RATIOS AND PROPORTIONS

Contributed by:

Paula McDonald Wed, Jul 20, 2022 08:32 PM UTC

SV NUMBERS

1. Number Sense and Operations
Unit 1: Number Sense Table of Contents
and Operations LESSON PAGES
You are surrounded by numbers. Whether paying 1: Whole Numbers 2-3
bills, negotiating a car loan, budgeting for rent or 2: Operations 4-5
groceries, depositing a check, or withdrawing money, 3: Integers 6-7
you use basic math skills such as addition, subtraction,
multiplication, and division to perform a variety of
4: Fractions 8-9
everyday tasks. 5: Ratios and Proportions 10-11
In the same way, number sense and operations 6: Decimals 12-13
__play an important part on the GED® Mathematical
7: Percent 14-15
Reasoning Test. In Unit 1, you will study whole
numbers, operations, integers, fractions, ratios and Unit 1 Review 16-23
proportions, decimals, and percent, all of which
will help you prepare for the GED® Mathematical
Reasoning Test.
People use essential math skills to complete everyday tasks such as budgeting, paying bills, and saving and investing money.

2. MATH CO NTENT TO PICS: Q.1.d, Q.6.c
MATH PRACTICES: MP.1.a, MP.1.b, MP.1.e, MP.2.c, MP.5.c
0 Learn the Skill
Whole numbers are written with the digits 0 through 9. The value of a digit in a whole number depends
on its place. The value of a whole number is the sum of the values of its digits. When you write a whole
number, place commas every three digits counting from the right.
Write a whole number in words just like you read it (for example, two hundred twelve would be written
numerically as 212). To compare and order whole numbers, compare digits that have the same place value.
In some problems, you may need to round whole numbers to a certain place value.
To successfully solve problems on the GED® Mathematical Reasoning· Test, you must understand place
value, how to read and write whole numbers, how to compare and order whole numbers, and how to round
whole numbers. Read the example and strategies below. Then answer the question that follows.
.~
0 Tables make information
easier to compare by
Millions Thousands Units
organizing it in labeled rows Cl) Cl) Cl)
"O "O "O
and columns. Most tables, Q) Q) Q)
I... I... I...
including this one, present "O Cl)
Cl) "O Cl)
Cl) "O Cl)
Cl)
C Q) C Q) C Q)
information from left to right
- -
C C C
and from top to bottom.
::::i
..c Q) C
0
::::i
..c Q) C
0
::::i
..c
-Q) C
0
3 0 6 2
0 The value of a whole number
is the sum of the values of . ~
its digits. For example, the
value of the 4 is actually
-
4 X 10,QQQ = 40,000
40,000 because it is in the
ten thousands place. 3 X 1,000 = 3,000
0 X 100 = 000
When you compare whole 6 X 10 = 60
G numbers, the number with 2 X 1 = 2
the most digits is greater. = 43,062
If two numbers have the
same number of digits,
compare the digits from 43,022 > 43,011
left to right. Understanding
these symbols will aid in The number 43,062 is read and written in words as forty-three
comparing whole numbers: thousand, sixty-two. When rounded to the hundreds place,
= means equals
43,062 is 43,100.
> means is greater than
< means is less than
1. Carrie needs to round her income to the thousands place. What is
$56,832 rounded to the thousands place?
n:-51-T"A-KIN&i TIPS
C---,v-c.-lc- the- d,~t ~OV A. $56,000
want to v-ovnJ If thc- B. $56,800
C. $56,900
d,8t to the- v-~t of
D. $57,000
the- c.-iv-c.-lc-d d,~t ic; 5
OY- mov-c-, add r to thc-
C.-IY-C.-/c-d d,8t If it ,c; lc-c;c;
than ~ do not c.-hans:-c-
thc- c.-1v-c.-lc-d di8t
2 Lesson 1 I Whole Numbers 1
j

3. E) Apply the Skill
DIRECTIONS: Read each question, and choose the 7. A professional cyclist bicycled 22,755 miles in
best answer. 2005; 20,564 miles in 2006; and 23,804 miles in
2007. If the three years are listed in order of the
2. Meredith wrote a check for $182 to pay a bill. How miles bicycled, from least to greatest, how would
is 182 written in words? the years be listed?
A. one hundred eight-two A. 2006,2005,2007
B. one hundred eighty-two B. 2006,2007,2005
C. one hundred and eighteen-two C. 2005, 2007,2006
D. one-hundred eighty and two D. 2007, 2005,2006
3. Mr. Murphy rounds his students' test scores to the DIRECTIONS: Study the information and table, read
tens place. Jonathan's test score is 86. What is each question, and choose the best answer.
his test score rounded to the tens place?
The table below shows a sporting goods store's
A. 80 monthly sales for the first six months of the year.
B. 86
C. 90 Monthly Sales
D. 100
January $155,987
4. Each book in a historical library is given a February $150,403
number. The books are arranged on shelves Ma·ch $139,605
according to their numbers. The range of A~ril $144,299
numbers for shelves I through L is shown below.
May $149,355
Shelf I 1337-1420 June $148,260
Shelf J 1421-1499
Shelf K 1500-1622 8. Based on the table, in which month did the store
Shelf L 1623-1708 have its highest promotion to increase sales?
On which shelf would you find a book numbered A. January
1384? B. February
C. March
A. Shelf I D. May
B. Shelf J
C. Shelf K 9. In which nonth might the store want to run a
D. Shelf L special promotion to increase sales?
5. Michael swam 2,450 yards on Monday, A. March
2,700 yards on Tuesday, and 2,250 yards on B. April
Wednesday. What is the order of his daily swim C. May
yardage from least to greatest? D. June
A. 2,450; 2,700; 2,250 10. Based on the table, what sales trend can you
B. 2,250; 2,700; 2,450 determine?
C. 2,250; 2,450; 2,700
D. 2,700; 2,450; 2,250 A. People purchased the most sporting goods
equipment during early spring.
6. Michael swam an additional 2,500 yards on B. Sales were at their highest in winter months.
Thursday. Place his swim yardages in order by C. Monthly sales remained the same from
day from greatest to least. January through June.
D. People purchased more sporting goods as
A. Monday, Tuesday, Wednesday, Thursday summer approached.
B. Tuesday, Thursday, Monday, Wednesday
C. Wednesday, Monday, Thursday, Tuesday
D. Tuesday, Thursday, Wednesday, Monday
Unit 1 I Number Sense and Operations 3

