Saxon 76 second Edition Solutions

150 Pages·1.031 MB·English

Answer Key for
Saxon 76
Second edition
isbn 0-939798-
74-3
**No problems have been double checked yet. If you find an error in my calcuations/inputs, please let me know and I will make the necessary
corrections. I will continue to work on double checking and update as neccesary.
Please also let me know if I have put an answer in the incorrect format (used decimal instead of a fraction, etc)
*** In the problem sets, there are some problems with an * before the number of the problem.
It appears that that problem is from the current lesson.
expanded form - 352 = 300+50+2 expanded notation - 352 = (3x100) + (5x10) + (2x1)
† see factor tree sheet/tab for factor tree starting lesson 64
I have tried to do this as more of a solutions manual rather than just an answer key.
However, if my work is confusing (or I forgot to put it in), you can use
https://www.cymath.com/
Enter any problem and it will not only give you the answer, it will also show you how to work the problem.
(Although I have noticed it doesn't seem to want to use the Cancel that is taught in lesson 69. It wants to use a/b * c/d = ac/bd.)
Saxon Math 76 2nd edition
# of # of
lesson Pr#a cinti ce ProSbeletm Eaxtr Description pg math equation learned/summary
1 4 25 Adding Whole Numbers, Adding Decimal Numbers and Money 1 addend + addend = sum
check subtraction by adding, result from subtracting is
2 4 25 Subtracting Whole Numbers, Subtracting Decimal Numbers and Money 2 called the difference
3 6 25 Multiplying Whole Numbers, Multiplying Decimal Numbers and Money 5 factor x factor = product
A 25 Set A
4 4 25 Dividing Whole Numbers and Money 7 A numer separated into a certain number of equal parts
B 25 Set B
5 8 25 Parentheses 9 ( ) - used to show which step to take first
6 6 25 Functional Parts 11 part of a hole
U.S. Customary system (inches, feet, yards...) & Metric
7 2 25 Linear Measure 14 system or SI (mm, cm, m, km)
8 5 25 Perimeter 16 distance around a shape, Add the length of all sides
<,>,= & addition sequence - 5,10,15,20 / multiplication
9 6 25 Comparing, Sequences, Odd-Even 18 sequence 5,10,20,40 & even - 0,2,4,6,8 / odd - 1,3,5,7,9
10 4 25 Reading Scales and Graphs 21 display of numbers with an indicator
Sum - add / differnce - subtract / product - multiply /
11 4 25 Operations of Arithmetic 24 quotient - divide
12 6 25 Place Value Through Billions 26 1,000,000,000
13 6 25 Reading and Writing Whole Numbers 28 commas help us read large numbers
C 25 Set C
14 4 25 The Number Line 31 negative numbers (-) -> positive numbers (+)
15 10 25 Negative Numbers 33 negative means below 0
CE1 10 Calculator Exercises 1
16 6 25 Rounding Whole Numbers and Estimating 36 another number close to the number
D 25 Set D
17 8 25 The Bar as a Divison Symbol 38 Dividend / Divisor = Quotient
Central number - Add all numbers then divide by the # of
18 12 25 Average 41 numbers
E 25 Set E
a whole number which divides another whole number
19 8 25 Factors 43 evenly
20 12 25 Greatest Common Factor (GCF) 46 greatest factor of a group of numbers
F 25 Set F
21 4 25 Naming Fractions 48 numerator / denominator
22 8 25 Fractional Part of a Group 50 equal parts of a whole
G 25 Set G
23 8 25 Adding and Subtracting Like Fractions 53 ?/# + or - /?/# where ? can be different, but # is the same
24 10 25 Fractions Equal to 1, Subtracting 55 2/2, 3/3, 4/4, 5/5....
