Download 8th Grade Math Packet

Name
8 th
Grade Summer Math rod t,
For Students who will be enrolled in Mrs. Kohrman's
8th Grade Math Class in the 2015/2016 school year.
e 0201.11.
Summer Math Packet Directions.
Please complete the following packet before the start of next school year.
This packet will be turned in for a grade. All odd problems in this packet
are required. All even problems are optional. All work for this packet
should be completed on a separate piece of paper and saved to turn in with
the final packet. Answers should be transferred from your work to the
packet. Each page of this packet begins with an example to guide your
practice. If you have questions while completing the packet, use what
resources you have available to you (last year's online textbook, family,
friends, the internet). All work and the original packet should be brought to
class on the first day of school. I recommend using a folder or a binder to
hold and organize the packet and your work.
In order to stay on top of the work, I recommend that you complete about 3
pages per week. Don't leave it all for the last minute! This packet is meant
to review previously learned concepts that will be essential to your success
this year. Remember, you get out of it what you put into it!
Good luck and have a great summer!
NAME
CLASS
Parenfin s a[
UNIT I
OBJECTIVE:
DATE
e Order of C_
s
Finding the value of an expression that contains parentheses
Often an expression contains parentheses. To find its value, you first
perform any operations inside the parentheses. Remember to follow the
correct order of the four basic operations.
EXAMPLE 1
Fiund the value of (9 + 3) X (17 — 8).
Solution
(9 + 3) X (17
— 8)
12 X 9
108
EXAMPLE 2
First work inside the parentheses.
Then multiply.
Find the value of 92 — 6(5 + 8).
Solution
92 — 6(5 + 8)
92 — 6(13)
92 — 78
14
First work inside the parentheses.
Then multiply Note that 6(13) means 6 X 13.
Then subtract.
Find the value of each expression.
2. (35 — 6) X 4
3. (12 — 4) + 2
4. (22 + 19) X 10
5. 36 X (12 + 6)
6. 45 — (9 + 27)
7. (18 — 3) X (4 + 7)
8. (25 — 9) + (3 + 5)
9. 38
— (14 — 2) + 9
10. 9 X (24 — 16) + 4
11. 27 + (3 + 14) X 6
12. 60 — (4 X 8) + 2
13. 6(33
14. (41 + 39)2
— 29)
15. 47 + 2(12 — 9)
16. 90 — 3(8 + 5)
17. 74 + (17 — 6) X (6 ± 2)
18. (49 — 7) ± (7 — 4) X 2
19. (16 — 2 X 4) + (64 ± 4 ± 2)
20. 36 + (9 X 2) + (6 + 18 + 2)
Unit 1 Order of Operations and Number Theory
Making Sense of Numbers
Copyright © by Holt,
Rinehartand Winston. Allrightsreserved.
1. 54 + (2 + 4)
DATE
CLASS
NAME
Using Exponents
OBJECTIVE: Writing expressions in exponential form and finding the value of
exponential expressions
You can write some multiplications in a type of "mathematical
shorthand" called exponential form.
Exponential Form
7 is the exponent.
X3X3X3X3X3X 3,= 37
3 is the base.
7 identical factors of 3
111118...._
r
EXAMPLE 1
Write each expression in exponential form.
b. 5 X 5 X 7 X7X7
a. 3 X 3 X 3 X 3
c,2
Solution
a. 3 X 3 X 3 X 3 = 34
EXAMPLE 2
c. 2=2'
b. 5X 5 X 7X 7X7= 52 X 73
Find the value of each exponential expression.
b. 24 X 32 X 71
a.53
Solution
a. 53 = 5 X 5 X 5
b. 24 X 32 X 71 = 2X2 X2 X2X3X3X7
=
=125
16
X 9 X7
1008
Write each expression in exponential form.
1. 7X 7X7X7X7
2. 2 X2 X 2X2X2 X2X 2 X 2
3. 3 X3X5X5 X5X 5
4. 5 X5 X5X7X 7X7
5. 2X2X 3X5 X5X 5
6. 2 X5 X5X7X 7 X7
Find the value of each exponential expression.
7. 23
8. 32
11. 131
12. 71
9 . 52
10. 73
13. 27
14. 35
15. 22 X 34
16. 23 X 112
17. 23 x 32 x 52
18. 23 x 32 x 72
19. 25 X 32 X 51
20. 24 X 31 X 72
Making Sense of Numbers
Unit 1 Order of Operations and Number Theory
NAME
DATE
CLASS
41
3
UNIT 2
Adding Fractions: UnF°:e D
hators
OBJECTIVE: Finding sums of two or more fractions with unlike denominators
To add fractions that have unlike denominators, you must first write
equivalent fractions that have a common denominator. Then add using
the method for fractions with like denominators.
3 1
Write each sum in lowest terms. a. +
3 5
+
b.
Solution
a. The LCM of 8 and 2 is 8. So the least common denominator is 8.
1
-
Fi rot
Then add.
rerie'
wt 2
1 1 X4
4
2 2X4 8
3
8
1
2
3 4 3+4
+ =
8
8 8
7
8
b. The LCM of 4 and 6 is 12. So the least common denominator is 12.
3
5
First rewrite- and 4
6.
3 3X3
9
4
4X3
5
6
5 X 2 10
=
6X2
2
Then add.
9
10 9 + 10 19
3 5
+ = + =
4 6 12 12
12 = 12
12
7
= 112
Write each sum in lowest terms.
9
3 11
10. 71 + Trzi-
- 10
6
'• 6, 8
7
5
11. —
12 + 20
12.
3 1 7
13. g + --4- +
1 3 3
14. + 3 +
1; 7 1 3
8 2 4
2 7 5
+
• 16. +
1 1 1
17. + + 3
2 2 5
19. + +
34
Unit 2 Fractions
R
1 _4_ 1
5 11
+
1
— 6 4 14
5
8 4_ 3
20. 9 + 15 10
Making Sense of Numbers
rightsreserved.
Copyright 0 by Holt, Rinehartand Winston. All
6
NAME
DATE
CLASS
Addini
imbers:
Unlike Dediuk.linators
UNIT 2
OBJECTIVE: Finding sums of mixed numbers with unlike denominators
To add mixed numbers that have unlike denominators, you must first
write equivalent mixed numbers that have a common denominator.
Then add using the method for mixed numbers with like denominators.
