Success step english 3 pdf

If instead of a place, the question calls for rounding to a certain number of significant digits, count that num-ber of digits starting from the left to reach the place digit.. If the s

1 Locate the place If the question calls for rounding to the nearest ten, look at the tens place Notice the place

digit Realize that the place digit will either stay the same or go up one

2 Look at the digit to the right of the place digit—the right-hand neighbor.

3 If the right-hand neighbor is less than 5, the place digit stays the same.

4 If the right-hand neighbor is 5 or more, the place digit goes up one.

5 If the place digit is 9, and the right-hand neighbor is 5 or more, then turn the place digit to 0 and raise the left-hand neighbor up one.

6 If instead of a place, the question calls for rounding to a certain number of significant digits, count that

num-ber of digits starting from the left to reach the place digit Now start with step 1

7 If the specified place was to the left of the decimal point, change all the digits to 0 that are to the right of the

place digit

3 The digit is 9; the 9 will either stay 9 or go to 0.

The number 6 is to the right of 9; it is more than

5, so change 9 to 0 and apply step 5, raising the 2

to the left of 9 to 3 Now apply step 7, and change

digits to the right of the tens place to 0 The

answer is 300

4 Here you need to apply step 6 Two places from

the left is the ten thousands digit, a 4 Now apply

step 1 and work through the steps: The digit is 4,

so it will either stay 4 or go up to 5 Since the

right-hand neighbor is 5, change the 4 to 5 Now

apply step 7 and change all digits to the right of

your new 5 to zero The answer is 350,000

Estimation

Estimation requires rounding numbers before adding,

subtracting, multiplying, or dividing If you are given

numerical answers, you might just want to multiply

the two numbers without estimation and pick the

answer that is the closest Most likely, however, the

problem will be more complicated than that

Sample Estimation Question

5 42 × 57 is closest to

a 45 × 60

b 40 × 55

c 40 × 50

d 40 × 60

e 45 × 50

Answer to Sample Estimation Question

Here’s how you could use the steps to answer the sam-ple question:

1 You can round 42 down and 57 up, resulting in

answer d.

2 Rounding the numbers to one significant digit

yields d also.

3 Eliminate a Eliminated: 45 is further from 42

than is 40 b Maybe c Eliminated: 50 is further from 57 than is 60 e Eliminated: 45 is further

from 42 and 50 is further from 57

4 Check the remaining answers The product of

choice b is 2,200 The product of choice d is

2,400 The actual product is 2,394, which makes

d the closest, and therefore the correct answer. Seven Success Steps for Rounding Questions

To do a problem like this, you might want to try some of the following strategies:

1 See whether you can round one number up and the other one down This works if by so doing you are adding

nearly the same amount to one number as you are subtracting from the other Rounding one up and one down makes the product most accurate For example, if the numbers were 71 and 89, you take one from

71 to get 70 and add one to 89 to get 90 70 × 90 is very close to 71 × 89

2 An estimation question may be on the test in order to test your rounding skills Round the numbers to one

significant digit, or to the number of significant digits to which the numbers in the answers have been rounded Find that answer and consider it as a possible right answer

3 Eliminate answers that are further away from those you obtained after doing steps 1 and 2 For example,

for 71 and 89, if answers given were 70 × 85 and 70 × 90, you can eliminate the former choice because 85 is further from 89 than is 90

4 After eliminating, you can always multiply (subtract, add, divide) out the remaining answers to make sure your

answer is correct

Decimal Equivalents

You may be asked to compare two numbers in order

to tell which one is greater In many cases, you will

need to know some basic decimal and percentage

equivalents

Decimal-Fraction Questions

See how many of these you already know For

ques-tions 6–11, state the decimal equivalent

6. 12

7. 34

8. 45

9. 18

10.13

11.16

For questions 12–14, tell which number is greater

12 a 0.93

b 0.9039

13 a 0.339

b. 13

14 a. 4951

b 0.52

Answers

6 0.5

7 0.75

8 0.8

9 0.125

10 0.3313or 0.33

11 0.1623or 0.166

12 a To compare these numbers more easily, add

zeros after the shorter number to make the num-bers both the same length: 0.93 = 0.9300 Com-pare 0.9300 and 0.9039 Then take out the decimals You can see that 9,300 is larger than 9,039

13 a Since 13= 0.33, extending the number would yield 0.333– (A line over a number means the number repeats forever.) 333 is smaller than 339

14 b Instead of dividing the denominator (91) into

the numerator (45), look to see whether the two choices are close to any common number You might notice that both numbers almost equal 12

45 is less than half of 91, so 4951 is less than half.

Half in decimals is 0.5 or 0.50; 0.52 is greater than

0.50, so it is greater than half Thus, b is larger.

Decimal-Percentage Equivalents

You already know that when you deposit money in an

account that earns 5% interest, you multiply the

money in the bank by 0.05 to find out your interest for

the year 5% in decimal form is 0.05

The percent always looks larger Here are some

examples:

Questions

Change the following numbers to percents

15 0.07

16 0.8

17 0.45

18 6.8

19 97

20 345

21 0.125

Change the following percents to decimals

22 5%

23 0.7%

24 0.09%

25 49%

26 764%

Answers

15 7%

16 80%

17 45%

18 680%

19 9,700%

20 34,500%

21 12.5%

22 0.05

23 0.007

24 0.0009

25 0.49

26 7.64

H O T T I P

To change a percent to a decimal, move the decimal point

two places to the left To change a decimal to a percent,

move the decimal point two places to the right If there is

no decimal indicated in the number, it is assumed that the

decimal is after the ones place, or to the right of the

number.

