Download 7th Grade Math Packet

Name
7th Grade Summer Math Packet
For Students who will be enrolled in Mrs. Kohrman's
7th Grade Math Class in the 2015/2016 school year.
AN.M.Y.Or
DATE
CLASS
NAME
1-1
The Order of the Four Basic Operations
UNIT I-
OBJECTIVE: Finding the value of an expression that involves whole number addition,
subtraction, multiplication, or division
41\
co
The four basic operations of mathematics are addition, subtraction,
multiplication, and division. Finding the value of some expressions
involves two or more of these operations. The order in which you
perform the operations is very important.
4;(4
)?e.
,3\
The Order of the Four Basic Operations
First multiply and divide in order from left to right.
Then add and subtract in order from left to right.
Find the value of each expression. a. 16 + 8 X 5
EXAMPLE
b. 24 — 6 ± 2 + 1
II Solution
Copyright ® by Holt. Rinehart and Winston. All rights reserved.
a. 16 + 8 X 5
16 + 40
56
First multiply.
Then add.
b. 24— 6 + 2 + 1
24 — 3 + 1
21 + 1
22
First divide.
Then subtract.
Then add.
Find the value of each expression.
1. 20 — 9 + 7
2. 16 + 30 —22
3. 25 —6 + 14— 4
4. 15 + 5 — 14 + 6
5. 18 + 3 X 2
6. 15 X 10 + 5
7. 12 X 6 + 3 X 4
8. 16 + 8 X 4 + 2
9. 27 — 12 + 3
10. 14 + 9 X 2
11. 48 + 6 — 2 X 2
12. 9 X 8 — 6 + 3
13. 21 + 12 + 3 + 1
14. 32 — 2 X 4 + 12
15. 36 — 16 + 4 X 4
16. 40 + 2 X 4 — 2
17. 72 + 3 + 6 X 3 — 2
18. 4 X 10 + 5 — 1 + 3
Making Sense of Numbers
Unit 1 Order of Operations and Number Theory
1
DATE
CLASS
NAME
UNIT_
P1reLJ es aud the 0:aler of Orations
1
JECTIVE: 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.
EXAM LE 1
Find the value of (9 + 3) X (17 — 8).
Solution
(9 + 3) X (17 — 8)
12 X 9
108
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 X 15.
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
H. 27 + (3 + 14) X 6
12. 60 — (4 X 8) + 2
13. 6(33 — 29)
14. (41 + 39)2
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
Unit 1 Order of Operations and Number Theory
Rinehartand Winston. All rightsreserved.
Copyright © by Holt,
1. 54 + (2 + 4)
2)
Making Sense of Numbers
NAME
CLASS
DATE
Us! ig Formulas
UNIT I
OBJECTIVE: Finding an unknown quantity by applying a formula
A formula is a mathematical sentence that describes how two or more
quantities are related. If you know the value of all quantities except one,
you can use the formula to find the unknown quantity. The following are
some basic formulas from geometry.
Some Basic Geometric Formulas
Rectangle with length .e and width w
perimeter: P = 2x,e+ 2 X w
area: A = _e X w
Square with one side of length s
perimeter: P = 4 X s
Cube with one edge of length e
surface area: S ---- 6 X e2
EXAMPLE
area: A = s2
./e
volume: V =- e3
The length of a rectangle is 19 and its width is 13. Find the
perimeter of this rectangle.
SoiLllon
Write the rectrigle perimeter formula.
P = 2 X 19 + 2 X 13
+ 26
Replace with 19. Replace w with 13.
Multiply first.
64
Then add,
P=
P=
38
Copyright© by Holt, Rinehartand Winston. Allrightsreserved.
P=2X _e +2X w
Find each quantity using one of the formulas given above.
1, the area of a rectangle with length 39 and width 9
2. the perimeter of a square with one side of length 58
3. the perimeter of a rectangle with length 12 and width 7
4. the perimeter of a rectangle with length 38 and width 23
5. the area of a square with one side of length 16
6. the surface area of a cube with one edge of length 12
7. the volume of a cube with one edge of length 10
8. the volume of a cube with one edge of length 21
6
Unit 1 Order of Operations and Number Theory
Making Sense of Numbers
NAME
DATE
CLASS
ivalent Fractions: Higher Terms
UNIT 2
OBJECTIVE: Writing an equivalent fraction with a greater denominator by drawing a
model or by multiplying
Fractions that represent the same amount are called equivalent
fractions. If a fraction is renamed with a denominator that is greater
than the given denominator, it is written in higher terms.