1
1
7
7
+ 3Write each sum in lowest terms. a. 86
5 + 3—b. 48
Siuhition
a. The LCM of 5 and 10 is 10.
b. The LCM of 8 and 6 is 24.
So the least common
So the least common
denominator is 24.
denominator is 10.
7
21
1
2
88-5
10
4
1
7
7
25
1
1
= 8724 = 7 + 124
24
9
1110
Write each sum in lowest terms.
2
1
1. 6- + 73
6
2. 9- + 38
2
1
5
+2
3. 53
3
1
4. 8- + 214
2
1
3
5. 1 4— + 2 10
1
4
+ 16. 36
15
7
1
7. 2i + g
11
7
8. m
i + 19
1
5
9. 7- + —
2
6
3
1
-o
CC
C-
10.
1
6
11. 3 - +
2
7 _4_ R 2
12
8
1
7
C
5
co
4
2
12. -3- + 13
3
4
4
5
6
13. 4- + —
6
9
14. —
9 + 6 1—5
15. 5- + 8-
5
7
16. 3- + 18
10
19
1
17. 4 7
2 ) + 4E
11
11
18' 71' + 2 12
1
1
4
5
2
5
3
5
7
10
1
19. 1- + 6- + 84
8
4
21. 1— + 3— +
1
2
Unit 2
1
6
2
3
1
7
3
22. 9- + 6 - + 2 4
8
4
1
2
23. 4- + 2- + 936
2
3
20. 2- + 4- + 9-
Fractions
3
5
11
24. 8- + — + 24
6
12
Making Sense of Numbers
a,
5
DATE
CLASS
NAME
5-4
Subtracting Mixed Numbers
Without Ren. wing
UNIT 2
OBJECTIVE: Finding differences of mixed numbers without renaming the
whole-number part
To subtract mixed numbers, you use the following general method.
Subtracting Mixed Numbers without Renaming
• 1. If necessary; write equivalent mixed numbers that have a
common denominator.
2. Subtract the fractions.
&• Subtract the whole .numbers,
4. If necessary, rewrite the difference in lowest terms.
EXAMPLE
1
7
Write each difference in lowest terms. a. 58
8 - 3Solution
3
7
b. 5a. 54 -->
8
Copyright 0by Holt. Rinehart andWinston. All rights reserved
9
5—
12
Write equivalent
mixed numl2ers
1
4 with common
- 1- -4 - 1—
12 denominators.
3
1
- 38
3
6
2-4
2=
8
1
3
1b. 53
4
Rewrite the
difference in
lowest terms.
5
412
Write each difference in lowest terms.
7
2
- 4-§2. 129
3
9
3. 711 - u
6 !
4. 9_
7
7
7
5. 58 -2
1
6. 142 - 10
4
1
7. 85 - 85
7
14
8. 1. 3 . - 1T;
1
9
9. 61-5 - 3-r)0--
1.
4
11
6-i5- - 5-13
8
2
10. 1549
9
3
5
11. 1-§ - -§
1
11
12. 18E - 1 1.
.
7
2
13. 5m - 33
7
2
14. 1112
3 - 2-
1
1
15. 5-g - 1Th
3
19
16. 7-gi - 6i
2
13
17. 10T-8- -
Making Sense of Numbers
1
1
Unit 2 Fractions
43
CLASS
NAME
DATE
plying Two Fractions
UNIT 2
OBJECTIVE: Finding the product of two fractions
To multiply two fractions, you can use the following method.
Multiplying Fractions
1. Multiply the numerators.
2. Multiply the denominators.
3. If possible, divide both numerator and denominator by a
common factor. This will give you the final product in
lowest terms.
Write each product in lowest terms. a.
4
b.
4 3
x
_
6
Solution
a.
1
4
4
b —
* 11
Copyright ©by Holt, R inehart andWinston. All rights reserved.
C. -§-
1X5
5
4 X 6 = 24
5
6
3
4
=
1X3
3
=—
11 X 1 11
11
X
= 5 X 2 _ 10
7 3 X 7 — 21
Divide each 4 by 4.
Divide
and 9 by 3.
Write each product in lowest terms.
1.
1
X
1
2
2. _
8
4 2
7 3
17
7.
5 4
9 5
3
8. 4
1
25
16.X
36
27 20
19. —
32 21
Making Sense of Numbers
12
4 5
11
2 3
13. — X
9 8
1
3
6
7 8
9
9. 10
12.
7
1
14.
5 3
18 20
3
15. ,7
17.
4 21
15 32
15
18. 28
8 25
5 16
21.
20.
14
1
25
16
15
9
14
Unit 2 Fractions
53
NAME
DATE
CLASS
6-3
Multiplying a Fraction and
a Whole Number
UNIT 2
OBJECTIVE: Finding and estimating products of fractions and whole numbers
To multiply a fraction and a whole number, write the whole number as
a fraction with a denominator of 1. Then follow the procedure for
multiplying two fractions.
EXAMPLE I
Write the product 15 X hi lowest terms.
O' Solution
5 5 X 5 25
5 15 5 _
1
2 =T=12-1
15 X;=TX;- 1 X;=i-7-
Divide 15
and 612 y 3.
You can estimate a product of a fraction and a whole number by rounding.
EXAMPLE 2
3
Estimate each product. a. Ti x 80
0. Solution
3
a. 17 X 80
X 80
20
20
Replace
47 with 45
t Stand
2
replace
48 x
20 , 2
-2--j with
b. 47 X
Replace
1
b. 47 X
3
1
- with
about 32
Write each product in lowest terms.
x 40
1
2. 42 X 7
2
3. 15 X 3
4.
1
5. - X 20
6
1
6. 30 X -
5
7 . - X 21
9
9
8. 24 X
1.1
3
X 48
Estimate each product.
1
9. 3 X 22
1
10. 30 X -8-
2
11. 3 X 19
7
12. 55 X -§-
4
13. — X 28
17
11
14. 54 X ;7
21
15. 35 X —
51
16.
54
Unit 2 Fractions
45
X 36
12
17. E X 61
Making Sense of Numbers
Copyright 0 by Holt Rinehartand Winston. Allrightsreserved.
about 20
F.
NAME
CLASS
7-3
UNIT 2
•
DATE
Dividing With Fractions
OBJECTIVE: Finding quotients involving fractions
2
In the division -3- ÷
62
6
3 is the dividend, is the divisor, and the result of
this division is called a quotient. To divide by a fraction, you can use the
following rule.
