1a. 4 X 2 = ___ 1b. -5 X -12= ____

2a. 3 X 3 = ___ 2b. -4 X -5= ____

3a. 5 X 8 = ___ 3b. -9 X -6= ____

4a. 6 X 4 = ___ 4b. -10 X -4= ___

5a. 7 X 9 = ___ 5b. -8 X -2 = ___ Opposite sign – multiply numbers and make a negative

o (+) X (-) = (-)

o (-) X (+) = (-)

1a. -5 X 12 = ____ 6a. 7 X -9 = ___

2a. -4 X 5= ____ 7a. -6 X 4= ___

3a. 9 X -6= ____ 8a. 5 X -8 = ___

4a. 10 X -4= ___ 9a. 3 X -3 = ____

5a. -8 X 2= ___ 10a. -4 X 2= ____ Multiplying more than two signed numbers

o If there are an even number of negative signs, give the product a positive sign.

o If there are an odd number of negative signs, give the product a negative sign.

29

Multiplying Integers Same Signs

1a. 8 1b. 60

2a. 9 2b. 20

3a. 40 3b. 54

4a. 24 4b. 40

5a. 63 5b. 16

Multiplying Integers Different Signs

1a. -60 6a. -63

2a. -20 7a. -24

3a. -54 8a. -40

4a. -40 9a. -9

5a. -16 10a. -8

Dividing Integers Same signs = positive Opposite signs = negative

Have the same sign, divide the numbers and give the quotient a positive sign.

1a. 20 ÷ 4= ____ 6a. -27 ÷ -9 = ___

2a. 25 ÷ 5= ____ 7a. -24 ÷ -4= ___

3a. 9 ÷ 3= ____ 8a. -40 ÷ -8 = ___

4a. 16 ÷ 4= ___ 9a. -3 ÷ -3 = ____

5a. 8 ÷ 2= ___ 10a. -4 ÷ -2= ____

Have opposite signs, divide the numbers and give the quotient a negative sign.

1a. -20 ÷ 4= ____ 6a. 27 ÷ -9 = ___

2a. 25 ÷ -5= ____ 7a. -24 ÷ 4= ___

3a. 9 ÷ -3= ____ 8a. 40 ÷ -8 = ___

4a. 16 ÷ -4= ___ 9a. 3 ÷ -3 = ____

5a. -8 ÷ 2= ___ 10a. -4 ÷ 2= ____

30

Dividing Integers Same Signs

1a. 5 6a. 3

2a. 5 7a. 6

3a. 3 8a. 5

4a. 4 9a. 1

5a. 4 10a. 2

Dividing Integers Different Signs

1a. -5 6a. -3

2a. -5 7a. -6

3a. -3 8a. -5

4a. -4 9a. -1

5a. -4 10a. -2

Integers Extra Practice

1a. -9 X -13 = 1b. -4 + -5 =

2a. -36 X -3 = 2b. -10 + 2 =

3a. 11 X -4 = 3b. -17 + -19 =

4a. -5 X 12 = 4b. 35 + -19 =

5a. 8 X -37 = 5b. -3 + 5 =

6a. -65 X -8 = 6b. -7 + 3 =

7a. 48 ÷ -3 = 7b. -23 + 6 =

8a. 68 ÷ -17 = 8b. -25 + -32 =

9a. -51 ÷ -17 = 9b. -10 + -5 =

10a. -91 ÷ 13 = 10b. -15 + -7 =

11a. 64 ÷ -16 = 11b. 12 + 9 =

12a. -804 ÷ 67 = 12b. 7 - -5 =

13a. -64 ÷ 8 = 13b. -3 - -13=

14a. -5 + 6 = 14b. -9 - -6 =

15a. -9 + -7 = 15b. 5 + -32 =

16a. 19 - -7 = 16b. -25 + -3 =

17a. -18 - -13 = 17b. -2 + 2 =

18a. -18 - 37 = 18b. -21 + 3 =

31

Integers Extra Practice Answers

1a. 117 1b. -9 10a. -7 10b. -22

2a. 108 2b. -8 11a. -4 11b. 21

3a. -44 3b. -36 12a. -12 12b. 12

4a. -60 4b. 16 13a. -8 13b. 10

5a. -296 5b. 2 14a. 1 14b. -3

6a. 520 6b. -4 15a. -16 15b. -27

7a. -16 7b. -17 16a. 26 16b. -28

8a. -4 8b. -57 17a. -5 17b. 0

9a. 3 9b. -15 18a. -55 18b. -18

32

Exponent/Power

Exponent/Power – a number multiplied by itself one or more times. Four to the third

power (first example) means 4 X 4 X 4 = 64 (4 X 4 = 16 X 4). A number raised to the

second power is known as a square and a number raised to the third power is known as

cubed.