25 10 25 Multiplying and Dividing Fractions 58 of means multiply
26 7 25 Reciprocals 60 4 is the same as 4/1, the reciprical of 4 is 1/4
27 8 25 Converting Improper Fractions to Whole Numbers or Mixed Numbers 62 improper - 9/5 , proper / mixed number - 1 4/5
28 10 25 Converting Mixed Numbers 65 mixed number 5 4/3 changes to 5 + 1 1/3 = 6 1/3
H 25 Set H
29 8 25 Reducing Equivalent Fractions 67 4/8 = 3/6 = 2/4 = 1/2
I 25 Set I
J 25 Set J
K 25 Set K
30 5 25 Least Common Multiple (LCM) 70 multiples of more than one number
L 25 Set L
31 4 25 Area 72 side1 x side2 = area
32 7 25 Decimal Place Value 75 .tenths, hundredths, thousandths
CE2 10 Calculator Exercises 2
33 12 25 Expanded Notation 77 (#x100)+(#x10)+(#x1)
M 25 Set M
34 12 25 Decimal Fractions 80 .1 = 1/10
CE3 10 Calculator Exercises 3
35 12 25 Reading and Writing Decimal Numbers 82 say the place value of the last digit
N 25 Set N
Saxon Math 76 2nd edition
# of # of
lesson Pr#a cinti ce ProSbeletm Eaxtr Description pg math equation learned/summary
36 0 25 Decimal Chart 85 Decimals Chart
37 10 26 Adding and Subtracting Decimal : "Line Up" 87 can not add unlike things
38 8 25 "Pin Decimal Point on Back of Whole Number" 89 4=4.0=4.00=4.000
O 25 Set O
Do Not line up decimals. Solve then count the total digits
39 8 25 Multiplying Decimal - "Multiply, Then Count" 91 to the right of the decimal point 0.25x0.7=0.175
40 9 25 "Fill Empty Places with Zeros" 94 0.5-0.32 = 0.50-0.32
P 25 Set P
41 8 25 The Name-Changer Machine 96 #/# x n/n (1/2 x 4/4 = 4/8)
42 6 25 Measuring to the Nearest 1/8 of an Inch 99 6/8 = 3/4
43 10 25 Subtracting Fractions with "Borrowing" 101 5 = 4 3/3
U 25 Set U
44 12 25 Dividing a Decimal Number by a Whole Number 103 divide by whole number - move decimal straight up
Q 25 Set Q
divide by decimal number - Over (divisor), over (dividend),
45 12 25 Dividing by a Decimal Number - Over, Over, Up 105 up (quotent)
R 25 Set R
46 9 25 Simplifying Decimal Numbers 108 003.00=3
CE4 10 Calculator Exercises 4
47 8 25 Equivalent Decimals 110 3 = 3.00 but 0.3<3.0
48 10 25 Comparing Decimal Fractions 112 0.2 ? .12 -> 0.20 > 0.12
49 6 25 Decimal Number Line (Tenths) 114 0.3=3/10
50 10 25 Rounding Decimal Numbers 116 0.1625 to the nearest cent is 0.16
S 25 Set S
"add zeros' (10x100=1000), ÷ means shift one place (3.75
51 10 25 Multiplying and Dividing by 10 or 100 118 ÷10=0.375)
T 25 Set T
CE5 12 Calculator Exercises 5 (Last one)
52 8 25 Forms of Money: Dollars, Cents 121 dime = 10/100
53 0 25 Fractions Chart 123 Fraction Chart
54 7 25 Common Denominators, Part 1 125 equal-size parts we have in total
55 5 25 Common Denominators, Part 2 128 1/2 + 1/3 -> 3/6 + 2/6
56 10 25 Adding and Subtracting Fractions - Three Steps 130 Shape (equivalent fraction), Operation (+,-,x,÷), Simplify
V 25 Set V
57 6 25 Comparing Fractions - Common Denominators 133 3/8 O 1/2 -> 3/8 O 4/8
58 10 25 Adding Mixed Numbers 135 2 1/2 + 1 1/6 = 2 3/6 + 1 1/6 = 3 4/6 = 3 2/3
59 9 25 Adding Three or More Fractions 138 find LCM of all three denominators
60 12 25 Subtracting Mixed Numbers with Borrowing 140 5 = 4 3/3
W 25 Set W
61 6 25 Prime Numbers 142 whole number with exactly two factors (1 and itself)
62 15 25 Writing Whole Numbers and Mixed Numbers as Improper Fractions 144 1 1/2 = 3/2
shapes with straight sides (triangle, quadrilateral,
63 3 25 Polygons 147 pentagon, hexagon, octagon...)