4. MATH CO NTENT TO PICS: Q.1.b, Q.2.a, Q.2 e, Q.7.a
MATH PRA CTICES: M P.1. a, M P.1.b, M P.2.c, M P.3.a, MP.4.a, M P.5.c
0 Learn the Skill
The four basic math operations are addition, subtraction, multiplication, and division. Add quantities to
find a sum, or total. Subtract to find the difference between two quantities.
Multiply quantities to find a product when you need to add a number many times. Divide when
separating a quantity into equal groups. The dividend is the initial quantity. The divisor is the number by
which you divide. The uotient is the answer.
Factors are numbers that can be multiplied together to get another number: Factors of a whole number
refer to other whole numbers that divide into the original whole number with no remainder.
f) Practice the Skill
To successfully solve problems on the GED® Mathematical Reasoning Test, you must determine the
correct operation(s) to perform and the proper order in which to perform them. Read the examples and
strategies below. Then answer the question that follows.
0 Add the numbers in each
column, working from right to --►0 G G Multiply the ones digit of
the bottom number by all
left. If the sum of a column of Addition Multiplication the digits in the top number.
digits is greater than 9, regroup Align each result, or partial
1 2
to the next column on the left. product, under the digit by
482 ~82 which you multiplied. Use
+ 208 X 34 zeros as placeholders. After
1
To subtract, align digits by 690 1,928 you've multiplied digits in the
place value. Subtract the X 14,460 top number by all the digits in
numbers in each column, the bottom number, add the
16,388
working from right to left. partial products.
When a digit in the bottom
number is greater than the digit
in the top number, regroup. --►0 '
517 R12
14}72~Q
Subtraction Division
14 X 5 = -7~!
517 R12
712 25!
48,2' 14)7250 14 X 1 = -1~
- 208 -70 110
274 25 14 X 7= -98
-14 12
110
-98
12
r. 1. Shirley has $1,256 in her bank account. She withdraws $340.
How much money is left in her bank account?
Tis:-5-Y:.TA-KINGir n:-c..rt .
'
C-ompvfov.-&;,r;e-d for;tr; ' A. $816
v.e-riv.e- 1\1\ovr;i~ c.-/ie,/c.,i~ B. $916
;,rid k-e-1&0;,v.d,~ r;k-irlr; C. $926
D. $996
All-in ifomr; v.e-riv.e-
p/;,e,i~ the- uv.r;ov. in the-
;,n<;we-v. &ox, e,/ie,/c.,i~ to
;,u/iv,,fo, ;,nd the-11 11/P'~ :
in the- ;,n<;we-v.
:
4 Lesson 2 I Operations

5. E) Apply the Skill
*
Spotlighted Item: FILL-IN-THE-BLANK
DIRECTIONS: Read each question. Then write 8. Each month, Anna pays $630 in rent. How
your answers in the boxes below. much rent does she pay over the course of
18 months?
2. Alex drove from Denver, Colorado, to
Chicago, Illinois, in two days. The first day he
drove 467 miles. The second day he drove
583 miles. What is the total distance that
Alex drove? 9. The quarterback on Scott's favorite football
team is closing in on a 4,000-yard passing
season. He has thrown for 3,518 yards with
two games remaining. How many yards would
the quarterback need to average during the
3. During a word game, Alicia had 307 points. final two games to reach his goal of 4,000
She was unable to use all of her letters, so yards?
she had to subtract 19 points at the end of the
game. What was Alicia's final score?
10. Which whole number is the largest common
factor of both the numbers 36 and 20?
4. Juan works 40 hours per week. He earns $9
per hour. How much does Juan earn in one
week?
11. What is the smallest whole number that has
both 6 and 9 as factors?
5. Carl pays $45 per month for car insurance.
How much does he spend on car insurance in
1 year?
DIRECTIONS: Study the diagram. Then write your
answer in the box below.
6. Four friends went out for pizza. The total cost
for appetizers, pizza, and drinks was $64. If
the friends split the cost equally, how much did 504 sq ft
each friend pay?
12. Claire is purchasing bags of mulch to cover
her vegetable garden. One bag of mulch
7. Not including 1 and 60, how many whole will cover 12 square feet. How many bags of
numbers are factors of the number 60? mulch will Claire need?
5
Unit 1 I Number sense and Operations