Dividing by a Fraction
1. Multiply the dividend by the reciprocal of the divisor.
2. If necessary, rewrite the result from Step 1 in lowest terms.
EXAMPLE 1
2 6 ,
Write
L
the quotient 3 + ,7 in lowest terms.
Solution
2. 6 2 v 7
37—
3—
1
2X7_1X7_7
6 = 3X — 3 X 3 — 9
3
When a division involves a whole number, write the whole number as a
fraction with denominator 1.
EXAMPLE 2
1
Write each quotient in lowest terms. a. 3 + 3
1
3= 1
b. 6—
§ = i9 _
—
1
A
I
1X 1
=1X
4
8
1
—
4-
4
Write each quotient in lowest terms.
1. ±
7
5.
3
5
2 . 2
Y
3
15 . 3
13. —
4
÷2
3 ±9
17. —
4
68
Unit 2 Fractions
2.
6.
3... 2
5•9
1.1
2 .., 2
3 • 9
24
10. E
14.
4. 2•
3' 7 7
. 34
g+6
2
18. § ± 4
7.
3'3
4.8
11. 9 . 13
3 .
15. — ÷
5
19. 6 ±
2
1
4 2.4
.
•7 • 7
1
1
•8.4 . 7
9 .12
5
16. ± 7
2O.8
.
3
Making Sense of Numbers
Copyright C)by Holt, RinehartandWinston. Allrightsreserved.
So 1 uti on
1
a' 3 ±
b. 6+
NAME
CLASS
Roundil ig
DATE
cima s
OBJECTIVE: Rounding decimals
When you round a decimal, you replace the given decimal with a
number that terminates at the specified decimal place.
ound each decimal to the specified decimal place.
a. 24.567 to the nearest hundredth
b. 18.42 to the nearest tenth
c. 93.5 to the nearest whole number
Solution
a. Identify the digit in the hundredths place. Look at the digit to
its right.
This is the hundredths place.
24.56T1
Since the digit in the thousandths
place is more than 5, replace 0 with 7.
Thus, 24.567 rounded to the nearest hundredth is 24.57.
b. Identify the digit in the tenths place. Look at the digit to its right.
This is the tenths place.
18.4©
Copyright ©by Holt, Rinehart andWinston. All rights reser
Since the digit in the hundredths
place is less than 5, leave 4 as 4.
Thus, 18.42 rounded to the nearest tenth is 18.4.
c. Identify the digit in the units place. Look at the digit to its right.
This is the units place.
93.CD
Since the digit in the tenths
place is 5, replace 5 with 4.
Thus, 93.5 rounded to the nearest whole number is 94.
Round each decimal to the specified decimal place.
1. 123.451; nearest hundredth
2. 123.45; nearest tenth
3. 0.333; nearest tenth
4. 0.543; nearest hundredth
5. 19.95; nearest whole number
6. 8.09; nearest whole number
7. 3.141; nearest hundredth
8. 1.414; nearest tenth
9. 0.0045; nearest thousandth
11. 18.001; nearest whole number
Making Sense of Numbers
10. 0.056; nearest tenth
12. 3.89; nearest whole number
Unit 3 Decimals
85
CLASS
NAME
UNIT 3
DATE
Writing a Terminat: Decima
as a Fraction
OBJECTIVE: Writing a terminating decimal as a fraction or a mixed number
A terminating decimal is a decimal that has a finite number of nonzero
digits to the right of the decimal point. For example, 12.345 is a
terminating decimal. Terminating decimals can be written as fractions.
EXAMPLE 1
Write each decimal as a fraction in 1 west terms.
a. 0.7
b. 0.45
So°--tion
a. 0.7 =
7
b. 0.45 =
10
45
9
= 100 20
Divide numerator and
cleriorniriator by 5.
If a terminating decimal is greater than 1, then you can write the decimal
as a mixed number.
EXAMPLE 2
Write each decimal as a mixed number with the fraction part in
lowest terms.
a. 3.75
b. 7.125
ig ht 0 by Ho lt, Rinehart andWinston. All rights reserved.
Solution
a. 3.75 = 3
75
= 31
100
4
b. 7.125 = 7
125
= 71
1000
8
Divi enumerator and
denominator by 25.
Divide numerator and
denominator by 125.
Write each decimal as a fraction in lowest terms or as a mixed number
with the fraction part in lowest terms.
1. 0.1
2. 0.6
3. 0.90
4. 04
5. 0.04
6. 0.25
7. 0.33
8. 0.78
9. 0.002
10. 0.100
11. 0.125
12. 0.375
13. 1.5
14. 1.7
15. 10.4
16. 99 9
17. 13.65
18. 10.250
19. 11.01
20. 35.76
21. 1.007
22. 4.555
23. 8.750
24. 6.222
Making Sense of Numbers
Unit 3 Decimals
87
DATE
CLASS
NAME
Multipl g a Decimal by a Power of 10
OBJECTIVE:
Multiplying a decimal by a power of 10
A power of 10 is any product of 10 with itself a finite number of times.
Each of the products below is a power of 10.
10 - 10 = 102 (10 squared)
10 10 10 = 103 (10 cubed)
The exponent of 10 indicates the power of 10, or the number of times
10 is a factor in the product.
To multiply a decimal by a power of 10, move the decimal point to the
right as many places as indicated by the number of zeros or the exponent
in the power of 10.
Multi ly: a. 624345 X 100
b. 120.6 X 104
Solutio
a. Locate the decimal point.
624345
2 places right
So, 624.345 X 100 = 62,434.5.
Copyright ©by Holt, Rinehart and Winston. Al l rights reserved.
b. Locate the decimal point.
Add three zeros.
120.6000
4 places right
So, 120.6 X 104 = 1,206,000.
Multiply.
3. 88.55 X 102
1. 12.225 X 102
2. 100.75 X 102
4. 85.6 X 102
5.
7. 0.435 X 103
8. 0.84 X 103
9. 0.01 X 103
10. 0.03 X 103
11. 0.007 X 103
12. 0.005 X 103
13. 1.006 X 103
14. 1.001 X 103
15. 0.0001 X 103
6. 103.46 X 103
35.25 X 103
16. 12,338.4 X 101
17. 17,229.05 X 101
18. 88,888.25 X 102
19. 7500.08 X 103
Making Sense of Numbers
Unit 3 Decimals
101
NAME
CLASS
10
2
a
UNIT
DATE
Multiplying Decimals
OBJECTIVE: Finding the product of two decimals
Multiplying two decimals is similar to multiplying whole numbers. The
following examples will show you where to place the decimal point in
the product.