Rewrite the statement at right. Replace ? with
the number that makes the fractions equivalent.
Solution
Method 1
Draw a model
2
of two thirds.
3
Split each third
8
into four parts
12
to make twelfths.
2
Using either method, you can write — =
3 12
2_?
3 12
Method 2
Multiply both the
numerator and
denominator by 4.
2 2X4 8
3 3 X 4 12
Method 2 above uses the following rule for equivalent fractions.
Equivalent Fractions: Higher Terms
number.
Rewrite each statement. Replace ? with the number that makes the fractions
equivalent.
?
1
1. — =
4 12
2.
1_?
5 10
3.
3
?
4 16
5.
7_?
312
9
?
6. 3 =
7
_ ?
7 14
8.
9
?
8 56
11.
13 _ ?
9 —54
6
?
13. — =
7 91
14.
11 _ ?
8
96
22
3
Unit 2 Fractions
2 ?
3 6
Making Sense of Numbers
Copyright0 by Holt, Rinehartand Wi nston. All rightsreserved.
To write a given fraction as an equivalent fraction in higher terms,
multiply both the numerator and denominator by the same nonzero
DATE
CLASS
NAME
3-7
UNIT 2
Equivalent Fractions: Lower Terms
OBJECTIVE: Writing an equivalent fraction with a lesser denominator by drawing a
model or by dividing
Fractions that represent the same amount are called equivalent
fractions. If a fraction is renamed with a denominator that is less than
the given denominator, it is written in lower terms.
Rewrite the statement at right. Replace ? with
the number that makes the fractions equivalent.
6_?
-3
Solution
Method 1
Draw a model
6
of six-tenths.
10
Redraw each
3
two-tenths
5
as one-fifth.
3
Using either method, you can write = 10 5'
Method 2
Divide both the
numerator and
denominator by 2.
6_6÷2 _3
10 - 10 ± 2 - 5
Method 2 above uses the following rule for equivalent fractions.
Copyright © by Holt, R inehart andWinston. All rights reserved.
Equivalent Fractions: Lower Terms
To write a given fraction as an equivalent fraction in lower terms,
divide both the numerator and denominator by,the same nonzero
number.
Rewrite each statement. Replace ? with the number that makes the fractions
equivalent.
1•
6
8
_
?
2.
4
?
4
4. 1-0- = 3
36
10.
20
5.
?
=
54 ?
=
364
36 ?
13. 7-4g = -4
Making Sense of Numbers
4
12
_
?
3
?
=4
81_?
8.
11. 32 =
3
?
1l0 ?
14. -3-5- _
9
?
3*12 = 4
6.
30 ?
T
=
16 _ ?
9.
12.
24
?
= 5-
175
15'
?
=
Unit 2 Fractions
23
NAME
DATE
CLASS
3-8
UNIT 2
Lowest Terms of a Fraction
OBJECTIVE: Writing a fraction in lowest terms
A fraction is in lowest terms if its numerator and denominator have no
common factor other than 1.
Write —in lowest terms.
Solution
Method 1
Divide both the numerator and denominator by common factors
until their greatest common factor (GCF) is 1.
54 54 ÷ 2 — 27
> 27 — 27 + 3 — 9
Method 2
Divide both the numerator and denominator by their GCF.
The GCF of 48 and 54 ie 6.
You can also use prime factors to write a fraction in lowest terms.
EXAMPLE 2
• 96 ,
Write — in lowest terms.
84
Solution
96
25 X 31
84 — 22 x 3ix 71
><><2X2X20 8
——
V/X IX 7
7
Write each fraction in lowest terms.
4
1. -a
9
2. 13
.
15
5. rid
35
6. -;(7)
7.
36
9. T3.
42
10.18
68
13. il
17.
24
189
126
Unit 2
Fractions
6
48
4.
4
28
12
18
18
8. ...
•45
4D
14
11. T2-
18
12. n
14.
65
78
15.
34
51
95
16. T8-
18.
132
198
19.
273
195
20.