6. LESSON
3
MATH CONTENT TOPICS: Q.1.d, Q.2.a, Q.2.e, Q.6.c
MATH PRACTICES: MP.1.a, MP.1.b, MP.1.c, MP.2.c, MP.3.a, MP.4.a
0 Learn the Skill
Integers include positive whole numbers (1, 2, 3, ... ), their opposites, or negative numbers (-1, -2, -3, ... ),
and zero. Positive numbers show an increase and may be written with or without a plus sign. Negative numbers
show a decrease and are written with a negative sign. Integers can be added, subtracted, multiplied, and
divided. There are specific rules for adding, subtracting, multiplying, and dividing integers.
In some cases, you may need to determine an integer's absolute value, or its distance from 0. Absolute
values are always greater than or equal to zero, never negative. So the absolute value of both 9-and -9 is 9.
E) Practice the Skill
Many mathematics problems relating to real-world situations use integers. You must understand and
follow the rules for adding, subtracting, multiplying, and dividing integers to solve such problems on the GED®
Mathematical Reasoning Test. Read the examples and strategies below. Then answer the question that follows.
0 If integers have like signs,
add and keep the common
sign. If integers have OPERATIONS WITH INTEGERS
different signs, find the
difference. Then use the
sign of the number with the Add Integers
greater absolute value. (+4) + (+7) = +11 (-5) + (-9) = -14
(-8) + (+4) = -4 (-5) + (+12) = +7
Subtract Integers
(+8) - (-5) = (+8) + (+5) = 13
8 - 5 = 8 + (-5) = 3
To subtract an integer, add
its opposite. For example,
Multiply and Divide Integers
the opposite of -5 is +5.
(4)(5) = +20 (-4)(5) = -20
(-4)(-5) = 20 (4)(-5) = -20
For multiplying or dividing
G integers: if the signs are 18 + 9 = 2 (-18)+9=-2
the same, the answer will
(-18) + (-9) = 2 18+(-9)=-2
be positive. If the signs are
different, the answer will be
negative.
1. In the morning, the temperature was -3°F. By mid-afternoon,
the temperature was 12°F. What was the change in temperature
fi:.ST-TA-K!N~ nPS between the morning and afternoon?
It ma1 be: he-lpfvl to v<;e- a
number /,ne- whe-n t;o/ving- A. -15°F
pvob/c,w; fhaf invo(vc, B. -9°F
info[¥'v<; To <;o/ve- 12-(-5), C. 9°F
be-t51n at -3 and C,Qvnf D. 15°F
<;paU,<; +o 12. Yov will <;e-e,
that the- cJ,<;tanU, i<; -rl5.
J I ,( I ; I : I ; I ,, I ; C ; C ; I ,
-4 -2 D 2 4 6 8 10 12 14

7. @) Apply the Skill
* Spotlighted Item: FILL-IN-THE-BLANK
DIRECTIONS: Read each question, and write There were 3,342 students enrolled at a
your answer in the box below. university. Of those students, 587 graduated
in May. Over the summer, 32 students left the
2. Uyen has a balance of $154 in her savings university, and 645 new students enrolled in the fall.
account. She withdraws $40 from a cash
machine. What is her new balance?
4. How many students were enrolled in the fall?
3. In a board game, Dora moves forward 3 spaces,
back 4 spaces, and forward again 8 spaces in 5. What is the change in the number of students
one turn. What is her net gain or loss of spaces? enrolled between May and the following fall?
DIRECTIONS: Read the question, and choose the best DIRECTIONS: Study the information and table, read
answer. each question, and choose the best answer.
6. Sasha's home is 212 feet above sea level. Melanie played a game and kept track of her score.
She participated in a scuba dive in which she The table shows her points earned for each round.
descended to 80 feet below sea level. Which
integer describes Sasha's change in position from MELANIE'S POINTS SCORED
her home to the lowest point of her dive?
Round Points Scored
A. -292 8
B. -132 2 -6
C. 132 3 -4
D. 292
4 3
5 4
DIRECTIONS: Study the number line, read the
question, and choose the best answer.
8. What was Melanie's score at the end of Round 5?
A B
... I I I I I I • I I I
-10 -5
I
O
I I I I I I • I I I
5 10
► A. 25
B.15
C. 7
7. The absolute value of the difference between two D. 5
numbers is the distance between the two numbers
on the number line. What is the absolute value of 9. Melanie played a sixth round and scored -8 in that
the difference between points A and B? round. What was her overall score?
A. -11 A. -13
B. -3 B. -3
C. 3 C. 13
D. 11 D. 18
Unit 1 I Number Sense and Operations 7