_miffisommito
EXAMPLE 1
r
Multiply: 6.33 X 7
Soiution
6.33
X 7
44.31
two decimal places
two decimal places
Thus, 6.33 X 7 = 44.31.
If both decimals have digits to the right of the decimal point, the product
will have as many decimal places as the sum of the numbers of places in
the given decimals.
EXAMPLE
2
Multiply: 4.25 X 3.6
Solution
two decimal places
one decimal place
three decimal places
Therefore, 4.25 X 3.6 = 15.300, or simply 15.3.
Multiply.
1. 12 X 8.5
2. 6.3 X 9
3. 12 X 3 6
4.125 X 4.8
5, 124X 3.1
6. 256 X 84
7. 1.5 X 2.5
8. 3.5 X 3.5
9. 4.4 X 3 2
10. 7.2 X 0.6
11. 0.3 X 11.6
12. 0.7 X 08
13. 17.2 X 3.65
14. 1.72 X 9.7
15. 8.68 X 1 7
16. 0.24 X 0.48
17. 0.65 X 0.65
18. 12.35 X 5.34
102
Unit 3 Decimals
Making Sense of Numbers
Copyright 0 by Holt, Rinehartand Winston. Allrightsreserved.
4.25
X3.6
255
1275
15.300
DATE
CLASS
NAME
Dividing Decimals
OBJECTIVE: Dividing a decimal by another decimal
To divide with decimals, transform the decimal division into a wholenumber division.
When dividing by a whole number, place the decimal point in the
quotient directly above the decimal point in the dividend.
When dividing by a decimal, move the decimal point in the divisor and
the dividend enough places to make the divisor a whole number. Then
divide as with a whole-number divisor.
Divide. a. 84.7 ± 7
Solution
12.1
a. 7)84.7
7
14
14
7
7
0
b. 2.3)11.96
o, 84.7 ± 7 = 12.1.
U,
-7-a
=
2,.
©
-
,
._
r_-
b. 11.96 ± 2.3
5.2
23)119.6
115
46
46
0
So, 11.96 ± 2.3 = 5.2.
Divide.
1. 42.5 ± 5
2. 72.18 ± 6
3. 213.3 ± 9
4. 530.4 ± 8
5. 1266.9 ± 3
6. 1863.5 ± 5
7. 85.2 ± 12
8.
55.5 ± 15
9. 223.2 ± 18
10. 124.8 ± 12
11. 235.3 ± 13
12. 355.3 ± 17
13. 2.55 ± 1.5
14. 32.66 ± 2.3
15. 33.92 ± 6 4
16. 35.88 ± 2.6
17. 91.98 ± 7.3
18. 129.05 ± 8 9
19. 121.33 ± 1.1
20. 204.96 ± 6.1
21. 509.74 ± 7 7
22. 240.45 ± 10.5
23. 452.6 ± 12.4
24. 1024.88 ± 18 4
Making Sense of Numbers
Unit 3 Decimals
111
NAME
CLASS
L
UNIT 4
DATE
Solving Proportions
OBJECTIVE: Solving a proportion for an unknown term
A proportion is an equality of two ratios. The four quantities in the
proportion are called terms. If the ratios are equal, then the proportion
is true.
4
2
Tell whether the proportion § -=- j. is true or false.
EXAMPLE 1
SoCution
4 2
Since 4 X 3 0 9 X 2, you may conclude that § 0
Therefore, the ratios are not equal. The proportion is false.
If a proportion involves an unknown, represented by a variable, you can
find the number that makes the proportion true. To solve a proportion,
find the cross products and set them equal to each other. Solve the
equation that results.
a c
If - - then ad = bc.
b=d'
!Wm. --011
I EXAMPLE 2
X
Solve - =
8
Solution
35
To make the proportion true, the cross products must be equal.
_x 35
8 40
40x = 8 X 35
Set cross products equal.
8 35
x
=7
Divide each side by 40.
40
Therefore, x = 7.
Tell whether the given proportion is true or false.
15 45
1. -6- =
178
13 25
2. 7 = —
14
15
=—
4
9
35
3. —
Solve each proportion.
Ai
x
30
5
Y
a
18
5° -. =
1_z
4
128
8
R 3
t
7
5
11. —
n = .§
Unit 4 Ratio, Proportion, and Percent
o 1
4
9
18
12. -i = —
m
Making Sense of Numbers
CLASS
NAME
UNIT 4
DATE
Solving Problems Involving Proportions
OBJECTIVE: Using proportions to solve real-world problems
When a constant rate is part of a real-world problem, you may be able to
use a proportion to find the unknown quantity.
If an inspector examines 20 light bulbs in 18 minutes, how many
light bulbs will the inspector examine in 72 minutes?
S'kiton
1. Write a proportion involving number of bulbs and time. Let x
represent the number of bulbs examined in 72 minutes.
number of bulbs
time
20 _ x
18 72
20 _ x
18 72
18x = 20 ° 72
Set cross products equal.
x -= 80
Divide each side 12y 15.
The inspector will examine 80 bulbs in 72 minutes.
2. Solve the proportion for x.
Solve each problem. Round answers as necessary.
1. If detergent costs $6.50 for 50 fluid ounces, what will be
the cost of 120 fluid ounces?
2. If a motorist drives 180 miles in 3.2 hours, how far will the
motorist drive in 4.5 hours?
3. If a student reads 18 pages of an assignment in 30 minutes,
how many pages will the student read in 48 minutes?
4. If 420 students enter a stadium in 25 minutes, how many
students will enter the stadium in 35 minutes?
5. How many students are in the reading club if the ratio of
boys to girls is 5 to 4 and there are 35 boys in the club?
6. If 3 CDs cost $39, how much will 7 CDs cost?
7. If a motorist drives 220 miles in 3.8 hours, how long
will it take the motorist to drive 550 miles?
8. How many sandwiches can be bought with $21 if three
sandwiches cost $9?
Making Sense of Numbers
Unit 4 Ratio, Proportion, and Percent
129
CLASS
NAME
DATE
WrriAg Percents as Fractions
UNIT 4
OBJECTIVE: Representing a percent as a fraction in lowest terms
You can write a percent less than 100% as a fraction in lowest terms.