171
513
Making Sense of Numbers
Copyright © by Holt, Rinehartand Winston. AUrightsreserved.
Write the prime factorization of the numerator and the denominator.
Divide by all common prime factors.
DATE
CLASS
NAME
• 4-2 Adding Fractions: Like Denominators
UNIT 2
OBJECTIVE: Finding sums of two or more fractions with like denominators
To add fractions that have like denominators, you can use the
following method.
Adding Fractions with Like Denominators
1. Add the numerators.
2. Write the sum from Step 1 over the like denominator.
3. If necessary, rewrite the result from Step 2 in lowest terms.
EXAMPLE 1
5 1
b. +
5 1
Write each sum in lowest terms. a. +
Solution
5
1
5+1
-77 -
- 76
5
1
b. 12+ 12 =
5+1_6
1
E 2
Sometimes a sum of fractions is a whole number or a mixed number.
2 7
Write each sum in lowest terms. a. -§ + 4
7 3
b. +
Solution
Copyright 0by Holt. Rinehart andWinston. All rights reserved.
2
7
2+7_
2
9—9
11
7
3
7+3
10
8 =
b -8 + 8-
=5= 1 14
Write each sum in lowest terms.
2
1. 3 +
32
3
1
4. m + 10
7
7
4
7
7
2
1
10. a +
13. -§- +
1
4 +
5. 15
8
15
2
15
13
1
11
1
3. a +
7
9.
+ 5
14.
13
5
5
+
5
11
12. 12 + 12
11. 1-2- + 7
1 2-
4
13
8
73 + 71 + 75
9
5
10
11
5
17
•
7
1
17. §. + § +
4
Making Sense of Numbers
Unit 2 Fractions
33
NAME
DATE
CLASS
rs
Ad, ling Fractions: Unlike D (11,,L
UNIT 2
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.
k 3 5
3 1
Write each sum in lowest terms. a° 8
u° 4
2
S lution
a. The LCM of 8 and 2 is 8. So the least common denominator is 8.
1
First
Then add.
rewrite 2.
3 1 3 4 3+4 7
1 1 X4 4
+ = +
8
8
2 2X48
8 2 8 8
b. The LCM of 4 and 6 is 12. So the least common denominator is 12.
3
5
Then add.
First rewrite - and 4 6
3 5
9
10 9 + 10 19
3 3X3
9
+ =
+
=
12
12
4 6 12 12
4 4 X 3 12
5
6
5X2
6X2
7
= 1—
12
10
12
Write each sum in lowest terms.
4
R
7
1
1
1
1
17
3
1
6 8
11.
3 1 7
13. g + 4 + -8-
5
11
12. m
1 + RI
5
7
+
ii 273
1 3 3
14. - + - + 5 5 4
5
2
7
16. - + — + 3 12 6
1 1
1
18. - + - + —
6 4 14
8
3
5
20. - + — + —
9 1 5 10
34
Unit 2 Fractions
Making Sense of Numbers
rightsreserved.
Copyright CD by Holt, Rineha rtand Winston. All
1
8
1. -3- + 3--
DATE
CLASS
NAME
4-4
Adding Mixed Numbers: Like Denominators
UNIT 2
OBJECTIVE: Finding sums of mixed numbers with like denominators
To add mixed numbers that have like denominators, you can use the
following method.
Adding Mixed Numbers with Like Denominators
1. Add the fractions.
2. Add the whole numbers.
3. If necessary, rename the whole number in the sum.
4. If necessary, rewrite the sum in lowest terms.
Write each sum in lowest terms.
8
6
5
1
7
b. 27 + 1
c. 3-4 +
a. 4-i-5 + 2I0--
EXAMPLE
01. Solution
1
a. 4T6
7
Copyright 0by Holt, Rinehart andW inston. All rights reserv
8
6-17
1)
b.
6
27
+1
6
3-
c.
32
9
8
+ 2-
13
Rename
the whole
number.
4
4
Write each sum in lowest terms.
3
1
1. 93 + 63
2
2
2. 7- + 19
9
5
1
3. 2- + 38
8
1
1
4. 46
6 + 5-
3
5. 1-m- + 5
3
6. 8 + 48
5 1
7. 37 + 7
7
1
8. 1-2- + 5E
13
7
2 ) + To10. 4 7
8
1
11. 59 + 79
4
7
13. 19
9 + 5-
11
8
14. 2 3 + 4
3
1
3
2
12. 13 + 6.