8. MATH CONTENT TO PICS: Q.1.a, Q.1.b, Q.1.d, Q.2.a, Q.2.d, Q.2,e, Q.6.c
MATH PRACTICES: MP.1.a, MP.1.b , MP.2.c, MP.4.a
0 Learn the Skill
'""' A fraction shows part of a whole or part of a group by separating two numbers with a fraction bar. The bottom
number is called the denominator. It tells the number of equal parts in a whole; if the denominator is 0, the
fraction is undefined. The top part is called the numerator. It tells the number of equal parts being considered.
E) Practice the Skill
By practicing operations on proper fractions, improper fractions, and mixed numbers, you will improve
your study and test-taking abilities, especially as they relate to the GED® Mathematical Reasoning Test.
Study the examples and strategies below. Then answer the question that follows.
0 A proper fraction shows a
quantity less than 1, such ~--<-~ Add l_ + 2- ➔ ~ = _§_ 6
-+----1-
5 _ 11 _ 3
4 4 8 4x2 8 8 8 8 8
as . A n improper
. f raction,
.
5 5 _ 1
such as 5 , 1s
. one where t h e 3 5 3x2 6 6
~ Subtract
4-8 ➔
4 x = ---
numerator is larger than the 4 2 8 8 8 8
denominator.
~-..~ Multiply 1-x2- ➔ 1-x2-=~
4 8 4 8 32
Q To add or subtract fractions,
Divide 5 . ,_ 2 ➔ 5 ..,_ 2 _ 5 X 3 _ 15 _ 5
find a common denominator >---->-...
~
(e.g., 8), rewrite the fractions 9 3 9 3 9 2 18 6
so they have a common
denominator, and write the Add 42_ + 2_!_
result as the sum of the
numerators over the common
-
• 5 + 1 _
6
5 X
4
2 + 1 X 3 _ 1Q + 3 _ 13 _ 1
denominator. An improper 4 2 4 2 4 2 6 7
fraction can be expressed as
6 4 6 X 2 4 X 3 12 12 12 12
a mixed number.
G To multiply fractions,
multiply the numerators Q To add mixed numbers, first find a common denominator. Then add
first, and then multiply the the fractions. If the sum is an improper fraction, change it to a mixed
denominators. To divide number. Then add the whole number and the sum of the fractions to
two fractions, multiply the the sum of the whole numbers. To multiply and divide mixed numbers,
dividend by the reciprocal first express the mixed numbers as improper fractions.
of the divisor. Always write
answers in lowest terms
15 5
(e.g., 18 ➔ 6).
1. There are two containers of milk in Eric's refrigerator. One has ;
'
Te:-5T-TA-KIN0r nPS gallon of milk. The other has ~ gallon of milk. How many gallons of
If ~ov <;frvff5-1e- to f ncl t milk are in Eric's refrigerator?
the- /owe-<; c..-ommon :1
cle-nomincito~ f ncl ci 9
;'
A. 20
c..-ommon cle-nomincitov-
b~ mvl-lipl~ins- the- 6
B. TT
cle-nomincitov-<; b~ one-
cinothe-v 7
C. 120
9
i:' D. 120
8 Lesson 4 I Fractions

9. 8 Apply the Skill
* Spotlighted Item: DRAG-AND-DROP
DIRECTIONS: Examine the information and table. DIRECTIONS: Read each question. Then use the
Then read each question and use the drag-and- drag-and-drop options to complete each answer.
drop options to complete each answer.
4. Jenny needs to add 2¾ and 1 ~.
In a water relay race, each team must fill a cup
She must find a common denominator. What
of water, race over to a bowl, and pour the water
improper fractions, expressed in terms of the
from the cup into the bowl. The relay is over when
lowest common denominator, correspond to
one team has filled its bowl to the top. The table
the two numbers?
below shows the results of the race.
WATER RELAY RESULTS □ 13
Team
Team 1
Bowl Capacity
1
5.
□·□
Clark is baking cookies. He needs 2; cups of
2
1 flour. What arithmetic equation properly
Team 2 expresses the number of times he needs to fill
1
3 his ; cup measuring cup to equal 2; cups?
Team 3
5
1
□
Team4
3 2.!cups+.!cups= D x D =D
4 2 2 2
Team 5
5
2. Starting with the first-place team, list the order
in which the various teams finished.
0]0000
DIRECTIONS: Examine the information and
number line. Then read the question and use the
Team D, Team D, Team D, drag-and-drop options to complete the answer.
Team D, Team D The following number line shows the interval
from O to 1, divided into 20 equal segments.
0]0000 A B C D E
3. If one poured the contents of Team 4's bowl ◄I• 1
0
•1•111+1111•11111 ►
into Team 1's bowl, what arithmetic equation
expresses the combined amount?
6. In increasing order, list the fractional values of
the points shown, reduced to lowest terms.
□
□ □·□
1 1
'5'
1 3
'4
0000~~
Unit 1 I Number Sense and Operations 9

10. MATH CO NTENT TOPICS: Q.2.a, Q.2.e, Q.3.a, Q.3.c
MATH PRACTIC ES: M P.1.a, M P.1.b, M P.1.e, M P.2.c, M P.4 .a
0 Learn the Skill
A ratio is a comparison of two numbers. You can write a ratio as a fraction, using the word to, or with
a colon (:). A proportion is an equation with a ratio on each side. The ratios are equal. You can use
proportions to solve problems involving equal ratios.
f) Practice the Skill
By practicing the skill of solving ratios and proportions, you will improve your study and test-taking
abilities, especially as they relate to the GED® Mathematical Reasoning Test. Study the information below.
Then answer the question that follows.
0 A ratio is different from
a fraction. The bottom Ratio
or second number of a
Jonathan earns $10 in 1 hour.
ratio does not necessarily
represent a whole.
Therefore, you do not
need to rename improper
The ratio of dollars earned to hours is
1
t 10 to 1, or 10:1.
fractions as mixed numbers. This also can be written as $10 per hour.
However, ratios still should
be simplified.
Proportion
6 4x6=8x3
A unit rate is a ratio with the = 8 24 = 24
denominator of 1. It can be
expressed using the word per.
3
=
X
---► 9x= 12 X 3
In a proportion, the cross 9x = 36
G products are equal. Use x=4
cross products to solve
proportions. If one of the
four terms is missing,
cross-multiply and divide the
product by the third number
(the number uninvolved in
the cross-product) to find the
missing number.
1. Carleen bought 3 gallons of milk for $12. How much would 4 gallons
of milk cost?
USING'! L-OG'IIC.
Whe-n 10v wvifo ;i A. $9
pvoportion to <;o/ve- ;i B. $12
pvoble-rY\ the- fovm<; in both C. $16
D. $18
v;ifio<; ne,e,J to be- wvitfon
in the- <;;ime- ovda: In
pvoble-m 1, the- top nvmbe-v<;
e,;in ve-pve-<;e-nt c¥1/on<; cind
the.- bottom nvmbe-v<; e,;in
ve-pve-<;e-nt c...o<;t
10 Lesson 5 I Ratios and Proportions