Write each percent as a fracti n in lowest terms.
b. 0.5%
a. 42%
EXAMPLE 1
Solution
Write each percent as a fraction with denominator 100.
0.5
5
1
42
21
a. 42% ->
b. 0.5% -> 100 1000 200
100 50
You can represent a percent greater than 100% as a mixed number with
the fraction part in lowest terms.
MAMPLE
Write 125% as a mixed number with the fraction in lowest terms.
2
Solution
Copyright 0 by Holt, R inehart andWinston. All rights reserved
Write 125% as a fraction with denominator 100.
125 5 1
= 1125%
100 4 4
Write each percent as a fraction in lowest terms or as a mixed number
with the fraction in lowest terms.
1. 1%
2. 5%
3. 20%
4. 25%
5. 60%
6. 75%
7. 80%
8. 100%
10. 140%
11. 160%
12. 350%
13. 1000%
14. 101%
15. 110%
16. 105%
17. 0.6%
18. 1.5%
19. 130.4%
20. 112.5%
1
21, 121%
22.
3
23. 62- %
5
2
24. 49- %
5
1
25. 8-%
8
3
26. 25- %
8
1
27. 44- %
16
7
28. 50- %
8
1
29. 34%
2
30. 66- %
3
2
31. 14-%
7
1
32. 11- %
9
9. 150%
'
Making Sense of Numbers
1
37%
Unit 4 Ratio, Proportion, and Percent
133
NAME
CLASS
_
DATE
Writing Fractions as Percents
UNIT
OBJECTIVE: Writing a fraction as a percent
You can use equivalent fractions to write a given fraction as a percent.
EXAMPLE 1
Write each fraction or mixed number as a percent.
3
3
a.
b. 15
Solution
3 3 X 25
75
=
=
a° 4 4 X 25
00 75%
3 8 8 X 20_160
b. 1 = =
= 160%
5 5 5 X 20 100
Sometimes you need to use division to write a fraction as a percent.
EXAMPLE 2
Write each fraction as a percent.
5
a. g
b 1
3
Solution
5
a.
0.3
0.625
1
b. - ---> 3)1.00
3
-> 8)5.00
5
- = 0.625, or 62.5%
8
1
1
- = 0.3, or 33-%
3
3
7
1. id
3
2. L
10
17
25
6.
a 27
20
10.
5.
12.5
50
7
3° TO
7.
18.45
50
3
4. 25
8. 16.25
25
7
11. zi
12. 9
3
3
14. 14
4
15. 35
3
16. 420
18. 7
8
19. 3
16
20. 4
16
1
21. 38
7
22. 18
2
23. 13
5
24. 26
25.
7
26. 216
27. 2-
1
5
13. 2-
17.
5
12
134
16
32
25
Unit 4 Ratio, Proportion, and Percent
5
1
3
11
1
28. 106
Making Sense of Numbers
Copyright © by Holt, Rinehartand Wi nston. All rightsreserved.
Write each fraction or mixed number as a percent.
DATE
CLASS
NAME
1/Vr:ng Percents as Decimals
OBJECTIVE: Writing a percent as a decimal
Recall that when you divide a number by 100, you move the decimal
point two places to the left.
EXAMPLE 1
Write each ercent as a decimal.
b. 7.3%
c. 136.4%
a. 6%
Solution
b. 7.3% = 7.3 ± 100 = 0.073
a. 6% = 6 ± 100 = 0.06
c. 136.4% = 136.4 ± 100 =- 1.364
Sometimes you need to change a fraction to a decimal before writing the
given percent as a decimal.
r . EXAMPLE 2
Write each percent as a decimal. a. 47:%
1
b. 33-%
3
SokK:on
3
a. 47-% = 47.6% = 47.6 ± 100 = 0.476
•5
1
b. 33% = 33.3% = 0.333 = 0.3
-d
>
1
Recall -that = 0.5.
Write each percent as a decimal.
2
5
>
..
_.
-L.
E
1. 21%
2. 2.1%
3. 98.5%
4. 53.3%
5. 0.3%
6. 0.04%
7. 0.9%
8. 0.003%
9. 0.04%
10. 0.001%
11. 0.999%
12. 0.101%
13. 129%
14, 108%
15. 118.5%
16. 206.1%
1
17. -°/o
2
1
18. -%
4
19. 40%
20. 35%
1
21. 50-%
2
1
22, 1-%
4
3
23. 28-%
4
4
24. 34-%
5
5
25. 98-%
8
3
26. 5-%
8
1
27. 124-%
7
28. 200-%
12
2
29. 66-%
3
2
30. 5-%
3
1
31. 120-%
3
5
32. 130-%
6
Making Sense of Numbers
1
Unit 4 Ratio, Proportion, and Percent
135
DATE
CLASS
NAME
iiizing Equivalent Fractims,
Decimals, and Percents
UNIT 4
OBJECTIVE: Writing equivalent fractions, decimals, and percents
The table below shows equivalence of frequently used fractions,
decimals, and percents. Having worked with these, you should
be able to change from any form given to an equivalent one.
ts, Deci als, and Fractions
Equivalence of Commonly Used Perc
0.2 = 5
15% = 0.25 = 4
0.125 = 128
2% =
16-% = 0.16 = 3
6
2
40% = 0.4 = 5
1
50% = 0.5 = 2
3
1
= 0.375 = 378
2%
1
1
33-% = 0.3 = 3
3
3
60% = 0.6 = 5
3
75% = 0.75 = 4
5
1
62-2% = 0.625 = 8
6640
3 = 0.6 = 23
4
80% = 0.8 = 5
100% = 1.00 = 1
7
1
0.875 = 878
2% =
831% = 0.83 = 5
3
6
20% =
EXAMPLE
a. Write the equivalent decimal and fraction for 62 -1 °/0.
b. Write the equivalent percent and decimal for ;
Copyright ©by Holt, R inehart a ndWinston. All rights reserved.
Solution
a. From the table above, 6*/0 = 0.625 = ;.
1
7
% = 0.875.
b. From the table above, - = 872
8
Given each fraction, decimal, or percent, write the other two equivalent forms.
1,
2
5° 2
3
2. g
3.