1. 43 = ___ 2. 6

3 = ____ 3. 8

3 = ___ 4. 5

2 = ___ 5. 3

4 = ____

Any number to the power of one is that number. Any number to the power of zero equals 1.

1. 41 =_4_ 2. 5

0= _1_ 3. 6

1 = ___ 4. 2

0 = ___ 5. 9

0 = ___ 6. 3

1 = ___

Square Roots

A number multiplied by itself equals that number. A positive number has two square

roots- a positive and/or negative. If a number is on the outside of the “check mark”,

find your square then multiply by that number. If performing an operation with square

roots, find your squares then perform the operation.

1a. √100 1b. 3√4 1c. √1

2a. √25 2b. √16 2c. 2√49

Answer Exponent/Power

1 64 1 4

2 216 2 1

3 512 3 6

4 25 4 1

5 81 5 1

6 3

Answers Square Roots

1a. 10 1b. 6 1c. 1

2a. 5 2b. 4 2c. 14

33

Square Roots/Exponents/Powers Extra Practice

1a.

√4

1b. 52

2a.

√9

2b. 43

3a.

√81

3b. 24

4a.

√49

4b. 32

5a.

√36

5b. 81

6a.

√16

6b. 12

7a.

√64

7b. 70

8a.

2√25

8b. 62

9a.

3√100

9b. 21

10a.

4√36

10b. 80

Answers Square Roots/Exponents/Powers Extra Practice

1a. 2 1b. 25

2a. 3 2b. 64

3a. 9 3b. 16

4a. 7 4b. 9

5a. 6 5b. 8

6a. 4 6b. 1

7a. 8 7b. 1

8a. 10 8b. 36

9a. 30 9b. 2

10a. 24 10b. 1

34

Absolute Value

Absolute Value is the POSITIVE value of a number regardless of its sign. The symbol for

absolute value is l l (2 straight lines).

1. l -4 l 2. l 7 l 3. l 0 – 9 l 4. l -1- (-6) l 5. l -4 +6 l 6. l 0 l

Absolute Value

1. 4 4. 5

2. 7 5. 2

3. 9 6. 0

Scientific Notation Scientific notation is a shorter way of writing numbers with multiple zeros. In scientific

notation a number is written as the product of two factors. The first is a number between

1 and 10. The second factor is a power of 10. A positive exponent means you move the

decimal to the right a negative exponent means you move the decimal to the left.

7.5 X 103= 7,500 4 X 10

-2= 0.04

1a. 6.3 X 102

= ____________ 1b. 9 X 106=__________________

2a. 8.5 X 10-5

= _____________ 2b. 7 X 10-6

=__________________

3a. 5,0000 = _______________ 3b. 30, 000 = __________________

4a. 0.03 = _________________ 4b. 0.0075 = __________________

Answers Scientific Notation

1a. 630 1b. 9,000,000

2a. 0.000085 2b. 0.000007

3a. 5 X 104 3b. 3 X 104

4a. 3 X 10-2 4b. 7.5 X 10-3

35

ORDER OF OPERATIONS

Please Excuse My Dear Aunt Sally-

Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction

(Left to Right)