– C B E S T M I N I - C O U R S E –

Common Equivalents

Here are some common decimal, percent, and fraction

equivalents you should have at your fingertips A line

over a number indicates that the number is repeated

indefinitely

CONVERSION TABLE

For more on fraction and decimal equivalents, see the

next lesson

 M a t h 4 : F r a c t i o n s

Fractions are the nemesis of many a CBEST taker

Consider yourself fortunate if you have had few

prob-lems with them Now that you have had a few more

years of education and are a little wiser, fractions may

not be as intimidating as they once seemed

Comparing Fractions

The Laser Beam Method

A CBEST question may ask you to compare two

tions, or a fraction to a decimal To compare two

frac-tions, use the laser beam method: 1 Two laser beams

are racing toward each other 2 They both hit numbers

and bounce off up to the number in the opposite

cor-ner multiplying the two numbers as they go 3

Exam-ine the numbers they came up with The largest num-ber is beside the largest fraction Use the laser beam method to compare 156and 25

32 > 25, so 25> 156

Practice

Which number is the largest?

1 a) 0.25

b) 1418

2 a) 45

b) 0.75

3 a) 37

b) 49

Which number is the smallest?

4 a) 133

b) 121

5 a) 0.95

b) 190

6 a) 13

b) 0.3387

H O T T I P

To change a fraction into a decimal, you simply divide the denominator of the fraction into the numerator, like this:

38= 0.375

8 3.0 00

2 4 60 56 40

5 16

2 5

1 a 11 ÷ 48 = 0.23 < 0.25

2 a. 45= 0.8 80 > 75

3 b Use the laser beam method.

4 b Use the laser beam method.

5 b. 190= 0.9 90 < 95

6 a. 13= 0.33 3,387 > 3,333

Reducing and Expanding

Fractions

Fractions can be reduced by dividing the same number

into both the numerator and the denominator

■ 24= 12because both the numerator and

denomi-nator can be divided by 2

■ 2346= 23because both the numerator and

denomi-nator can be divided by 12

Fractions can be expanded by multiplying the

numerator and the denominator by the same number

■ 18= 126= 450because the original numerator and

the denominator are both multiplied by 2, and

then by 5

Adding and Subtracting Fractions

When adding fractions that have the same

denomina-tors, add the numeradenomina-tors, and then reduce if necessary:

14+ 54= 64= 124= 112

When subtracting fractions that have the same

denominators, subtract the numerators Then reduce

if necessary:

57−37= 27

When adding or subtracting fractions with

dif-ferent denominators, find common denominators

before performing the operations For example, in the

problem 38+ 16, the lowest common denominator of 6 and 8 is 24

Convert both fractions to 24ths: 38= 294

16= 244

Add the new fractions: 294+ 244= 1234

To subtract instead of add the fractions above, after finding the common denominator, subtract the resulting numerators: 294−244= 254

When adding mixed numbers, there is no need to turn the numbers into improper fractions Simply add the fraction parts Then add the integers When fin-ished, add the two parts together Don’t forget to

“carry” if the fractions add up to more than one

13 57

+ 6 67

19 171

171= 147

147+ 19 = 2047

Subtraction uses the same principle Subtract the bottom fraction from the top fraction, and the bottom integer from the top integer If the top fraction is smaller than the bottom one, then take the following steps:

1 Notice the common denominator of the

fractions

2 Add that number to the numerator of the top

fraction

3 Subtract 1 from the top integer.

4 Subtract as usual.

Suppose the problem above were a subtraction problem instead of addition:

– C B E S T M I N I - C O U R S E –

− 667

1 Notice the common denominator

2 Add that number to the numerator

3 Subtract one from the top integer: 13 − 1 = 12

4 Subtract as usual: 12172

−667

667

Multiplying and Dividing Fractions

When multiplying fractions, simply multiply the

numerators and then multiply the denominators:

56×78= 3458

When dividing, turn the second fraction

upside-down, then multiply across:

12÷23is the same as 12×32= 34

When working with problems that involve mixed

numbers such as 612 × 513, change the numbers to

improper fractions before multiplying With 612, multiply the denominator, 2, by the whole number, 6,

to get 12, then add the numerator, 1, for a total of 13 Place 13 over the original denominator, 2 The result is

123

When multiplying or dividing a fraction and an integer, place the integer over 1 and proceed as if it were a fraction

13 ×12= 113×12= 123= 612

Choosing an Answer

When you come up with an answer where the numer-ator is more than the denominnumer-ator, the answer may be given in that form, as an improper fraction But if the answers are mixed numbers, divide the denominator into the numerator Any remainder is placed over the original denominator In the case of2068, 208 divided

by 6 is 34 with a remainder of 4 yielding 3446 This answer probably will not be there, so reduce 4

6 to 2

3  If

2068 is not an answer choice, 342

3 probably will be But don’t worry about having to choose between these two answers Since they signify the same amount, the test would not be valid if both 2068 and 342

3  were there unless the question specifically asked for a fully reduced answer

H O T T I P

When you’re working with two fractions where the numerator of one fraction can be divided by the same number as the denominator of the other fraction, you can reduce even before you multiply:

612× 513= 123×136 Divide both the 2 and the 16 by 2:

H O T T I P

When adding or subtracting fractions, you can use the

laser beam method.

1 First change to improper fractions, then multiply

crosswise:

2 Next, multiply the denominators: 6 × 7 = 42

3 Add or subtract the top numbers as appropriate and

place them over the multiplied denominator to get your

answer: 7 + 18 = 25

2452 

1 6

3 7

1

6

3

7

13

2 163

104 3

2 3

1

8

34