1
4
3
6. 4-
5
7. -6"
2
8. 3
10. 0.125
11. 0.4
12. 0.375
13. 0.83
14. 0.6
15. 0.3
16. 0.16
1
17. 62-%
2
1
18. 33-%
3
1
19. 37-%
2
1
20. 83fo
1
21. 1622%
1
22. 1333%
1
23. 1371%
1
24. 1833%
9. 0.8
Making Sense of Numbers
Unit 4 Ratio, Proportion, and Percent
137
NAME
&9N IT 4
CLASS
DATE
Ca culatirg Ti7s and Total Cost
OBJECTIVE: Finding an amount to leave for a tip and the total cost of a meal
For service rendered, a customer may leave a tip when paying for a meal.
A rule of thumb is to leave a tip that is 15% of the cost of the meal when
service is done well.
EXAMPLE 1
Find the amount of the tip for a meal that costs $34.22. Assume that
the tip is 15% of the cost.
SolOon
Method 1: Calculate 15% of 34.22.
15% of 34.22 = 0.15 X 34.22 = 5.133
1
Method 2: Use — and 35 as estimates of 15% and 34.22.
7
1
1
— of 35 = — X 35 = 5
7
7
The value of the tip is $5.13, or about $5.
The total cost of a meal is the sum of the tip and the meal cost.
EXAMPLE 2
Find the total cost of the meal in Example 1.
Copyright © by Holt, Rinehart andWinston. Ad rights reserv
S lution
Method 1: Add $5.13 and $34.22.
5.13 + 34.22 = 39.35
Method 2: Add $5 and $35.00.
5 + 35 = 40
The total cost is $39.35, or about $40.00.
Assume the tip is 15%. Use 0.15 to find the actual amount of tip and total cost.
1
Then use — to estimate the tip and total cost.
7
1. $21.95
2. $98.75
3. $50.30
4. $110.46
5. $13.80
6. $235.68
7. 7.05
Making Sense of Numbers
Unit 4 Ratio, Proportion, and Percent
149
DATE
CLASS
NAME
411 Calcule a S
UNIT 4
Tax arid Total Cost
OBJECTIVE: Finding the amount of sales tax and total cost including the amount of tax
In many states, consumers pay a tax on certain purchases. The tax is a
fixed percent of the purchase price. In one state, the sales tax may be 5%
of the cost of an item.
r
EXAMPLE 1
If the sales tax is 5%, find the amount of tax on a table that costs
$495.50.
Solution
To find the amount of tax, calculate 5% of S495.50.
0.05 X 495.5 = 24.775
5% of S495.50
The amount of tax is $24.78.
The total cost of an item is the sum of the purchase price and the
amount of tax. There are two ways to find total cost.
EXAMPLE 2
Find the total cost of the table in Example 1.
Solution
Find the amount of tax and total cost.
1. sales tax 6%; purchase price: $102.45
2. sales tax 4%; purchase price: $329.90
3. sales tax 6.5%; purchase price: S39.95
4. sales tax 5%; purchase price: $1200.66
5. sales tax 6%; purchase price: $4356.99
6. sales tax 4%; purchase price: $5488.75
7. sales tax 5.5%; purchase price: $6885.44
150
Unit 4 Ratio, Proportion, and Percent
Making Sense of Numbers
Allrightsreserved.
Copyright © by Holt, Rinehartand Winston.
Method 1: To find the total cost, add the purchase price and the
amount of tax.
$495.50 + $24.78 = $520.28
Method 2: Multiply the cost of the table by 105%.
1.05 X 495.5 = 520.275
105% of $495.50
By either method, the total cost is $520.28.
CLASS
NAME
DATE
Solving 9iscount Problems
OBJECTIVE: Finding the amount of discount and reduced sale price
To encourage consumers to buy a product, sellers may offer a discount, a
reduction of the original price to a lower sale price.
A coat ordinarily sells for $238.45. If the price is reduced by 20%,
find the amount of the discount.
EXAMPLE 1
Solution
0.2 X 238.45 = 47.69
20% of 238.45
The amount of the discount is $47.69.
To find the new sale price after discount, apply either Method 1 or
Method 2 below.
Find the reduced sale price of the coat in Example 1.
EXAMPLE 2
Solution
Method 1: Subtract dollar amounts.
$238.45 - $47.69 = 190.76
Method 2: Calculate 80% of the original price.
0.8 X 238.45 =- 190.76
80% of 238.45
By either method, the reduced sale price is $190.76.
Use any method to find discount and reduced sale price.
0
1. 20%; $120
2. 25%; $250
3. 40%; $480
4. 50%; 12.50
5. 10%; $380.30
6. 10%; $18.42
7. 30%; $111.10
8. 50%; $1000.00
1
9. 3y/o; $330
Co
2
11. 16/o; $360
3
13. 14%; $420.70
15. 20.5%; 268.50
Making Sense of Numbers
10. 12 1%. $560
2 '
2
12. 66- %• $150
3 '
1
14. 83%.' $720
3
16. 18.5%; $337.80
Unit 4 Ratio, Proportion, and Percent
151
UNIT 4
DATE
CLASS
NAME
Solving IVhrk p Problems
OBJECTIVE: Finding the amount of markup and the new selling price
To pay expenses and make a profit, a seller will buy a product for one
price, mark the price up, and sell the product for a higher price.
EXAM LE 1
A store owner buys a product for $12.50 and marks the price up 60%.
Find the amount of markup.
Soluti n
3
0.6 X 12.5 = 7.5 or — X 12.5 ---- 7.5
5
By either method, the amount of markup is S7.50.
Calculate 60% of 12.50.
To find the selling price after markup, add the amount of markup to the
original price or multiply the original price by 100% plus the percent of
markup.
EXAMPLE 2
Find the final selling price of the product in Example 1.
Solution
Copyright ©by Holt, Rinehart an dWinston. Al l rights rese
Method 1: Add markup and original price.
S7.50 + S12.50 = $20.00
Method 2: Multiply original price by 160%.
160% of S12.50 = 1.6 X 12.5 = 20
By either method, the final selling price is S20.00.
Find the amount of markup and final selling price.
1. original price: 35.60; markup: 80%
2. original price: $64.20; markup: 100%
3. original price: 99.00; markup: 95%
4. original price: $591.22; markup: 84%
5. original price: 78.95; markup: 120%
6. original price: $33.10; markup: 150%
7. original price: $278.66; markup: 133-1%
Making Sense of Numbers
Unit 4 Ratio, Proportion, and Percent
153
DATE
CLASS
NAME
A
UNIT 5
Th ig and S iltracting With Integers
OBJECTI E. Simplifying an expression involving both addition and subtraction
of integers
To find the value of an expression involving both addition and
subtraction of integers, follow the order of operations.