1. 6 ÷ 2 + 5 X 4= 2. (3 + 62) + 9 = 3. 9 − (9 − 7 × 5

2 × 9) =

4. (2 − 5 − 4 − 7) = 5. (6 + 8) + (63 ÷ 3) + 4 = 6. (25 X 3) + (15 -3) =

7. (6 + 9) − 7 = 8. 3(34-19) = 9. (82 × 3

3) − 1 =

10. (4 − 5 − 2 ÷ 2) = 11. 15 ÷ 5 X 3 12. 6 X 3 ÷ 9 – 1 =

13. (3 + 9) + 4 = 14. 96 ÷ 12 (4) ÷ 2 15. 52 × (8 − 9

2 + 3) =

16. (7 × 9 − 8 − 4) × 4 = 17. (8 + 6 + 1) = 18. (62 × 9 + 9) − 2 =

19. (5 − 6) − 1 = 20. 7 − (93 − 4

3 + 8 − 6) =

21. 36 - 9

6 - 3

22. (7 − 12 − 5) = 23. (9 + 5) + 8 = 24. (2

3 ÷ 2

2) + 9

2 − 9 =

25. (3 − 53 − 9) = 26. (8 ÷ 8) + 3 + 4 =

27. 86 - 11

9 + 6

28. 4[ 12 ( 22 - 19 ) -3 X 6 ] 29. 2[ 5 (4+6) – 3] = 30. (7 − 1 × 2 − 83 − 6) =

36

Order of Operations

1. 23 2. 48 3. 1575

4. -14 5. 90 6. 87

7. 8 8. 45 9. 1727

10. -2 11. 9 12. 1

13. 16 14. 16 15. -1750

16. 204 17. 15 18. 331

19. -2 20. -660 21. 9

22. 1 23. 22 24. 74

25. -131 26. 8 27. 5

28. 72 29. 94 30. -513

Order of Operations

1a.

6 ÷ 2 + 5 X 4 =

2a.

12 ÷ 3 + 12 ÷ 4 =

3a.

6 X 3 ÷ 9 -1=

4a.

15 ÷ 5 X 3=

5a.

36 ÷ (4 X 3) = 6a. 24 ÷8 - 2 =

7a.

3(7+4)-18 ÷ 9 =

8a.

(5+3)2

9a.

6(7-5) + 4 =

10a.

28 ÷ 4 + 28 ÷ 7 =

11a. 5[3 + 4(22)] =

12a. 32[(11+3) -4] =

37

Answers Order of Operations

1a. 23 8a. 64

2a. 7 9a. 16

3a. 1 10a. 11

4a. 9 11a. 95

5a. 3 12a. 90

6a. 1

7a. 31

Combining Like Terms

Combine like terms- you can only combine those that are EXACTLY alike, letters &

exponents. You are NOT solving the equation.

1. 5a + 5a + 4b 2. 4a + 3b + 2c 3. 17r – 3r – 2t 4. 4a2 + 5a

2-2a

2 5. 3c

3+5c

2+ c 6. 5a

3+4b+ 4c

2

Answers Combine Like Terms

1. 10a + 4b 4. 7a2

2. 4a + 3b +2c 5. 3c3+5c2+c

3. 14r - 2t 6. 5a3+4b+4c2

Combine Like Terms Extra Practice

1a.

2xy + 5xy -4xy

2a.

4r + 19 - 8

3a.

9 + 5x + 4x +6x

4a.

4k + 3 - 2k + 8 + 7k -16

5a.

6ab + 7c

6a.

1a + 2s + 3t + 4j

Answers Combine Like Terms Extra Practice 1a. 3xy

2a. 4r +11

3a. 9 + 15X

4a. 9k -5

5a. 6ab + 7

6a. 1a + 2s + 3t + 4j

38

Algebra

Variables (letters) represent the unknown. In algebra you try to solve for the unknown,

often doing the opposite operation. A letter by itself has an understood 1 in front of it.

Answers Algebra

1. 10 2. 10 3. -9 4. 11

5. -5 6. -4 7. 30 8. -10

9. -4 10. 48 11. 6 12. 20

13. 1 14. 6 15. 9 16. 7

17. 5 18. 3 19. 3 20. 3

1. 10 + y = 20

2. -10 y = -100

3. -2 + x = -11

4. 9 y = 99

5. 1 - x = 6

6. -4 - y = 0

7. -10 + y = 20

8. -7 + y = -17

9. 5 + y = 1

10. y + 9 = 57

11. 3 + x = 9

12. x + 9 = 29

13. 8 + y = 9

14. 8 y + 9 = 57

15. 4x = 36

16. 9x = 63

17. 5 + 4x= 25

18. 8 y + 9 = 33

19. 3 + 7x= 24

20.. x + 9x = 30

39

Algebra Extra Practice 1

1a. x + 3 = 9 1b. 4s = 20 1c. 5y = 32.5

2a. y - 12 = 37 2b. n + 10 = 24 2c. 7y = 16.8

3a. 3z = 39 3b. x - 3 = 7 3c. x/5 = 4

4a. a/15 = 3 4b. 8n = 48 4c. y/3 = 6

5a. n + (-4) = 15 5b. 6y = 54

5c.

y/3 = 9

6a. n/3 = 12 6b. y + 2.75 = 7.5 6c. x - 7 = 12

7a. x + 6 = 15 7b. n + 9 = 14 7c. x + 23 = 47

8a. 9a = 72 8b. 4x = -32 8c. x + (-5) = 8

9a. a + 5 = 2 9b. x -12 =13 9c. b - 3 = -7

10a. 6p = 42 10b. 4n = -28

10c.