11. E) Apply the Skill
DIRECTIONS: Read each question, and choose the DIRECTIONS: Read each question, and choose the
best answer. best answer.
2. Sam averages 65 miles per hour on a road trip. 7. The GED® preparation class has a teacher-to-
How many hours will it take him to drive 260 miles? student ratio of 1:12. If there are 36 students in the
class, how many teachers are present?
A. 3
B. 4 A. 2
C. 5 B. 3
D. 6 C. 4
D. 6
3. The Jammers basketball team had a
win-to-loss ratio of 5:1 during their season. They 8. Sarah can ride 4 miles in 20 minutes on her bike.
won 25 games. How many games did they lose? How many miles can she bike in 120 minutes?
A. 5 A. 12
B. 6 B. 15
C. 7 C. 24
D. 8 D. 480
4. A store sold 92 pairs of pants and 64 shirts. What 9. The ratio of adults to children on a field trip is
is the ratio of the number of pants sold to the 2:7. If there are 14 adults on the trip, how many
number of shirts sold? children are there?
A. 23:16 A. 1
B. 16:23 B. 7
C. 64:92 C. 28
D. 16:92 D. 49
5. Amanda traveled 558 miles in 9 hours. What is the 10. The ratio of cars to trucks at an auto dealership
unit rate that describes her travel?
is ~. If there are 144 cars at the dealership, how
A. 52 miles per hour many trucks are there?
B. 61 miles per hour
C. 62 miles per hour A. 288
D. 71 miles per hour B. 240
C. 216
6. Jill mixed 2 cups of sugar with 10 cups of water to D. 96
make lemonade. What ratio of sugar to water did
she use? 11. In the recent college football season, Max threw
32 touchdowns and only 12 interceptions. In the
most simplified form, what was his ratio of
touchdowns to interceptions thrown?
A. 16:6
B. 8:3
C. 8:2
D. 4:1
Unit 1 I Number Sense and Operations 11

12. MATH CONTENT TOPICS: Q.1.a, Q.2.a, Q.2.e, Q.6.c
MATH PRACTICES: MP.1.a, MP.1.b, MP.1.e, MP.2.c, MP.3.c, MP.4.a
0 Learn the Skill
A decimal is another way to write a fraction. It uses the base-ten place value system. You can compare and
order decimals using place value. Decimals include place values such as tenths, hundredths, and thousandths.
Decimals can represent amounts much smaller than 1. You can round decimals as you do whole numbers.
As with fractions, you can add, subtract, multiply, and divide decimal numbers. When you perform
operations with decimals, you must pay close attention to the placement of the decimal point. For example,
when you add or subtract, write the numbers so that the place values and decimal points align.
f) Practice the Skill
By practicing the skill of operations with decimals, you will improve your study and test-taking abilities,
especially as they relate to the GED® Mathematical Reasoning Test. Study the table and information below.
Then answer the question that follows.
Whole numbers are to the
Compare Decimals
0 left of the decimal point, and Compare the following decimals by using the > or < signs.
decimals are to the right. ---► 0.~ > 0.~ 14.359 ~ 14.374
Each place in a decimal is
0.458 ~ 0.559 17.117 ~ 17.329
worth 10 times as much as
the place to its right and
one-tenth as much as the Operations with Decimals
place to its left. Compare Addition Subtraction Division
decimals as you would
12.283
G Multiply as you do
compare whole numbers,
place by place, from left to
right. ~ if 8)98.264
-§
18
-16
with whole numbers.
The number of
decimal places in
the product is the
When adding or subtracting, ~ 22 sum of the numbers
align decimal points. Then -16 of decimal places in
add or subtract as you do 66 the factors.
with whole numbers. -64 Divide as you do
24 with whole numbers,
Multiplication but first move the
14 decimal points in the
5,(§} +- 2 decimal places divisor and dividend
1
x 3{e) +- 1 decimal place the same number
4488 of places to make
+ 16830 the divisor a whole
21.318 +- 3 decimal places number.
1. Molly bought coffee for $2.95 and a muffin for $1.29. She paid with
a $5 bill. How much change did she receive?
T~ST-TA-KINGit TIPS
To mvl-tip/1 0110, move.- A. $0.76
the- de-vim;,/ one- pl;,ve- to B. $0.86
C. $2.05
the- vigit To divide- 01
D. $4.24
1DD, move- the- de-vim;,/
-/wo pl;,ve-<; to the- le-ft:
The- nvmoe-v of z..e.,voc;
<;how<; the- ;imovnt of
c;p;,ve-<; to move-.
12 Lesson 6 I Decimals '