1
3
1
16. 78 + 18 + 98
5
5
15. 9- + 86
6
4
1
4
17. 39 + 109 + 29
6
2
4
18. 8- + 3- + 37
7
7
7
1
7
19. 19 + 39 + 69
Making Sense of Numbers
Unit 2 Fractions
35
NAME
DATE
CLASS
A 'ding Met!
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.
7
-1
1
7
b. 4- + 3 6
+ 3Write each sum in lowest terms. a. 810
8
5
SCutiou
b. The LCM of 8 and 6 is 24.
a. The LCM of 5 and 10 is 10.
So the least common
So the least common
denominator is 24.
denominator is 10.
7
21
1
2
488 i-o424
8
5
1
4
7
7
+ 3 10
+3—
+ 3- -4 +3
10
6
9
1110
25
1
1
7=
7
+
1=
824
24
24
Write each sum in lowest terms.
1
3
2. 9- + 32
8
1
5
+ 23. 53
12
3
1
4. 8- + 214
2
3
1
+ 25. 14
10
1
4
6. 36 + 115
1
7
7. 2- + 84
17
". 18 ' 1 9
1
5
9. 7- + 2
6
Q 11
7
2
10. E +5- 13. 4
-8 + 19
6
7
5
16. 3- + 18
10
1
6
+11. 32
7
2
4
12. 3 + 13
4
7
1h
14. § + 6 T
3
5
15. 5- + 86
4
19
1
— + 4 12
17. 4 20
11
11
18. 7-17
5 + 212
1
1
1
19. 1- + 6- + 84
4
8
2
1
2
20. 2- + 4- + 93
6
3
4
2
1
+21. 1- + 35
2
5
7
3
1
22. 94 + 68 + 24
7
1
3
23. 4- + 2- + 95
10
2
3
5
11
24. 8- + - + 24
6
12
36
Unit 2
Fractions
Making Sense of Numbers
Copyright © by Holt, Rinehartand Winston . All righ
2
1
1. 63 + 76
1
DATE
CLASS
NAME
5-2
UNIT 2
Subtracting Fractions: Like Denominators
OBJECTIVE: Finding differences of two fractions with like denominators
To subtract fractions that have like denominators, you can use a method
similar to that for adding fractions with like denominators.
Subtracting Fractions with Like Denominators
1.Subtract the numerators.
2. Write the difference from Step 1 over the like denominator.
3. If necessary, rewrite the result from Step 2 in lowest terms.
EXAMPLE 1
EXAMPLE 2
2
8
Write each difference in lowest terms.11a —
11
Solution
9
2_8—2_6
8
b
*
isT)
M=
a'
— — 11
Find the difference 1 —
30
b. — T-
15
5
4
Copyright 0by Holt. Rinehart andWinston. All rights reserved
Solution
15-2 . 13
2 15 2
15.
1 — ID = 15 51 . 15 Th5Rewrite 1 as
Write each difference in lowest terms.
5
1
11 1
4
12
2. --i — i.- .
3 1
3' i — i
5 173
18 — M
8 5
9 9
7 1
8 — -i
11
5
11. 1 — TA
13
12. 1 — To-
5 1
•
1
10. 1 — yo-
Find the value of each expression by using the order of operations.
8
15. 9
18. 1 — (1 —
Making Sense of Numbers
Unit 2 Fractions
41
NAME
DATE
CLASS
53
Subtracting Fractions: Unlike
Denominators
UNIT 2
OBJECTIVE: Finding differences of two fractions with unlike denominators
To subtract fractions that have unlike denominators, you must first write
equivalent fractions that have a common denominator. Then subtract
using the method for like denominators.
5
3
b. — 1—4
23 2
30 5
Write each difference in lowest terms.
Solution
a. The LCM of 30 and 5 is 30.
So the least common denominator is 30.
2
First rewrite-6.
2
5
2X6
5X6
Then subtract.
12
30
23
30
23
30
2
5
12
30
23 — 12
30
9
42
35 — 9
42
11
30
b. The LCM of 6 and 14 is 42.
So the least common denominator is 42.