5q = 120

Answers Algebra Extra Practice 1

1a. 6 1b. 5 1c. 6.5

2a. 49 2b. 14 2c. 2.4

3a. 13 3b. 10 3c. 20

4a. 45 4b. 6 4c. 18

5a. 19 5b. 9 5c.

27

6a. 36 6b. 4.75 6c. 19

7a. 9 7b. 5 7c. 24

8a. 8 8b. -8 8c. 13

9a. -3 9b. 25 9c. -4

10a. 7 10b. -7 10c

24

40

Algebra Extra Practice 2

1a. 4 + b = - 13 1b. z + 16 = -33

2a. x + 13 = 9 2b. b + 4 = 17

3a. 18 + m = - 57 3b. w + 42 = -51

4a. b + 63 = 44 4b. z + 13 = -22

5a. g + -19 = 24 5b. -17 + z = 5

6a. -12 + k = -37 6b. p + (-8) = -21

7a. x + (-21) = -59 7b. q + (-3) = 17

8a. m + 37 = 14 8b. x + (-100) = 283

9a. a - 16 = 33 9b. t - -16 = 9

10a. y - 8 = -22

10b. x - 25 = -18

11a. y + -7 =19

11b. c - -9 = 74

12a. b + -14 = 6

12b. k - 12 = -14

13a. z - -7 = -19

13b. m - -21 = 0

14a. t - -34 = 66

14b. y - -47 = 42

15a. 4y = -52

15b. -15h = -60

16a. -9m = 99

16b. -3t = 51

17a. -3y = 42

17b. -6a = 84

18a. -13a=52

18b. 21s = 315

Answers Algebra Extra Practice 2

1a. -17 1b. -49 10a. -14 10b. 7

2a. -4 2b. 13 11a. 26 11b. 65

3a. -75 3b. -93 12a. 20 12b. -2

41

4a. -19 4b. -35 13a. -26 13b. -21

5a. 43 5b. 22 14a. 32 14b. -5

6a. -25 6b. -13 15a. -13 15b. 4

7a. -38 7b. 20 16a. -11 16b. -17

8a. -23 8b. 383 17a. -14 17b. -14

9a. 49 9b. -7 18a. -4 18b. 15

Distributing

Multiply the number outside the parenthesis by the items inside the parenthesis.

Combine like terms first. If an exponent is involved you must add the exponents while

multiplying the whole numbers. If one is not visible it is an understood 1.

1. 4n(3n2

+ 2) = 2. 5c(c + 7) = 3. 6a2(2a

3 – 5)= 4. 5x + y(4y

2-3y)=

5. 7x(3 + 4y)= 6. 2a(a+3)= 7. 18z(3 -2)= 8. 3a +2b(4-3)=

9. -4(3a + 2b) -2ab= 10. 3x – 2y(4x+3y)= 11. -4(2c +3d) -3d = 12. -1(5x + 5y) –y =

Answers Distributing

1. 12n3+8n 5. 21x + 28xy 9. -12a -8b-2ab

2. 5c2+ 35c 6. 2a2+6a 10. 3x-8xy-6y2

3. 12a5-30a2 7. 18z 11. -8c-15d

4. 5x+4y3-3y2 8. 3a+2b 12. -5x-6y

Distributing

1a.

5(x + 4) =

2a.

4(2a + 6b) =

3a.

2m(3m +2)=

4a.

3p(8 - 6p) =

5a.

8z(2z + 3z2 +3z

3)

6a.

5x-y(3x - y)

7a.

6xy(3x2-4y

2)

Answers Distributing

42

1a. 5x + 20 5a. 16z2 + 24z

3 + 24z

4

2a. 8a + 24b 6a. 5x - 3xy +y2

3a. 6m2+4m 7a. 18x

3y - 24xy

3

4a. 24p - 18p2

tabe math refresher

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