Simplify —17 + 6 + (-7) + 13.
Solution
Method 1: Use the order of operations.
—17 + 6 + (-7) + 13 = —11 + (-7) + 13
= —18+13
Add: —17+ 6 = —11
Add: —11 + (-7) = —10
=-5
Method 2: Group —17 and —7. Group 6 and 13.
—17 + 6 + (-7) + 13 -= —17 + (-7) + 6 + 13
= —24 + 19
= —5
Remember to simplify any expressions within parentheses first.
EXAMPLE 2
Simplify —[12 + (-15)] — [7 — (12)].
Solution
7— 12 = — 5
— (-3)= 5
=8
L —5 + 6 — (-7)
2. 10 — 13 — [2 +(— 4)]
3. — [-3 +(-24) — 30]
4. —5 + 6 — (2 — 7)
5. —9 — (-9) — (-3 + 7)
6. 10 — (-10) — 18 + 1
7. —5 + 9 + 5 — 9
8. —(4 — 7) — (-2 + 3)
9. 7 + (-8) — (- 5 — 1)
10. 12 — [-2 — (-3)]
11. —[-7— (-7)]
12. 3 + (-11) + 11
13. 10— [2 + (-5)]
14. —[3 — (-5)] — (- 3)
170
Unit 5 Integers
Making Sense of Numbers
pu e Tieqeum I0HAq g lq OuAdoo
12 + (-15) = —5
. paniosaa spibu I IV
—[12 + (- 15)] — (7— 12) = —(-3) — ( 7— 12)
= — ( -3) — ( -5)
=3+5
NAME
CLASS
DATE
Mu tiplying Integers
UNIT 5
OBJECTIVE: Finding the product of two integers
When finding the product of two integers, there are three possibilities.
• The factors have like signs. The product will be positive.
o The factors have unlike signs. The product will be negative.
• The product of 0 and any integer is 0.
To multiply, find the product as if both factors were positive. Then decide
whether the product is positive, negative, or zero.
TEXAMPLE 1
Multiply: a. — 7 X 4
b.
( -7)( -9)
c. 0 X 24
Solution
a. 7 X 4 =- 28
b. 7 X 9 = 63
c. 0 X 24 = 0
Therefore, —7 X 4 = — 28.
Therefore, ( —7)( —9) = 63.
unlike signs
like signs
the product of zero and any integer is zero
You can multiply three or more integers using the rules above.
EXAMPLE 2
Multiply: 5( — 2) ( — 3)
Solution
Copyright © by Holt, Rinehart andWinston. All rights reserved.
5(-2)(-3) = (-10)(-3)
=30
5(-2) = —10
Multiply.
1. 7 X 8
2. 1 X 8
3. 11 X 0
4. 0 X (-20)
5. — 7 X ( -7)
6. —6 X (-12)
7. — 10 X 20
8. —6 X 13
9. 9 X (-9)
10. 2 X (-46)
11. (-11)2
12. ( -12)2
13. — 4 X 4
14. 4 X ( -4)
15. — ( -5)2
16. (-2) X 5 X
(-3)
17. (-4) X (-4) X (-5)
18. 6 X (-2) X (-3)
19. (-6) X 1 X (-7)
20. (-3) X ( -2)>< 11
21. (-3)2(-2)2
Making Sense of Numbers
Unit
5
Integers
171
8
th
Grade Answer Ke%
Compare your solutions to the answers as you work
through the packet to check your understanding.
MATHEMATICS
is not about
numbers, equations,
computations, or
alorithms:
it is about
UNDERSTANDING.
Akeiketm,Pt7humitsoil
CHAPTER 1 Order of Operations
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
9
116
4
410
72
9
165
2
35
18
129
44
24
160
53
51
107
28
16
17
1. 75
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
28
32 X 54
53 X 73
22 x 31 X 53
71 X 52 X 73
8
9
25
343
13
7
128
243
324
968
1800
3528
1440
2352
CHAPTER 4 Addition of Fractions and Mixed Numbers
1.
13
3
1
2. *,or 1-8
1
7
3. 3, or 1-g
4
4. 3
5.
12
1?
U. -3-55
7. Tg
4_
8. 15.
5
29
9. Tri, or
15
43 or 1F
3
10.
23
30
11. 29
12' 45
1
3
2
2, or 113. 11
31
14' -20' or 120
1
17
15.
25 or 2+2.
1
31
17' -30' or 130
16.
41
18. 84
9)
19i), or 1-1119. T
7
25, or lri
20. m
1. 136
13. 51
18
2.12k
14.7k
3
3. 74
5
4. 107
17
3_
5.
20
13
6. 430
81
7. 3-
15. 14-177216. 54103
1
17. 930
13
18. 10 -
3 88. 2 -17
1
9. 83
10. 64
1
21. 5-0
7
11. 45
14
7
15
12' 2-
20
19. 151
1
20. 161
22. 18 8
4
23. 165
1
24. 122
CHAPTER 5 Subtraction of Fractions and Mixed Numbers
CHAPTER 6 Multiplication of Fractions and Mixed Numbers
5.
4
6.
3
9. 5
2
10. 33
10
'it 33
21
12. 50
1
13. Ti
1
14. 1-42
15. 55
16. -§
7
'. -4-66
18.
9 45
1 . Tg
5
1
20. or 21
19
44
40
or 1E-
3. 10
1
5. -3-, or 33
15
1
6.
35
2
7. -3-, or 11-3
4.18
8. --7-, or 157
1. 8
2. 6
108
3
9-17. Estimates may vary. Accept any reasonable answer.
9. about 7
111 about 4
11. about 8
12 about 42
13. about 7
14. about 9
15. about 14
16. about 24
17. about 30
CHAPTER 8 Decimal Fundamentals
CHAPTER 7 Division of Fractions and Mixed Numbers
1. 123.45
2. 123.5
3. 0.3
4. 0.54
• 10
3
9
10
15. 10 25
2
5
16. 999
10
5. T
15- •
17.13 -1
1
6. 1
4
33
100
18. 1012 °
8. 39
50
1
9.
500
20. 3519
25
5. 20
6. 8
7. 3.14
8. 1.4
9. 0.005
10. 0.1
11. 18
12. 4
4.