3
14
35
42
26
42
_13
21
Write each difference in lowest terms.
5
1•8
• 11 2
— 12 3
1
2
a 31 3
— 36 4
7
1
1
1
4
6. — §
1
1
O 4
6
10
'" 5
7
9
1
10.14 —
12. To —
Find the value of each expression by using the order of operations.
11 (7 1\
\ 8 2/
16.
42
1
8
/17 2\ _ 1
18 3/ 6
Unit 2 Fractions
11
/1 —1)
15. — — — —
12
3 6
18.
/9 _ 1\ _ 1
00 2/ 3
Making Sense of Numbers
Aq 1q6uAdoo
5
6
IAA p ue
5 5 X 7 35
6 6 X 7 42
9
3
3X3
14 14 X 3 42
Then subtract.
amuse.' sppp IIV
5
3
First rewrite — arid —
14:
DATE
CLASS
NAME
5-4
UNIT 2
Subtracting Mixed Numbers
Without Renaming
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.
3. Subtract the whole numbers.
4. If necessary, rewrite the difference in lowest terms.
Copyright 0by Holt. Rinehart and Winston. A ll rights reserved.
EXAMPLE
7
1
— 3Write each difference hi lowest terms. a. 58
8
Solution
3
7
b. 51- —>
a. 58
1
1
— 1— 33
8
6
3 Rewrite the
= 2 .71
difference in
3
1
b. 53
4 — 19
5E
4
Write equivalent
mixed numbers
with common
denominators.
5
lowest terms.
Write each difference in lowest terms.
11
4
1. 6-it — 513
7
2
2. 129 —4
3. 7.2ii — 3u
6 1
4. 97 — 7
7
5. 5- — 2
8
1
6. 142 — 10
1
4
7. 85 — 85
14
7
8. 1.17 — 1
1
9
9. 6 —
10 — 310
8 2
10. 15-§ — 4§
5 3
11. 1 -8- —
11 1
12. 18E — E
7
2
13. 57) — 33
7
2
— 214.113
12
1
1
15. 5- — 16
18
19 3
16. 7yo — 64
13 2
17. 10-rg —
1 1
18. 93 — E
Making Sense of Numbers
Unit 2 Fractions
43
NAME
CLASS
DATE
Multiplying Two Fractions
'II, 33 3 7 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.
EXAMPLE
Write each product in lowest terms. a.
4
b
. 11
3
5
c. §
Soluton
a.
1 5 1X5
5
4 6 4 X 6 24
1X3
1l 1 _-11
ight 0 by Holt, Rinehart and Winston. All rights reserved.
5 X 2 10
3 X 7 21
Divide each 4 by 4.
Divide 6 at 9
Write each product in lowest terms.
1.
1
X
1
2
4 2
4. ,7
1
7. g
5. §
3
4
8. —.
1
1
4
11. 1/
2 3
13. -;-, X
9 8
5
14. i-g
4
16. 25
36 5
17.
4 21
i5 32
27 20
19. 77.
52, 21
20.
7:
Making Sense of Numbers
8
—
2
25
16
Unit 2 Fractions
53
NAME
UNIT
DATE
CLASS
Multiplying With Mixed Numbers
2
OBJECTIVE: Finding products that involve mixed numbers
To multiply with mixed numbers, use the following method.
Multiplying With Mixed Numbers
1. Write each mixed number and whole number as a fraction.
2. Multiply the fractions.
3. If necessary, rewrite the result from Step 2 in lowest terms.
Write each product in lowest terms. a.
Sohitiorii
1 1 1 33
a. X4 = 7.J
8
l
1
1
1
b. 3- X 52
3
1
1
b. 3- X 5 3
2
1
X 48
7
—
2
16
11
X 8
1 X 11
1X8
_ 11 _ 13
8
8
3
1
4. X 3i
2
1
7. - X 4-
3
2
8. 2-
3
9. 12 X 23
4
1
11. 14 X 24
12. 2- X 16
5
6
3
4
2
1
15. 1- X 23
4
1
3
14. 1- X 2-
1 6 1
16. 3- X — X 92 7
3
17. 4- X
2
1
18. 7- X 8 X 22
5
7
3
19. 1- X 3- X 6
9
4
56
Unit 2 Fractions
4 1
5
—
Making Sense of Numbers
CopyrightCD by Holt, Rinehartand Wi nston . Allri ghtsreserved .
