Comparing and ordering fractionsName

Order TheseWrite in order from least to greatest. Use scratch paper if necessary.

271t,8,2! 1?g'2'3A *,*, 1

=t-r:

513}',2',4

B. qg36' 7 '21

7 211s '5's

3218'5'4

311E'2'4c. ? 13

5' 2' 10

419t,r,fi

a number line andsometimes I use

Sometimes I use

5316'6'']

24115'0' 15

1313'8'4

D. 99 74'5'10

1116,7'6

g ! I6'5'4

2 5 39 'iE '6

E. ? 11s',3', 4

22 37 '8,fr

5226 '5'5

1342'To'6

F. ? q g3'6' 4

1325' 10 '5

2227'11 's

1115'5'5c. !7?

6', 12', 3

FS-10219 Pre-Algebra18@ Frank Schaffer Publications, lnc.

Adding and subtracting fractionr

1013413

1415I+t

Name

Watch the Signs

611

2+ t't

1I4+5

?31+5

A.

320

, 11-20

tI2+0

B. 11

12512

?31

6

91o1

-2

7121+o

c.?51T2

g847

7245

'12

D. 13182I

?54

l-' 15

310g6

+?5

1

01

12

Add or subtract. Write your answer in the simplest form.

2158-ls

':|

.:.

t51

-3

131

7

tI13

+f

E.tI3+o

FS-l0219 Pre-Algebra19@ Frank Schaffer Publications, lnc.

Name Adding mixed numbers

?#*e i

sL

+Z\b

A.

11 1o

+ ?L

8+^5+b a

6+o*zft

B. 123

^7+ on

g?

*2?4I

*7t??

^3*b;5

C. 1:b

^1+o,

2t*83

2z-3*5a

3i^1+o,

D. 61o

* 1 ,1L,

2L

13

*3?

63

1l*31

E. a1t3

42o

*1+

3?

1L

*42

?T,

ft++ 4?

5

2+11

'?=5

+ t.1

F. tr1u4o1"12

++!o

Mixed Number Sums

-1c2

2!+11 1

b

Add. Write your answer in the simplest form. I have to find theleast common

denominator

FS-10219 Pre-Algebra20@ Frank Schaffer Publications, lnc.

Subtracting mixed numbers

^3\t 10

-2

Name

8?

^5- z6

o7"g-1"3

_3'10

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A.

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1

2

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B.

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L

4;

-11

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63

^3- 216

o

"10-4 2

5

D.

Mixed Number Differences

9

Subtract. Write your answer in the simplest form.

c. o4i6n2

3

3

-+

p?3

8*$L

_o9"16

P#1720

8l-43

E.

e1^1-o,

14*

o2"3

4L

-21Did you remember to find theleast common denominator?Did you regroup when you

needed to?

@ Frank Schalfer Publications, lnc. 21 FS-10219 Pre-Agebra

Adding and subtracting fractionsName

Fraction Practice

d!,2

+ ro ]]

tr16fi ^4o7

+z!5

4t*4tr

q43

-8

1

53

' 10

A.

e*^3+ba

t5tr+1ib

B.

Add or subtract. Write your answers in the simplest form.

I

c. oE-u14

-s9

8+*3 *

7

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b

6++3

D.

o1"4^2

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F. 11

14

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6

. 19_t_

'21

FS-10219 Pre-Algebra22@ Frank Schaffer Publications, lnc

actions Name Multiplying fractions

Products From FractionsMultiply. Divide any numerator and denominator by a common factorto make the fractions easier to multiply. Write your answers in the simplest form.

720-o--821

723sa-=11 42

57-a-_-710

F.

) A. !.! -49

910-o-=169

B. z.g -87

52-a-=35

34-o-=85

c.

26-a-=35

32-a-=49

D. 9.5=26

73-a--127

41-O- =58

E.