64 10 25 Composite Numbers and Prime Factorization 149 more than 2 factors 8=2*2*2
X 25 Set X
65 10 25 Multiplying Mixed Numbers 151 2 2/3 x 2 = 8/3 x 2/1
Y 25 Set Y
66 8 25 Using Letters to Represent Unknowns 154 23 + f = 41 -> 41-23 = f...18=f
67 10 25 Dividing Mixed Numbers 156 2 2/3 ÷ 1 1/2 = 8/3 ÷ 3/2 = 8/3 x 2/3
Z 25 Set Z
68 9 25 Lines 158 Line, Ray, Segment
69 8 25 Cancel 161 5/6 x 1/5 = 5/6 x 1/5 = 1/6 x 1/1
70 8 25 Multiplying Fractions - Three or More Factors 163 cancel then simplify
Y 25 Set Y
Z 25 Set Z
71 8 25 Decimal Part of a Whole, Part 1 166 0.3 = 3/10
AA 25 Set AA
Saxon Math 76 2nd edition
# of # of
lesson Pr#a cinti ce ProSbeletm Eaxtr Description pg math equation learned/summary
72 12 25 Writing Decimal Numbers as Fractions in Lowest Form 168 0.5 = 5/10 = 1/2
73 12 25 Writing Common Fractions as Decimals 170 1/2 = 0.5
BB 25 Set BB
74 6 25 Decimal Part of a Whole, Part 2 172 2/5 = 0.4
75 10 25 Comparing Fractions - Decimal Form 175 5/8 O 4/5 -> 0.625 O0.800
"3/5 of 20" means 20 ÷ into 5 equal parts and three
76 6 25 Fractions Part of a Number 177 counted
CC 24 Set CC
77 6 25 Decimal Part of a Number 180 0.8 of 60 means divided into 10 groups
78 6 25 Classifying Quadrilaterals 182 Classifying Quadrilaterals Chart
79 3 25 Area of a Parallelogram 184 base x height
80 8 25 Other Multiplication Forms 187 x = * = #(#)
81 4 25 Percent, Part 1 189 25% = 25/100
82 18 25 Percent, Part 2 191 25% = 25/100 = .25
DD 24 Set DD
83 8 25 Changing Percents to Fractions 194 8% = 8/100 = 2/25
84 10 25 Changing Percents to Decimals 196 Percent = "per hundred" so 25% = .25
EE 25 Set EE
85 10 25 Operations with Common Fractions and Decimals 198 0.5 + 1/4 = 0.5 + .25 = .75 OR 0.5 + 1/4 = 2/4 + 1/4 = 3/4
FF 25 Set FF
86 6 25 Finding Missing Factors 201 5n = 21 21÷5 n=4 1/5
87 3 25 Area of a Triangle 204 A=bh/2
88 8 25 Comparing Negative Numbers 206 -5 O -2
89 0 25 Naming Solids 209 Naming Solids Chart
face = flat surface, edge = two faces meet,
90 11 25 Faces, Edges, Vertices 212 vertex = point where edges come together
91 10 25 Exponents 214 2^3 = 2*2*2
92 12 25 Writing Mixed Numbers as Decimals 216 1 1/2 = 1.5
100% = 100/100, to change a number to a percent,
93 10 25 Writing Fractions as Percents, Part 1 219 multiply by 100%
94 12 25 Writing Fractions as Percents, Part 2 221 to change fraction to percents, multiply by 100% (100%/1)
GG 25 Set GG
95 15 25 Writing Decimals as Percents 224 to change any number to a percent, multiply by 100%
HH 25 Set HH
96 14 25 Writing Mixed Numbers as Percents 226 to change any number to a percent, multiply by 100%
97 3 25 Fraction-Decimal-Percent Equivalents 229 1/2 = 0.5 = 50%
II 25 Set II
98 4 25 Volume 232 volume = space it "takes up" X x Y x Z
99 0 25 Volume of a Rectangular Prism 235 area of layers x number of layers
radius = distance from center of circle, diameter =
100 4 25 Radius, Diameter, Circumference 238 distance across, circumference = distance around
101 0 25 Comparing Fractions - Cross Products 240 21/35 3/5 > 4 /7 20/35
102 6 25 Ratio 243 relationship girls/boys 4/6 = 2/3 = two girls/three boys
JJ 25 Set JJ
103 6 25 Proportions 246 3/5 = 6/?