10. 1
10
11. -813
12. 1.-3
CHAPTER 10 Multiplication of Decimals
1. 1222.5
2. 10,075
3. 8855
4. 8560
5. 35,250
6. 103,460
7. 435
8. 840
9. 10
10. 30
11. 7
12. 5
13. 1006
14. 1001
15. 0.1
16. 123,384
17. 172,290.5
18. 8,888,825
19. 7,500,080
1. 102
2. 56.7
3. 43.2
4. 600
5. 384.4
6. 2150.4
7. 3.75
8. 12.25
9. 14.08
10. 4.32
11. 3.48
12. 0.56
13. 62.78
14. 16.684
15. 14.756
16. 0.1152
17. 0.4225
18. 65.949
CHAPTER 11 Division of Decimals
11
1. 8.5
2. 12.03
3. 23.7
4. 66.3
5. 422.3
6. 372.7
7. 7.1
8. 3.7 •
9. 12.4
10. 10.4
11. 18.1
12. 20.9
13. 1.7
14. 14.2
15. 5.3
16. 13.8
17. 12.6
18. 14.5
19. 110.3
20. 33.6
7
10
14. 1-
21. 66.2
22. 22.9
23. 36.5
24. 55.7
4
1
19. 11100
21.1j
0700
111
4200
3
23. 84
111
24.
6500
22.
CHAPTER 12 Ratio and Proportion
1. $15.60
2. 253.125, or
1 miles
253a-
1. true
2. false
3. false
4. x = 15
5. y = 25
6. a = 54
7. z = 8. t=i-7,or6/
3. 28.8 pages
4. 588 students
5. 63 students
6. $91
7. 9.5 hours
8. 7 sandwiches
9. a = 52
• 5
1
10' c=2' or22
63
3
11 n = -or 12*
5'
5
12. m = 38
_ CHAPTER 13 Percent Fundamentals
12. 32
13. 10
1
14. 1j4.
1
3
5. 3
6. 3
4
7I. 3
8. 1
9. 11
2
10. 15
11.1k3
15. 11
io
1
16. 120
3
17. 500
3
18. 200
38
19. 1125
1
20. 18
1
21.
8
3
22. 8
313
500
247
24. 500
13
25. 160
203
26. 800
141
27.
320
407
28.
800
1
29. 3
2
30.
3
1
31.
7
1
32.
9
23.
1. 70%
2. 130%
3. 35%
4. 12%
5. 68%
6. 25%
7. 36.9%
8. 65%
9. 135%
10. 128%
11. 175%
12. 180%
13. 220%
14. 175%
15. 380%
16. 415%
2
17. 4130/0
18. 87-%
2
1
19' 331-%
4
3
20' 468-%
4
1
21. 312-%
2
1
22. 187-%
2
2
23. 166-%
3
1
24. 283-%
3
•
1
25. 131-%
4
3
26. 243-%
4
1
27' 233-%
3
2
28. 1016-%
3
CHAPTER 13 Percent Fund
1. 0.21
2. 0.021
3. 0.985
4. 0.533
5. 0.003
6. 0.0004
7. 0.009
8. 0.00003
9. 0.0004
10. 0.00001
11. 0.00999
12. 0.00101
13. 1.29
14. 1.08
15. 1.185
16. 2.061
17. 0.005
18. 0.0025
19. 0.00025
20. 0.006
21.
22.
23.
24.
25.
26.
27.
28.
29,
30.
31.
32.
entth
1. 0.4 and 40%
2. 0.375 and 37.5%
0.505
0.0125
0.2875
0.348
0.98625
0.05375
1.24125
2.005873
0.6
0.05-61.203
1.308-3-
3. 0.3 and 331%
3
4. 0.8 and 80%
5. 0.5 and 50°/o
6. 0.75 and 75%
7. 0.85 and 831%
3
8. 0.6 and 661231%
4
- and 80°/o
5
1
1
10. - and 12-°/o
8
2
2
11. - and 40%
5
3
1
12. - and 37-%
2
8
13. -5g and 83-k%
2
14. 3 and 66-3-%
1
1
15. - and 33-7,%
3
2
1
16. - and 16-°/o
3
6
5
17. - and 0.625
8
1
18. - and 0.3
3
3
19. - and 0.375
8
5
20. - and 0.85'
6
5
21. 1- and 1.625
8
1
. 17, and 1.5.
3
. 1- and 1.375
8
5
24. 1- and 1.85
6
CHAPTFR 15 Applications I Percent
1
-- $3 and $24
1. 15%: $3.29 and $25.24; 7'
1
' $14 and $112
2. 15%: $14.81 and $113'56'•-•
7
1
3. 15%: $7.54 and $57.85., 7. $7 and $57
1
4. 15%: $16.57 and $127.03,. 7. $16 and $128
1
-. $2 and $16
5. 15%: $2.07 and $15.87'- 7°
1
6. 15%: $35.35 and $271.03.' 7' $34 and $272
1
7. 15%; $1.06 and $8.11; .7: $1 and $8
1.
2.
3.
4.
5.
6.
7.
$6.15; $108.60
$13.20; $343.10
$2.60; $42.55
$60.03; $1260.69
$261.42; $4618.41
$219.55; $5708.30
$378.70; $7264.14
1. $24; $96
2. $62.50; $187.50
3. $192; $288
4. $6.25; $6.25
5. $38.03; $342.27
6. $1.84; $16.58
7. $33.33; $77.77
8. $500; $500
9. $110; $220
10. $70; $490
11. $60; $300
12. $100; $50
13. $61.42; $359.28
14. $600; $120
15. $55.04; $213.46
16. $62.49; $275.31
1.
2.
3.
4.
5.
6.
7.
$28.48; $64.08
$64.20;$128.40
$94.05; $193.05
$496.63; $1087.84
$94.74; $173.69
$49.65; $82.75
$371.55; $650.21
CHAPTER 18 Subtraction of Integers
1. 8
2. -1
3. 57
4. 6
5. -4
6. 3
7. 0
8. 2
9. 5
10. 11
11. 0
12. 3
13. 13
14. -5
CHAPTER 19 Multiplication of Integers
1. 56
2. 8
3.0
4. 0
5. 49
6. 72
7. -200
8. -78
9. -81
10. -92
11. 121
12. 144
13. -16
14. -16
15. -25
16. 30
17. -80
18.36
19. 42
20. 66
21. 36