43-O- =52

13-a-=38

42-O-=57

65-a-=712

H. 9.? =53

614-o-=715

94-a-=103

815-a-=516

45-a-=38

341-a-a-=453

523-a-a-=2310

L. 1 .9.9 =357

325-o-=56

211-o-=11 24

27-a-=78

515-a-=38

74-a-=821

47-o-=72

l. 7.5=108

J' i'3 =

K. 5-1Fa-=22

lJ.

tsi :

-a-= r-d(::!

iP Ji

FS-'10219 Pre-Algebra@ Frank Schafier Publications, lnc.

Name Multiplying mixed numbers

Find the products. Rewrite mixed numbers as improper fractionsbefore you multiply. Write your answers in the simplest form.

Mixed Number Multiplication

sf.o=

7J.29 =

c!.2 =-2 6

A18'7 g =

q1.o1="3 "g

A.

B.

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20.3 =

s].to=

sl. zl =

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J. 29.1=-4I

H.

s f.to = *'r3=

!'z+ =

ts.aJ=

zt. to =

62r.. 24 =K.

@ Frank Schaffer Publications, lnc. 24 FS-10219 Pre-Algebra

Dividing fractions

How Many Equal Parts?'lhfiuftle fractions, rewrite the problem and multiply by the reciprocal of the divisor. CircleEft quotient in the simplest form.

778'8

A. 9.1=9'5

55_:_ =6' 12B. 1.3-:- =2'4

7112' 12

21-i.- =3'3

53-_:_- =2' 'to

11_:_=3' 12

318' 10

314'8

E. t.z-5'5

119'3

1. 1=3'911-l- =3'2

F.

11-g-

-10'572-:- =10' 3

G. q.q_8'4

13-::- - =2' 1A

51-:- =4'82.9._2'4

l. 51-:- =8'4

't7-3_ =5' 10

3910' 10

53-3- =2'8

J.

9.9 _8'4

31-:- =5'4K. !.? =10'5

D. 4.1_5'8

4.1=10' 5

52-:- =6'3H.

I I i..L+2+ ii. i

ii

, tvf-irli ,-.., _ a,i\,i''^' : - \:'':"4i

i

FS-10219 Pre-Algebra25@ Frank Schatfer Publications, lnc.

Name Dividing mixed numbe

Mixed Number DivisionChange the mixed numbers to improper fractions. Then multiply the first fraction

by the reciprocal of the second fraction. Circle each answer in the simplest form.

1e+z| =

A27+2=

7.n1 -g'"2

)47+4=c

sl+ z=

+2 * z1=

et+a=

o+tfr=

ro J + 4?=o]+s=

e]+r$=

^1 .5_"3 6

^! ' ^?--J^ 'Vaoo

o**g*=

ot+r] =

A' +t+z=

B' o] +r 2t=

s]+rf=C. -5..5-I a . I a-oo

e]+r$=

1o+s]=

zt +ttu ='' 2t * u?=

. 1 .3-'10'5-

D' 1s+t|=

E. 2.11 -3' '3-

F. .1.3-'2'B-

G' t|+ +|=

H. ^1 ..1_zu= tr-

J. zla*s * =

K' s+sJ=

FS-10219 Prs-Algel26@ Frank Schafier Publications, lnc.

ld numbers Name

DN

m.

Problem solving with fractions

III

Revise the amount of each ingredient to serve the number of people shown.

Georgina's Famous Chili

-IGeorgina's Famous Chili

2 ] tbsp. oil

,t.rp onion

S ] tO. ground beef

1 ] cups diced tomatoes

*.rp tomato paste

Here are the ingredients Georgina uses in her chili.

4 cups kidney beans

t tsp. salt

3 trp. pepper

3 tbsp. chili powder

2 cloves garlic

II

lngredient 16 servings 4 servings 20 servings 6 servings

oil r.. .ri. ,..: I i:,t:Li j

i: | ,.. i';..j

onion

ground beef

tomatoes

tomato paste

kidney beans

salt

pepper

chili powder

garlic

I Pre-Algobra @ Frank Schaffer Publications, lnc 27 FS-10219 Pre-Algebra

Making a frequency tabName

How Many Vowels?Complete the frequency distribution table by tallying the vowels in the following paragraph.

(The cumulative fiequency is the sum of the frequency and all the frequencies above it

on the table.)