Write each product in lowest terms.
CLASS
NAME
DATE
7-2 Reciprocals
UNIT 2
OBJECTIVE: Finding the reciprocal of a given number
Two numbers whose product is 1 are called reciprocals of each other.
The following are some examples of reciprocals.
1 2
3x7
7
3 =1 8x
17.7 =1
1
5X3=1
Every number except zero has exactly one reciprocal. Zero has no
reciprocal. To find the reciprocal of a number, write it in fraction form
and interchange the numerator and denominator.
rniErATINIm
Write the reciprocal of each number. a.
10 Solution
2
11
a. 11
2
The reciprocal
211
of ITs in
T.
Copyright © by Holt, Rinehart andW inston. AD rights reserved.
•
0
b. 8 =
IX
2
c. 3i
The reciprocal
.1
.1
of 8 is 8'
b. 8
c. 3
2
=VX1*7
The reciprocal
. 5
of 33 is .
Write the reciprocal of each number as a whole number or as a fraction in lowest
terms. If there is no reciprocal, write none.
5
1. -§
14
2. i
1
1
5.
6.200
1
10. 3.-1
9. 1-.1-
3.12
4. 50
7.0
8.1
5
11. 46
11
12. 8E
Tell whether the numbers in each pair are reciprocals of each other. Write Yes or No.
1
13. 16, -1E6-
14.
1 10
16. 1 ,
10
.
6 7
15.
14
4' 5
18. 0, 1
'T
Fill in each blank with the number that makes the statement true.
1
19. 7 X 17 =
T.
1
20. i X
22.
x8
3= 1
25.
2
X 7=1
3
Making Sense of Numbers
=1
3
7
23. 5X -=
7 38
26. 1 X
=1
21. 23 X
=1
3 X
24. -0
=1
27. 13 X
Unit 2 Fractions
67
NAME
DATE
CLASS
Divid. ig With Fractions
UNIT
OBJECTIVE: Finding quotients involving fractions
2 62
6
In the division — ± — — is the dividend — is the divisor, and the result of
3 7' 3
'7
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
Write the quotient -3- ± ,7
6 in lowest terms.
Solution
1
7_ ZX71X77
6
3X
3X39
2.6
3*7
When a division involves a whole number, write the whole number as a
fraction with denominator 1.
n
EXAMPLE 2
1
Write each quotient in lowest terms. a. 3 ± 3
Solution
1. 3
1.
y=
8 6 8
b. 6 ± — = ± — =
9
9 1_
1
A
1
1X1
1
9 _ 3 X 9 _ 27
1 X 4 4
63
4
Write each quotient in lowest terms.
1.
68
2.3
7 5
3.2
2. —5
2.2
9•3
6.
Unit 2 Fractions
2.2
3.
4
±
2
1 1
7. 5 . 3
24
10. — ±
25 5
4 . 8
11. § 15
14. - 1 . - 6
3
15. — ± 2
5
2 .
18. -0- 4
19. 6 ± —
2
4.
2.4
8. 1.1
-,- -7-
1
Making Sense of Numbers
Copyright © by Holt, Rinehartand Winston. All ri
a.
CLASS
NAME
$
UNir 3
DATE
Riu 'TA lecim s
OBJECTIVE: Rounding decimals
When you round a decimal, you replace the given decimal with a
number that terminates at the specified decimal place.
ounal 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.
Since the digit in the thousandths
place is more than 5, replace S with 7.
Thus, 24.567 rounded to the nearest hundredth is 24.57.
24.56©-0
b. Identify the digit in the tenths place. Look at the digit to its right.
This is the tenths place.
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.
Copyright ©by Ho lt, Rinehart an d Winston. All rights reserv
18.4©
c. Identify the digit in the units place. Look at the digit to its right.
This is the units place.
Since the digit in the tenths
place is 5, replace 5 with 4.
Thus, 93.5 rounded to the nearest whole number is 94.
93.0 1
Round each decimal to the specified decimal place.
L 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
DATE
CLASS
NAME
DecimE s
UNIT 3
OBJECTIVE: Adding decimals
You add decimals by using what you know about decimals together with
what you know about adding whole numbers.
