ABE Math Review Package

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ABE Math Review Package

This material is intended as a review of skills you once learned and wish to review before your

assessment.

Before studying Algebra, you should be familiar with all of the topics included here. Read the explanations

carefully, and do as many of each type of question in each exercise until you have mastered the material.

Section One: Check your answers in the answer key at the end of each topic in section one.

Section Two: Check your answers in the answer key on pages 55 - 56.

Do not use a calculator, unless you are instructed to.

Students wishing to take placement tests for math 030 should complete section one. Students wishing to take

placement tests for math 045, math 046 and math 047 should complete section one and two.

TABLE OF CONTENTS

SECTION ONE

page

Whole Numbers¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­..

Decimals¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­.....

Exponents and Roots¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­.

Fractions¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­.

Percent¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­

2

6

14

16

38

SECTION TWO

Signed Numbers¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­.

Add and Subtract signed numbers¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­..

Multiply and Divide signed numbers¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­.

Exponents¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­...

Order of Operations¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­....

Three Rules of Exponents¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­..

Solving Equations ¨C add and subtract¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­

Solving Equations ¨C multiply and divide¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­...

More solving equations¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­..

Factoring ¨C common factor¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­

Factoring ¨C difference of squares¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­...

Factoring ¨C basic trinomials¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­

Answer Key for Section Two.¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­

Appendix 1 ¨C Graphing a Line¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­...

VIU/CAP/\\capitan\redirects\h\hunterg\Desktop\math assessment\CompleteMathReview.doc/Jan 13, 2010

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44

45

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48

49

50

51

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53

54

55

57

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Whole Numbers Review

Before studying fractions, you should be familiar with all operations on whole numbers.

This work will provide a quick review. Answers are at the end on p.4.

1. ADDITION

In addition, remember to begin with the right hand column, and work to the left.

e.g. 423

+ 134

557

Try these:

(a) 19

+2

(b) 345

+123

(c) 951

+111

Remember that when the total of any column is greater than 9, you must carry the left digit in that total to the

column to the left.

1

e.g. 437

+126

563

Here is some practice:

(d) 489

+ 96

(e)

2754

+ 1666

(f) 238

+ 777

(g)

1069

+ 888

2. SUBTRACTION

Remember to begin at the right hand column and move column by column to the left.

e.g. 768

¨C 15

753

Do these:

(a) 1349

¨C 36

(b)

864

¨C 333

(c) 3834

¨C 2222

Remember that you should check the accuracy of your answer by adding it to what you took away. If it is

correct, your result should be the number you began with. In the example above, 753 + 15 = 768, so we can

assume that it is correct.

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Remember that when a digit in the bottom number is too big to subtract from the digit in the top number,

you borrow from the next column in the top number first.

31

e.g.

43

¨C 19

24

Try these:

(d) 753

¨C 409

You can not

subtract 9 from

3, so you

borrow 1 ten

from the tens

column first

(e)

70

¨C 18

1. Cross out the 4 in the tens place, and replace it with 3.

2. Borrow 10 from 4 to make 13 in the ones column.

3. Subtract 9 from 13

4. Subtract 1 from 3.

(f) 8104

¨C 1987

(g) 7512

¨C 943

(h)

1000

¨C 369

(i)

3084

¨C 2294

3. MULTIPLICATION

Take the time to learn your multiplication tables. That will save you a lot of time later on!

Multiply each digit in the top number by the bottom number.

Write the answer from right to left, starting in the ones column.

e.g.

12

41

x4

x 9

Remember that any number multiplied by 0 is 0.

48

369

Try these:

(a) 430

x 3

(b)

702

x 41

(c) 3011

x

7

When you multiply by a two or three digit number, be sure to begin your answer under the ones column.

Then continue on the line below the tens and then the hundreds. Always multiply from right to left.

Leave a space under the bottom digit that has already been multiplied OR add a zero in that space to keep the

columns lined up neatly and correctly.

Carrying in multiplication is like carrying in addition. Multiply first and then add the

number being carried. Line up the digits carefully under the correct column.

e.g.