13. E) Apply the Skill
DIRECTIONS: Study the information and table, read 5. How many packages of deli meat weighed less than
each question, and choose the best answer. 2.25 pounds?
Coach Steve needed to purchase new soccer A. 1
equipment for the upcoming season. B. 2
C. 3
Equipment Price Quantity . D. 4
Soccer ball $12.95 6
Shin guards $10.95 12 DIRECTIONS: Read the question, and choose the best
Knee pads $8.95 12
answer.
Uniforms $17.00 12
6. Paper Plus sells reams of paper for $5.25 each.
Discount Paper sells the same reams of paper
2. How much will Coach Steve spend on uniforms and for $3.99 each. How much would you save by
soccer balls? purchasing 15 reams of paper at Discount Paper
instead of at Paper Plus?
A. $47.95
B. $97.80 A. $1.26
C. $211.77 B. $18.90
D. $281.70 C. $78.75
D. $138.60
3. How much more will Coach Steve spend on shin
guards than knee pads? DIRECTIONS: Study the information and table, read
each question, and choose the best answer.
A. $16.00
B. $24.00 The Warriors softball team had five players
C. $36.00 competing for the league's batting title.
D. $48.00 ....
Pl_aye·r
'
.·
. ' '
Batting Average
.
..,~
. -~
DIRECTIONS: Study the information and table, read Jennifer .3278
each question, and choose the best answer. Ellen .3292
Krysten .3304
Sliced deli meat is sold by the pound. Shana bought
four different meats at the deli. Marti .3289
. Deli Meat ' ' \ . ' Weight. ' 7. Marti believes that if the season were to end today,
Chicken 1.59 pounds she would have the highest batting average. Which
Turkey 2.07 pounds explains the error in her reasoning?
Ham 1.76 pounds
A. She found the lowest batting average.
Roast beef 2.15 pounds
B. She compared digits in the tenths place.
C. She rounded all batting averages to the nearest
4. Which package of deli meat weighed the least? thousandth.
D. She compared the digits moving right to left.
A. Chicken
B. Turkey 8. Which player had the highest batting average?
C. Ham
D. Roast beef A. Jennifer
B. Ellen
C. Krysten
D. Marti
Unit 1 I Number Sense and Operations 13

14. M ATH CONTENT TOPICS: Q.2.a, Q.2 e, Q.3.c, Q.3.d
MATH PRACTICES: MP.1.a, MP.1.b, MP.1.e, MP.2.c, MP.4.a
0 Learn the Skill
As with fractions and decimals, percents show part of a whole. Recall that, with fractions, a whole can
be divided into any number of equal parts. With a decimal, the number of equal parts must be a power of
10. Percent always compares amounts to 100. The percent sign,%, means "out of 100."
There are three main parts of a percent problem-the base, the part, and the rate. The base is the whole
amount. The part is a piece of the whole or base. The rate tells how the base and whole are related. The
rate is always followed by a percent sign. You can use proportions to solve percent problems.
f) Practice the Skill
By practicing the skills of finding percents and solving percent problems, you will improve your study and
test-taking abilities, especially as they relate to the GED® Mathematical Reasoning Test. Study the table
and information below. Then answer the question that follows.
0 To convert a fraction to a
decimal, divide the numerator
1
by the denominator. To convert ----+---¾ 1 + 5 = 0.2 ---0.2 X 100: 20 ➔ 20%
5
a decimal to a fraction, write the
decimal digits as the numerator
and the place value of the
last digit as the denominator.
1 /o o
=
5 --!-- 25 + 100 = 0.25 -----25%
Simplify. To write a decimal as a j__
2 - 50 ---+----------+---- 50%
- 100
percent, multiply by 100. Do the
reverse to write a percent as a
decimal. To write a percent as Use a Proportion _
a fraction, write the percent as
the numerator of a fraction with
Zach answered 86% of the questions on a math exam correctly. If there
denominator 100, then simplify. were 50 questions, how many questions did Zach answer correctly?
Part = Rate _]_ = 86 50 x 86 = 4300 --+ 4300 + 100 = 43 questions
To find a percent of change, Base 100 50 100
subtract the original amount
from the new amount to find
~Find Percent Increase or Decrease Interest Problems
the amount of change. Divide Last year, Kareem paid $750 a month Kelly took out a $20,000 loan
the difference by the original in rent. This year he pays $820 a for 4 years at 3% interest. How
amount. Convert the decimal month. What's the percent increase? much interest (/) will she pay?
to a percent. To compute $820 - $750 = $70.00 I= prt
interest (/), multiply the amount
$70.00 + $750 = 0.09 I= $20,000 x 0.03 x 4
borrowed (p) by the rate (r),
written as a decimal, and the 0.09 X 100: 9% I= $2,400
time (t), written in years.
1. In a neighborhood, 27 of the 45 children are in elementary school.
What percent of children in the neighborhood are in elementary
VSIN&r L--O&rlC.. school?
fZe-e,,a/1 +ha+ a fvadion
i~ a vafio of pav+ +o A. 20%
B. 40%
whole-. A pe-ve,,e-n+ i~ a
C. 60%
vafio with a de-nominatov
D. 166%
of 100. Whe-n v~i~ a
pvopovfion, ~e-+ +he- vafo
ove.-v 100 to e-reial +he-
pav+ ov'e-v the- Da~e-.
14 Lesson 7 I Percent

15. f) Apply the Skill
*
"'1111
Spotlighted Item: DROP-DOWN
~
DIRECTIONS: Read each situation, and choose DIRECTIONS: Read each situation, and choose
the option that best completes each sentence. the option that best completes each sentence.
2. Shelly's Boutique is advertising 25% off all 7. Tia earns $552 per week. Of this amount, 12%
merchandise. is deducted for taxes.
Customers will save I Drop-down I off the $ I Drop-down I is deducted each week.
original price during the sale.
A. 6.62 B. 55.20 C. 66.24 D. 485.76
A. j_ B. j_ c.1- o.l__
4 2 3 4 8. Andrew received a raise from $24,580.00 per
year to $25,317.40 per year.
3. City Electric provides electricity for ~ of the He received a raise of I Drop-down I%.
homes in Center City.
A. 2 8.3 C. 7.4 D. 29
City Electric provides electricity for
I Drop-down I % of homes. 9. Isabelle paid $425 plus 6% sales tax for a new
bicycle.
A. 8 B. 10.5 C. 12.5 0.80
She paid a total of$ I Drop-down I.
4. In a survey, 0.22 of the respondents answered
"Yes" to the question, "Would you consider A. 25.50 B. 27.50 C. 450.50 D. 457.50
voting for a candidate from a third party?"
10. A sofa is regularly priced at $659 but is on sale
I Drop-down I of respondents answered "No." for 20% off.
A.11 B. 39 c.78 D. 22 The sale price of the sofa is $ I Drop-down I.
50 50 10 100
A. 639.00 B. 527.20 C. 450.80 D. 131.80
5. The Strikers girls soccer team won 9 of its
13 games. 11. A computer company received 420 customer
service calls in one day. Forty-five percent of
The Strikers won approximately I Drop-down I % the calls were about software issues.
of the games.
I Drop-down I of the calls were about software.
A. 61.5 B. 66.7 C. 69.2 D. 76.9
A. 19 B. 189 C.229 D. 231
6. At Bright Minds Learning, 75% of employees
work as instructors. There are 300 employees 12. Daria invested $5,000 in an account that earns
at Bright Minds Learning. 5% interest annually.
I Drop-down I employees work as instructors. She will earn $ I Drop-down I in interest over
nine months.
A. 150
B. 175 A. 5,250.00
C. 200 B. 1,875.00
D. 225 C. 250.00
D. 187.50
Unit 1 I Number Sense and Operations 15

