Success step english 4 pdf

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 divid

− 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 of206, 208 divided8

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

Have you improved your skills with fractions? Try

these for practice:

1 512+ 423+ 616=

2 3161× 1319=

3 534− 212=

4 818− 258=

5 A recipe called for 234cups of flour Jessica

wanted to triple the recipe How much flour

would she need?

a 734

b 778

c 814

d 812

e 834

Answers

1 1613 The common denominator is 6 or 12

2. 4101or 3171

3 314

4 512

5 Jessica needs to multiply 234cups of flour times 3

234× 3 = 141×31= 343= 814

For more practice, look at some of the books in

the “More Help” section

 M a t h 5 : M e a s u r e m e n t ,

P e r i m e t e r, a n d A r e a

There are certain numbers, formulas, and

measure-ments, such as decimal equivalents, area formulas, and

weight conversions that you will be expected to have at

It’s a good idea to put them on flash cards for memorization

Common Measurements

You will be asked to figure problems using measure-ments of length, weight, and volume as well as speed, time, and temperature Here are the common meas-urements you may be asked to use Knowledge of the metric system was not on the CBEST when this book went to print

Weight Measurements

Weight measurements are usually measured on a scale

1 pound = 16 ounces

1 ton = 2,000 pounds

Liquid and Dry Measurements

Liquid and dry measurements are usually made in a measuring spoon, cup, or larger container Think of the dairy department of your grocery store Units smaller than a cup probably will not be on the test

1 cup = 8 ounces

1 pint = 2 cups = 16 ounces

1 quart = 2 pints

1 quart = 4 cups = 32 ounces

12gallon = 2 quarts

12gallon = 4 pints = 8 cups

12gallon = 64 ounces

1 gallon = 2 half gallons

1 gallon = 16 cups = 4 quarts

1 gallon = 128 ounces

Distance

Distance is measured by rulers or tape measures Miles are measured by odometers

1 foot = 12 inches

1 yard = 3 feet

1 mile = 5,280 feet

1 mile = 1,760 yards

Square and Cubic Measurements

Here are some conversions you should know You

won’t need to know any of the larger numbers on the

CBEST For example, you won’t need to memorize

1,728—just be able to figure it out if you need it

1 square foot = 144 square inches

1 cubic foot = 12 × 12 × 12 inches

or 1,728 cubic inches

1 yard = 3 feet

1 square yard = 9 square feet

1 cubic yard = 27 cubic feet

Temperature

Temperature is measured by a thermometer in degrees

The only tricky thing here is to know that the

differ-ence between 40 below 0 and 65 above 0 is not 25, but

105 If you can’t visualize the distance between 40

below and 65 above 0, a rereading of Math Lesson 2 on

negative numbers might help

Speed

Speed is usually measured by speedometers in miles

per hour Time, distance, and rate problems are

dis-cussed in Math Lesson 7

Time

Time is measured by a clock or by a calendar You can

figure out the number of seconds in an hour (3,600) by

multiplying 60 seconds by 60 minutes

1 minute = 60 seconds

1 hour = 60 minutes = 3,600 seconds

1 day = 24 hours = 1,440 minutes

1 week = 7 days = 168 hours

1 year = 12 months = 52 weeks = 365 days

Sample Measurement Question

1 Samuel, a friend of yours, has an uncle in the

wholesale fertilizer business “And I don’t even have a garden,” he remarked to you one day The two of you decide to make a garden in a 21 feet

by 25 feet patch in his back yard You suggest he put 4 inches of his uncle’s fertilizer on the top and then dig it in He asks you to help him decide how much to order Try to solve your

friend’s problem in cubic feet and write down

your answer

You give Samuel your answer and he calls his uncle His uncle is most obliging, but insists that since he’s a wholesale dealer, he can only accom-modate orders in cubic yards He also warns Samuel that his fertilizer does not smell very good, and needs to be dug in right away You re-figure your calculation in terms up cubic yards You finally come up with a figure and Samuel calls his uncle What is the amount he orders?

a 9,600 cubic yards

b 58.3 cubic yards

c 19.4 cubic yards

d 6.5 cubic yards

e none of these Answer

Look for your answer below and read to discover the exciting conclusion

a 9,600 cubic yards Suddenly, it grows dark You try

looking out the window, but fertilizer is stacked

up against the window as high as you can see You can’t even get out of your house You changed everything to inches and divided by 36 because there are 36 inches in a yard, so how could you have been wrong?

b 58.3 cubic yards Suddenly, it grows dark Your

windows are covered with fertilizer Fertilizer is

piled to the roof and the garden is buried You

changed inches to feet and divided by 3, so where

did you go wrong?

c 19.4 cubic yards There is a pile of fertilizer about

three feet high covering your garden This is more

than you expected so you pile it up and give it to

your neighbors You were clued into the cube idea

and divided by 9, so why didn’t you get it right?

d 6.5 cubic yards You spread exactly 4 inches on top

of the garden with a rake Quickly, you and

Samuel dig the fertilizer under You feel proud

that you could get the right answer to a

compli-cated math problem

e You couldn’t find your answer so you redo your

math You choose the closest answer

In this volume problem, three dimensions need

to be multiplied to get a cubic measurement, but they

need to be in the same units of measurement You can’t

multiply 21 feet by 4 inches In this case, it is easiest to

change the 4 inches into feet Four inches is 13of a foot

and 13of 21 is 7, times 25 is 175, the answer to the first

part of the question Now that you’re working in cubic

feet, you need to convert to cubic yards

Suppose you had a square with sides of one yard

each Since there are 3 feet in a yard, a square yard

would include 9 square feet

Now suppose you made your square into a cube

You would have 3 layers of 9, or 27 square feet So since

you need 175 cubic feet of fertilizer, you should divide

by 27 cubic feet: 175 ÷ 27 ≈ 6.5 cubic yards

Practice

Try your hand at some additional measurement problems

2 Casey bought 3 lbs 5 oz of boneless chicken at

$1.60 per pound How much did she pay?