KK 20 Set KK
104 2 25 Ratio Word Problems 249 Ratio 5/7 actual count 20/?
105 15 25 Measuring to One Sixteenth of an Inch 252 16 equal parts
106 3 25 Perimeter and Area of Complex Shapes 254 find p & a of smaller parts
107 0 25 Acute Angles, Right Angles, Obtuse Angles, Straight Angles 257 Acute <, Right L, Obtuce \_, Straight ___
108 4 25 "Similar" 260 the same shape BUT not necessarily the same size
109 0 25 "Congruent" 263 the same shape AND equal in size
110 6 25 Classifying Triangles 266 Triangles Chart
LL 25 Set LL
111 9 25 Writing Division Answers 269 3 r3 = 3 3/4 = 3.75
MM 25 Set MM
112 8 25 Finding a Given Percent of a Number 271 What is _% of __?, What is #/# of __?, What is 0.__ of __?
Saxon Math 76 2nd edition
# of # of
lesson Pr#a cinti ce ProSbeletm Eaxtr Description pg math equation learned/summary
NN 25 Set NN
113 6 25 Expanded Notation Using Exponents 275 (5*10^3)+(2*10^2)
OO 25 Set OO
114 15 25 Multiplying by Powers of Ten 278 6.2*10^2 = 620
115 10 25 Writing Rates as Ratios 281 __ mph = __m/1hr
116 6 25 Unit Cancelling 284 __ mph / 1 hr x 2 hr / 1
117 3 25 Rounding Numbers - A Three-Step Method 287 Mark (876,285), Zero (870,000), round (880,00
__ is what fraction of __?, __ is what decimal of __?,
118 10 25 What Percent? 291 __ is what percent of __?
PP 25 Set PP
circumference / diameter - number of diameters in the
119 1 25 Circle Measure - Circumference (Project) 293 circumference
120 6 25 Pi (π) 296 circumference of circle = π times diameter Pi (π)=3.14....
121 6 25 Adding Integers 299 "Sign Wars"
QQ 25 Set QQ
122 8 25 Finding the Whole When a Fraction is Known 302 20 is 1/5 of what?
SS 25 Set SS
√1=1 √4=2 √9=3 √16=4 √25=5 √36=6 √49=7 √64=8
123 7 25 Square Root of Perfect Squares 305 √81=9 √100=10
124 6 25 Writing Units with Exponents 308 ft x ft = ft ^2 , in x in = sq in
125 5 25 Evaluating Expressions 311 A=1/2 b h when b is # and h is #
126 7 25 Opposites and Subtracting Integers 313 3 is opposite of -3
RR 25 Set RR
127 10 25 Finding the Whole When a Decimal Part Is Known 316 Six is .3 of what number?
SS 25 Set SS
use known √ to figure out which 2 the given number is
128 12 25 Estimating Square Roots 319 between
TT 25 Set TT
129 6 25 Unit Conversion 322 multiply by a fraction equal to 1
130 8 25 Circle Measure - Area 325 π r^2
UU 25 Set UU
131 5 25 Probability 327 Favorable / Possible
132 5 25 Geometric Formulas 330 Perimeter & Area of Shapes Chart
133 7 25 Finding the Whole When a Percent Is Known 333 Thirty percent of what number is 120?