The alphabet consists of 26 letters. Five of them are vowels. Some vowels are

used more often than others. Which do you think is used most in this paragraph?

Vowels Used in EverydaY Writing

Use the frequency table to answer the questions.

A. How many vowels were used in theparagraph?

Altogether, how many times werea and e used in the paragraPh?

B. How many more times was o usethan u?

Was e used more often or less oftt

than the other vowels combined?D.c.

E. Write a question that can be answered by reading the frequency table. Then answer i

O Frank Schaffer Publications, lnc 28 FS-10219 Pre-Alge

Name Making a line plot

Line UpA line plot shows how numbers are distributed. Make a dot on the line plot to record eachheight listed in the box. Then cross off the number in the box.

Heights of Students in Ms. Gagnon's Class(inches)

.56 59 52 57 58 57 6359 59 63 64 59 61 5755 66 60 66 57 64 5860 57 67 57 61 58 59

raph.it

'l__l

tuttit" Ilncy Il--l

=r used

55 56 57 58 59 60 61

height in inches

Use the line plot to answer the questions.

A. Which height is most common tothis class?

c. How many students are 63 inchestall or taller?

E. How many students are between54 and 62 inches tall?

F. Write something you know from reading the line plot.

B. What is the difference (in inches)between the shortest and thetallest student in the class?

How many students are 56 inchestall or shorter?

F. Which heights on the line are notrepresented by the students in Ms.Gagnon's class?

D.

s often€d?

wer it.

rre-Algebra 6 Frank Schatfer Publications, lnc. 29 FS-10219 Pre-Algebra

Name

Stem-and-Leaf PlotsMake a stem-and-leaf plot to organize the test scores listed in the box. Inthe sfem column, write the tens digits of the scores in order from least togreatest. ln the leaves column, write the digits that go with the tens digitsin order from least to greatest. Gross off each number as you record it.

Test Scores for Ms. Woo'sMath Class

.56' t-5$"" g3

67 9595 7487 88BB 8679 8090 90

7482657682

68789295B97692

Use your stem-and-leaf plot to answer the questions.

A. What was the lowest score? B. What was the highest score?

c. How many students scored 90or above?

D. How many students scored below 70?

How many students scored between70 and 89, including 89?

What single score was the mostcommon in Ms. Woo's class?

G. Use information from the stem-and-leafplot and the grading scale at the rightto find the number of students whoreceived each letter grade. Write thenumbers on the grade record at theright.

Making a stem-and-leaf plot

F.

E.

6ffi

Grade Record

Score Grade Number of Students

90-1 00 A

8H9 B

70-79 c6H9 D

1-59 F

@ Frank Schatfer Publications, lnc. 30 FS-10219 Pre-Algebra

Name Making a pictograph

Picture ThisMake a pictograph for the data shown in the table below. Write a title on the line above thegraph and make a symbol key. List the sports along the left side of the graph and usesymbols to indicate the number of people who participate in each.

Mountain Climbing 60 peopleWalking 120 peopleRunning 75 peopleSwimming 30 peopleBicycling 45 peopleAerobics 15 people

Use your pictograph to answer the questions.

A. Why did you choose your title?

B. What does each symbol represent? Why did you choose that number value?

C. Write something you know from reading your picture graph.

31I Pre-Algebra @ffi Sffiler Publications, lnc. FS-10219 Pre-Algebra

Making a bar graph

Bars for Gars

Make a double bar graph for the data shownat the right. List the autos along the left sideol the graph. For each car, show the numbersold in March with one color and the numbersold in April with another color. Write a titleon the line above the graph and fill in thecolor key.

March April

1,000 1,500

cars sold

2,000 2,500

Use the information given to answer the questions.

A. Which car sales did not increase B. Which car style had the largestbetween March and April? increase in sales?

March April

Compact 2,000 2,3002-Door Sports 1,200 1,8004-Door Sedan 1,100 950Station Wagon 900 850Van 1,750 2,300

o(do

c. How many more compact cars weresold in April than in March?

E. Write something you know from reading the double bar graph.

Which two car styles had the samesales in April?

D.