a $0.50

b $4.80

c $5.30

d $8.80

e $12.00

3 Frank cut 2′8′′ off a 6′3′′ board How much was left?

a 3′5′′

b 4′5′′

c 3′7′′

d 4′7′′

e cannot be determined

4 Eight scouts each need two 3′ dowels for some banners they are making Before being cut, the dowels are 10 feet long How many dowels should the scoutmaster buy?

a 2

b 3

c 4

d 5

e 6

5 Three full containers each held one of the

fol-lowing amounts: one ounce, one cup, and one

quart If all three containers were dumped into a

gallon jar, how much room would be left?

a 2 196pints

b 5 176pints

c 6 156pints

d 9 1156pints

e 141156pints

6 A strip of wallpaper 5 yards long measured 5

inches wide How many square feet of wallpaper

were there?

a 6.25

b 8.3

c 60

d 12.4

e 19.7

7 Cooking a turkey takes 20 minutes for every

pound in an oven heated to 350 degrees If a

turkey weighing 20 pounds has to be ready by

2:00 P.M., at the latest, when should the turkey be

put in the pre-heated oven?

a 6:20 A.M.

b 6:40 A.M.

c 7:00 A.M.

d 7:20 A.M.

e 7:40 A.M.

Answers

2 This problem can be solved at least two ways You

can turn the ounces into 156of a pound and mul-tiply 1.60 × 3156 Alternately, you can multiply 1.60 by 3, then multiply 1.60 by 156 and add the

two together Choice c is the answer.

3 When subtracting 8 inches from 3 inches, borrow

one foot from the 6 feet Add 12 inches to the 3 inches to get 15′′ 15 − 8 = 7 and 5 − 2 is 3 The

answer is c.

4 The trick here is to realize that the 10’ dowels are

really only good for 9’ since the scouts need 3’ pieces The scouts need a total of 48’: 8 × 2 × 3 =

48 Five dowels would only be good for 45’, but six dowels would provide more than enough (54’)

The answer is e.

5 There are 128 ounces in a gallon 128 − 1 oz =

127 127 − 8 oz (1 cup) = 119 oz 119 − 32 oz (1 qt.) = 87 oz There are 16 ounces in 1 pint, so

8176= 5176pt The correct answer is b.

6 The easiest way to do this one is to change

every-thing to feet to begin with 5 yards is 15 feet ×152

= 6.25 The answer is a.

7 Multiply 20 × 20 to get the total time Convert the answer, 400, from minutes to hours by dividing by

60, to get 623, or 6 hours, 40 minutes From noon

to 2 p.m is 2 hours Subtract the remaining 4 hours and 40 minutes from 12 noon; think of 12 noon as 11 plus 60 minutes 11:60 − 4:40 = 7:20 A.M.

Perimeter and Area Formulas Rectangle

Area: length times width (A = lw) One side times

the other side tells you how many fit inside

Perimeter: 2 length + 2 width (2l + 2w) To

meas-ure all the way around something rectangular, you need to include 2 lengths and 2 widths— that’s all four sides

H O T T I P

On the CBEST, there is usually one question that goes

something like this:

A school of 240 children want to go on a field trip A bus

can hold 50 children How many buses are needed?

Among the answers are 4, 4 45, and 5 Four buses would

not be enough There is no such thing as 45of a bus So

5 is the answer.

Measuring the area and perimeter of a square is

basi-cally the same as a rectangle, only the length and width

are the same measurement

Area: side × side

Perimeter: side × 4

Triangle

Remember that a triangle is half a rectangle

Area:12b × h Multiply the height and the base.

Since the triangle is half, divide by two Note:

The height of a triangle is not always one of the

sides For example, in triangle ABC which

fol-lows, side AB is not the height, BD is the height.

AC is the base To find the area, ignore all the

numbers but the base and the height The base

can be found by adding 4 and 8: 4 + 8 = 12 The

height is 5.12× 5 × 12 = 620or 30

Perimeter: Add the sides all around: 12 + 6 + 9 = 27

Circle

The diameter of a circle goes from one point on the

circle, through the middle, and all the way across to

another point on the circle The radius (r) is half of the

diameter When working with π, consider the

follow-ing: The symbol π is usually found in the answers so

you don’t have to worry about converting it to a num-ber But ifπ is not found in the answers, and the ques-tion calls for an approximate answer, substitute 3 for π The question may tell you to use 272or 3.14

Area:πr2 Square the radius and look at the answers

Ifπ is not found in the answers, multiply by 3 In

the example above, A = π42or 16π

Circumference: 2πr Circumference is to a circle what

perimeter is to a rectangle Multiply the radius by

2 and look for the answers Ifπ is not in the answer choices, multiply by 3 In the example above, the circumference is 2π4, or 8π

Other Areas

Cut the figure into pieces, find the area of each, and add If you’re asked to find the area of a figure with a piece cut out of it, find the area of the whole figure, find the area of the piece, and subtract

Other Perimeters

For any perimeter, just add the outside lengths all the way around

Practice

8 Find the area of a circle with a diameter of 6.

a 36π

b 24π

c 16π

d 9π

e 6π