23

x 22

46

46_

506

638

x 51

638

31900

32538

405

x 266

2430

24300

81000

107730

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Now try these:

(d) 789

x 46

(e)

5106

x 203

When you multiply by 10, 100, 1000, etc,

add the same number of zeroes to the right of the number.

e.g. 35 x 10 = 350

41 x 100 = 4100

60 x 1000 = 60 000

Tricky!

4. DIVISION

You will need your multiplication tables here too! Learn them well!

Division is the opposite of multiplication. That helps you to check your division answer.

Pay careful attention to lining up digits, as you did in multiplying large numbers, so that you can keep your

working straight.

Here are the words: 168 (the dividend) divided by 7 (the divisor) is 24 (the quotient) OR 7 into 168 is 24.

e.g.

24

7 168

-14

28

-28

0

Step 1: Divide the divisor 7 into 16 = 2. Place the 2 above the 6.

Step 2: Multiply 7 x 2 = 14. Place the 14 under the 16.

Step 3: Subtract: 16 ¨C 14 = 2.

Step 4: Bring down the next number to the right = 8

Step 5: The new number is 28.

Step 6: Divide 7 into 28 = 4. Multiply 4 by the divisor 7 and the answer is 28.

Step 7: Subtract 28 from 28 = 0. The division is complete.

Check: In division, it is easy to check the answer by multiplying your answer

Division problems

do not by

always

work out

with

even answer

in the last example.

(the quotient)

the number

you

arean

dividing

by (theasdivisor).

24 x 7 = 168 so the answer is likely to be correct.

Sometimes there is an amount left over, which is called the remainder.

It is placed on the top line with the letter r for remainder and is part of the quotient.

e.g.

569 r 3

6 3417

¨C 30

41

¨C 36

57

¨C 54

3

Try these:

(a) 4 1631

(b) 7 1046

(c) 9 3004

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When you check your answer for a division problem with a remainder, multiply your answer (the quotient)

by the number you are dividing by (the divisor) and add the remainder.

When you divide by a double or triple digit number, you need to use another different skill. You need to

estimate, which is a process of thoughtful guessing. This takes time and practice.

e.g.

223

28 6244

¨C56

64

¨C 56

84

¨C 84

0

Step 1: Think of about how many times 28 goes into 6244.

To do that, round 28 to 30 (28 ¡Ö 30) and divide that into 62.

The answer is approximately or close to 2.

Step 2: Place 2 above the last digit of 62.

Step 3: 2 x 28 (the divisor) = 56. Then 62 ¨C 56 = 6.

Step 4: Bring down 4. Estimate how many times 28, ¡Ö 30,

divides into 64 ¡Ö 2. Place 2 on the top line.

Step 5: 2 x 28 = 56. 64 ¨C 56 = 8.

Step 6: Bring down 4. Estimate how many times 28, ¡Ö 30, divides into 84 ¡Ö 3.

Sometimes your estimate is not quite right, but it should only be 1 more or 1 less than the correct

number, so the estimate gives a good starting point. Here is an example with a remainder:

e.g.

337 r 32

41 13849

¨C 123

154

¨C123

319

¨C 287

32

Try these:

(d)

57 3477

Round 41 ¡Ö 40. Divide 40 into the first part of the number.

40 goes into 138 about 3 times. Place 3 above the last digit of 138.

3 x 41 = 123. Subtract 123 from 138 = 15.

Bring down 4. Estimate how many times 41 ? 40 goes into 154 ? 3.

Multiply 3 x 41 = 123. 123 from 154 = 31.

Bring down 9. Estimate how many times 41 ? 40

goes into 319 ? 7. 7 x 41 = 287.

Step 7: 319 ¨C 287 = 32. Divide 41 into 32. It cannot divide,

so 32 is the remainder.

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Step 6:

(e)

(f)

36 7601

(g) 29 13796

67 13467

ANSWERS

Addition:

Subtraction:

(a) 21

(a) 1313

(h) 631

Multiplication: (a) 1290

Division:

(a) 407 r 3

(b) 468

(b) 531

(i) 790

(b) 28782

(b) 149 r 3

(c) 1062

(c) 1612

(d) 585

(d) 344

(e) 4420

(e) 52

(f) 1015

(f) 6117

(c) 21077

(c) 333 r 7

(d) 36294

(d) 61

(e) 1036518

(e) 211 r 5 (f) 201

(g) 1957

(g) 6569

(g) 475 r 21

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