@ Frank Schaffer Publications, lnc. 32 FS-10219 Pre-AIgebra

Name Making a line graph

Video Rental Records

Make a line graph for the data shown on the chartat the right. Write a title on the line above thegraph. Put labels along the horizontal and verticalaxes. Make a dot to show the number of videosrented each day. Connect the dots with lines.

nr graPh

\-/vr-ln0 I

too I50lsol1_]

ame

Use your line graph to answer the questions.

A. On which day were video rentalshighest? Lowest?

Did video rentals increase or decreasebetween Tuesday and Wednesday?

B. On which two days were video rentalsthe same?

What does the graph tell about thetrend of video rentals during thecourse of the week?

D,c.

Day of Week Number of Videos

MondayTuesdayWednesdayThursdayFridaySaturdaySunday

60486072

10812096

I Pre-Algebra @ Frank Schaffer Publications, lnc. 33 FS-10219 Pre-Algebra

lnterpreting a hisiogramName

Heavyweight HistogramStudy the histogram below. Then answer the questions'

Weights of Junior League Football Players

24

22

20

C)

516f

[14rr 12

10

8

6

4

2

91-1 05 1 06-1 20 12't-135Weight in Pounds

A. What does the width of each bar on the histogram represent?

1 36-1 50

B. What does the height of each bar on the histogram represent?

c.

D.

E.

F.

How many players weigh more than 135 pounds?

What is the weight range with the greatest frequency?

How many players weigh less than 106 pounds?

Write something you know from reading the histogram'

@ Frank Schalfer Publications, lnc. 34 FS-10219 Pre-Algebra

Measures of Central TendencyEleven students from each math class competed ina math competition. Their scores are shown below.

Find the range, the mean to the nearest tenth, the median,and the mode for each class. Write them on the chart below.

Use your data to answer the questions.

A. Whose class had the highest mean?

Name Range, mean, median, and mode

c. Whose class had a five-pointdifference between the medianand the mode?

range-the differencebetween the least and

greatest numbers

mean-the average

median-the middlenumber in a set of data

mode-the number thatoccurs most frequently in

a set of data

B. Whose class had the smallest range?

D. Whose class had the lowest median?

Teacher Scores

Ms. Rowe 79, 83, 96, 75, 100,80, 91,87,72,86,79Mrs. Midqelv 86, 89, 93, 86, 95, 82, 77, 86,95, 98, 86

Mr. Maynard 68, 95, 72, 100,82, 85, 72,73, 68,72, 80Mr. Arnaiz 80, 75, 78, 80, 92, 66, 70,78,68, 90, 78Ms. Silver 73, 68, 75,82,69, 85, 75,78,75,88,78Ms. Choi 94, 90, 85,87,72,79,86, 95, 94, 98, 89

Teacher Range Mean Median Mode

Ms. Rowe

Mrs. Midgely

Mr. Maynard

Mr. Arnaiz

Ms. Silver

Ms. Choi

@ Frank Schaffer Publications, lnc. 35 FS-'|0219 Pre-Algebra

Name Box-and-whisker graphs

Box-and-Wh isker G raphsA box-and-whisker graph organizes data and helps you interpret it. Study the box-and-

whisker graph shown below. The median is the middle number in the ordered data. The

first quartile is the median of the lower half of the data. The third quartile is the median of

the upper half of the data.

19 22Ii

lowerextreme

23 25 28 29 36 38ll1st quartile median

2s 37

40 42 46 50

I3rd quaftile

46

62 65I

{upper

extreme

Answer the following questions about the box-and-whisker graph shown at the right.

A. What is the lower extreme?

B. What is the first quartile?

C. What is the median?

D. What is the third quartile?

E. What is the upper extreme?

Study the unfinished box-and-whisker graph below. Then answer the questions and record

the information on the box-and-whisker graph.

36 39312926211713103 32

F.

H.

J.

What is the lower extreme?

What is the median?

What is the upper extreme?

What is the first quartile?

What is the third quaftile?

G.

l.

@ Frank Schatfer Publications, lnc. 36 FS-10219 Pre-Algebra