V V 25 Set V V
134 18 25 Multiplying and Dividing Signed Numbers 335 (+) *or÷ (+) = (+) & (-) *or÷ (-) = (+) |&| (+) *or÷ (-) = (-)
WW 25 Set WW
135 6 25 Divisibility 338 Tests for Divisibility Chart
136 3 25 Surface Area of a Prism 341 area1+area2+area3+area4+area5+area6
137 4 25 Sum of the Angles of a Triangle 344 180-(angle 1+ angle 2)
138 20 25 Roman Numerals 347 M=1000, D=500, C=100, L=50, X=10, V=5 I=1
XX 25 Set XX
139 10 25 Angle Measure - Using a Protractor 350 Protractor
YY 25 Set YY
140 6 25 Rectangular Coordinates 352 x-axis and y-axis
ZZ 25 Set ZZ
1054 Total practice
3501 Total problem set
1420 Total Extra (Supplemental & Calculator Exercises 1-5)
4555 Total practice and problem set
5975 Total all
1 Adding Whole Numbers,
Adding Decimal Numbers and Money
Practice Problem set
A. 5458 1 65
B. 56 2 235
C. 26.73 3 3044
D. 5.89 4 483
5 6.37
6 2.55
7 160
8 887
9 1054
10 4615
11 412
12 4841
13 3860
14 2941
15 201
16 4.39
17 25.60
18 1.50
19 1.08
20 13.03
21 6.25
22 6.25
23 7
24 77
25 16
% through book
0.71
2 Subtracting Whole Numbers,
Subtracting Decimal Numbers and Money
Practice Problem set
A. 5206 1 83
B. 1815 2 18
C. 4.65 3 33
D. 137 4 964
5 2218
6 3.75
7 22.50
8 12.75
9 226
10 2708
11 2643
12 717
13 278
14 36
15 2813
16 31005
17 2838
18 0.09
19 3.68
20 76.67
21 6.25
22 5.07
23 9
24 47
25 375
% through book
1.43
3 Multiplying Whole Numbers,
Multiplying Decimal Numbers and Money
Practice Problem set
A. 740 1 300
B. 851 2 37
C. 2944 3 13
D. 20440 4 2325
E. 15059 5 94.20
F. 8 6 39
7 3312
8 32560
9 392
10 51800
11 10000
12 18090
13 60
14 9106
15 3634
16 974
17 282
18 5.44
19 14.62
20 4.04
21 8.10
22 2.70
23 36
24 744
25 6.85
% through book
2.14
4 Dividing Whole Numbers and Money
Practice Problem set
A. 2014 1 4
60
B. 16 r 8 2 25
16 8
C. 1.68 3 20
D. 2.13 4 21
5 124
6 31.50
7 206
8 720
9 14 r2
14 2
10 222 r2
222 2
11 23
12 15
13 29 r4
29 4
14 17302
15 963
16 694
17 4920
18 2252
19 6000
20 28800
21 1.60
22 2.65
23 33.75
24 6.84
25 3.57
% through book
2.86
5 Parentheses
Practice Problem set
A. 9 1 $3.15
16- 7 5- 1.85
B. 17 2 102
13 +4
C. 8 3 85
24÷ 3
D. 2 4 104
4 ÷2 12+60+32
E. 19 5 367
8+ 11
F. 19 6 47
14 +5
G. 63 7 17
9x 7 5+ 12
H. 31 8 32
27 +4 8 x4
9 475
800- 325
10 150
600÷ 4
11 225
350 -125
12 6
30 ÷5
13 3
144÷ 48
14 108
18 x6
15 3.15
5- 1.85
16 2180
17 3.12
18 41 r16
41 16
19 24192
20 187220
21 21
22 5.30
23 6.25
24 376
25 6
% through book
3.57