16. DIRECTIONS: Read each question, and choose the DIRECTIONS: Read each question, and choose the
best answer. best answer.
1. Two-thirds of Mrs. Jensen's class passed the 6. A new movie has opening-day ticket sales of
science exam. If there are 24 students in her $21,343,845. How is 21,343,845 written in words?
class, how many passed the exam?
A. Twenty-one million, three hundred and forty-
A. 13 three thousand, eight hundred forty-five
B. 14 B. Twenty-one million, three hundred forty-three
C. 15 thousand, eight hundred forty-five
D. 16 C. Twenty-one million, three forty-three
thousand, eight hundred forty-five
2. Dina purchased a new dining room table for D. Twenty-one million, three hundred forty-three
$764.50 and four new chairs for $65.30 each. thousand, eight four-five
What was the cost of the whole set?
7. Not including 1 and 24, how many whole
A. $829.80 numbers are factors of 24?
B. $895.10
C. $1,025.70 A. 4
D. $1,091.00 B. 5
C. 6
3. The Martins drove 210.5 miles on the first day of D. 7
their trip and 135.8 miles the second day. How
many more miles did they drive the first day than DIRECTIONS: Study the information and table
the second day? below, read each question, and choose the
drop-down option that best answers each question.
A. 74.7
B. 149.4 The table shows the breakdown of after-school
C. 271.6 options for students at Oak Ridge Elementary
D. 346.3 School.
WHAT STUDENTS DO AFTER SCHOOL
4. Erin must add 4 ~ cups of flour to her cookie
; · · '· ·_option · I Number of Students
batter using a 1 ~ -cup measuring cup. How Parent pickup 118
Walk 54
many times will she need to fill the measuring Bus 468
cup with flour?
After-school programs 224
A. one
B. two 8. What fraction of students walk home?
C. three IDrop-down I
D. four 1 1
A. 48 B. 32
5. What is the smallest whole number that has both
6 and 8 as factors? 9. What fraction of students take the bus or stay
after school? I Drop-down I
A. 14 56 468 117 173
B. 18 A. 117 B. 864 C. 216 D. 216
C. 24
D. 48
Unit 1 Review I Number Sense and Operations

17. DIRECTIONS: Read each question, and choose the DIRECTIONS: Read the question, and choose the
best answer. best answer.
10. Kara invested $1,250 in the production of a 14. Tracy bought two pretzels for $1.95 each and
friend's music CD. Her friend paid her back at two soft drinks for $0.99 each. If she paid with
6% simple annual interest after 36 months. How a $10 bill, how much change did she receive?
much money did Kara get back?
A. $4.12
A. $225 B. $5.11
B. $1,025 C. $5.88
C. $1,325 D. $7.06
D. $1,475
DIRECTIONS: Study the information and table
11. Ken needs a cable that is 41 meters long. below, read each question, and choose the drop-
down option that best answers each question.
He has a cable that is 5 ~ meters long. What
A number of women participate in five different
fraction of a meter will Ken need to cut off? intramural college sports. The fraction of women
who participate in each sport is shown in the table.
A. J_
2 WOMEN'S INTRAMURAL SPORTS
B. _l_
12 Sport Fraction of Women
1
c.1- Basketball
6
3
1
D.1- Volleyball
20
4
1
12. Evan is developing a table of population data for Soccer
3
cities in his state and is rounding the numbers to 1
Ultimate frisbee
the nearest hundred. What would he enter for a 5
city with a population of 93,548? 1
Lacrosse
4
A. 93,500
B. 93,550 15. In which sport do the reatest number of
C. 93,600 women participate? Drop-down
D. 94,000
A. Basketball
13. Fred receives a phone call from his accountant B. Volleyball
and is told that his investments gained one C. Soccer
hundred three thousand, seven hundred fifty D. Lacrosse
dollars in value during the past 12 months.
What number would Fred write down? 16. What fraction of women articipate in lacrosse
and basketball? Drop-down
A. $103,705
5
B. $103,715 B.12
C. $103,750
D. $130,750 17. What percent of women partici ate in volleyball
and ultimate frisbee? Drop-down
A. 4% B. 5% C. 20% D. 25%
Unit 1 Review I Number Sense and Operations

18. DIRECTIONS: Read each question. Then write your DIRECTIONS: Read the question. Then write your
answer in the box below. answer in the box below.
18. Benjamin drove a distance of 301.5 miles in 25. What number is the largest common factor of
4.5 hours. If Benjamin drove at a constant rate, both 18 and 42?
how many miles per hour did he drive?
DIRECTIONS: Study the information and table
19. Scarlett purchased 20 shares of AD stock below, read each question, and choose the
at $43 per share. She sold the 20 shares at best answer.
$52 per share. How much money did Scarlett
make on her investment? Kurt and his family went to the state fair. They ate
lunch at a wild game restaurant. The menu is shown
below.
MENU AT THE STATE FAIR
20. A group of 426 people is going to a rally. Each
· 1tem Price
bus can take 65 people. What is the minimum
number of buses needed? Walleye fillet $5.89
Elk sandwich $9.65
Wild boar barbecue $9.19
Salmon on a stick $5.45
21. What is [(-1) x 2 x (-3) x 4 x (-5)] divided Kid's buffalo platter $3.50
by 6?
26. What is the most expensive item on the menu?
A. Walleye fillet
B. Elk sandwich
22. The proportion of students to chaperones for C. Wild boar barbecue
a school trip is required to be no more than D. Salmon on a stick
7 to 1. If 45 students go on the trip, what is
the minimum number of chaperones that must 27. Kurt ordered 1 wild boar barbecue, 1 walleye
accompany the students? fillet, and 3 kid's buffalo platters. If he brought
$50 with him to the fair, how much does he
have left?
A. $18.58
23. Donovan rode 135 miles on his bike at a unit B. $24.42
rate of 27 miles per hour. How many hours did C. $25.58
he spend riding? D. $31.42
28. How much more do 2 elk sandwiches cost than
3 kid's platters?
24. Steak on sale at the local grocery store costs A. $6.15
B. $7.88
$8 per pound. How many dollars would 3 ~
C. $8.80
pounds cost?
D. $15.80
Unit 1 Review I Number Sense and Operations

19. DIRECTIONS: Read each question, and choose the DIRECTIONS: Read each question, and choose the
best answer. best answer.
29. Alice typed her income into tax-preparation 34. Thirty-five percent of residents surveyed were
software. If her income was fifty-six thousand, in favor of creating a new road. The remaining
two hundred, twenty-eight dollars, which series residents objected. If 1,200 people were
of digits did she type? surveyed, how many objected to the new road?
A. 5,6,2,2,0,8 A. 780
B. 5,0,6,2,2,8 B. 420
C. 5, 6, 2, 0, 8 C. 360
D. 5, 6, 2, 2,. 8 D. 35
30. Delaney has $198 in her checking account. 35. Tom makes $200 per week working a part-time
She deposits $246 and writes checks for job. He pays $300 per month for his share of the
$54 and $92. How much is left in her account? rent where he lives. How much money does he
have left for other expenses in one year?
A. $98
B. $298 A. $1,200
C. $482 B. $5,200
D. $590 C. $6,000
D. $6,800
31. The ratio of men to women in a chorus is 2:3.
If there are 180 women in the chorus, how many DIRECTIONS: Study the table below, read each
men are in the chorus? question, and choose the best answer.
A. 72 BICYCLE TRAINING OVER THE WEEKEND
B. 108
Miles Biked
C. 120
Jackson 26.375
D. 270
Ben 25¾
2 Stefan 32.95
32. Anna can knit a scarf in 13 hours. How many
scarves can she knit in 4 hours?
36. How many more miles did Stefan ride than Ben?
A. 7
B. 7.15
3
C. 7
5
D. 7.25
1
D. 3
5 37. The distance Stefan rode is greater than the
33. Eighty-four percent of student athletes attended distance Jackson rode by about what percent?
a preseason meeting. If there are 175 student
athletes, how many attended the meeting? A. 23%
B. 24%
A. 28 C. 25%
B. 84 D. 26%
C. 128
D. 147
Unit 1 Review I Number Sense and Operations

20. DIRECTIONS: Study the information and table DIRECTIONS: Read each question, and choose the
below, read each question, and choose the best best answer.
41. The population of a city grew from 43,209 to
During an election year, 200 people were 45,687 in just five years. What was the percent·
surveyed about their political affiliation. The results increase in the population to the nearest whole
are shown in the table. percent?
VOTERS'POLL A. 4%
B. 5%
Party Affiliation Number of People
C. 6%
Democratic 78 D. 7%
Republican 64
Independent 46 42. Fifty-four percent of customers at a grocery
store bought milk on Friday. What fraction of the
Green 10
customers is this?
Libertarian 2
27
A. 50
38. What is the ratio of Green Party supporters to
14
Libertarian Party supporters? B. 25
9
A. 5 to 1 C.17
B. 1 to 5
3
C. 10 to 1 D.5
D. 2 to 10
43. Rodrigo pays $165.40 per month on his car loan.
39. If 400 people were surveyed, how many would How much does he pay on his loan in 1 year?
you expect to affiliate themselves with the
Democratic Party? A. $992.40
B. $1,654.00
A. 278 C. $1,984.80
B. 156 D. $3,969.60
C. 78
3
D. 39 44. A muffin recipe calls for 1 cups of oil. If Sean
8
triples the recipe, how many cups of oil does he
40. What percentage of those surveyed was neither need?
Democrat nor Republican?
1
A. 3
A. 71%
8 cups
1
B. 59% B. 4
C. 41%
8 cups
1
D. 29% C. 4
4 cups
3
D. 4
8 cups
45. A certain type of cheese sells for $8.99 per
pound. What is the cost of a 1.76-pound block
of cheese?
A. $5.10
B. $14.38
C. $15.80
D. $15.82
Unit 1 Review I Number Sense and Operations

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