Recall that all whole numbers are decimals with an invisible
decimal point.
23 = 23.0
Recall that you can place O's at the far right of a decimal and get an
equivalent decimal.
15.7 = 15.700
15.7 = 15.70
.60321669111•1
Adding Decimals
1. Arrange the decimals so that decimal points align. Add zeros as
needed to make equivalent decimals Then place the decimal point
in the sum.
2. Add as with whole numbers.
Add: 23 + 15.75 + 14.6
Solution
2. Add as with whole numbers.
1. Arrange the decimals.
23. 00
Acid two zeros.
15. 75
+ 14. 60
1213
Add one zero.
Place the decimal
point the sum.
.
00
15. 75
+ 14. 60
53. 35
Therefore, 23 + 15.75 + 14.6 = 53.35.
Add.
1. 11.4 + 20.3
2. 7.5 + 8.5
3. 21.6 + 21 8
4. 11 + 54.8
5. 19.5 + 24.84
6. 9.3 + 12.78
7. 42 + 34.95 + 18.5
8. 18.1 + 13.2 + 19.65
9. 13.4 + 28 + 19.5
10. 94.95 + 89.9 + 17.49
11. 7.8 + 17 + 11.98 + 27.79
12. 28.19 + 12 + 45.15 + 17.40
13. 10 + 18 + 37.3 + 43.1
14. 100.45 + 32 + 18.9 + 18 3
Making Sense of Numbers
Unit 3 Decimals
91
NAME
CLASS
9 5
DATE
S uL racting Decim s
UNIT 3
OBJECTIVE: Finding the difference when one decimal is subtracted from another
You subtract one decimal from another by using what you know about
decimals together with what you know about subtracting whole numbers.
Subtracting Decimals
1. Arrange the decimals so that decimal points align. Then place the
decimal point in the difference. Add zeros as needed to make
equivalent decimals.
2. Subtract as with whole numbers.
EXAMPLE 1
• ..
Subtract: 10 - 4.04
Solution
Subtract as with whole numbers.
Align decimal points.
10. 00 Acid -two zeros.
10. 00
- 4. 04
- 4. 04
Place the decimal
5. 96
point in the difference.
Copyright © by Holt, Rinehart andWinston. All rights reserved.
Therefore, 10 - 4.04 = 5.96.
EXAMPLE 2
Subtract: 98.24 - 74.39
Solution
Align decimal points.
Subtract as with whole numbers.
9 8. 2 4
98. 24
- 74. 39
-74.39
Place the decimal
2 3. 8 5
point in the difference.
Therefore, 98.24 - 74.39 = 23.85.
Subtract.
1. 12 - 8.7
2. 20 - 19.9
3. 100 - 99.95
4. 18 - 0.1
5. 14.22 - 12.66
6. 8.38 - 43
7. 18.1 - 16.41
8. 13.88 - 12.5
9. 10.89 - 9.89
10. 11.3 - 11.28
11. 96.3 - 96.03
Making Sense of Numbers
12. 16.7 - 126
Unit 3 Decimals
95
CLASS
NAME
9
UNIT $
DATE
Adding and Subtracting with Decimals
OBJECTIVE: Finding the value of an expression involving both addition and
subtraction of decimals
To find the value of an expression involving both addition and
subtraction, follow the order of operations.
EXAMPLE 1
Evaluate 43.24 + 18.11 - 50.89.
Solution
43.24 + 18.11 - 50.89 = 61.35 - 50.89
= 10.46
Thus, 43.24 + 18.11 -50.89 = 10.46.
EXAMPLE 2
Add 43.24 arid 13.11.
Subtract 50.59 from 01.35.
Evaluate 132.5 - (45.98 + 23.76).
Solution
132.5 - (45.98 + 23.76) = 132.5 - 69.74
= 62.76
Thus, 132.5 - (45.98 + 23.76) = 62.76.
Add 45.95 and 23,70.
Subtract 09.74 from 132.5.
Copyright 0by Holt, Rinehart andW inston. Al l rights reserved.
Evaluate each expression.
1. 16.2 + 18.1 - 7.1
2. 100 - (33.22 + 55.1)
3. 13.2 - (0.5 + 9.4)
4. 1200 - (1000 + 45.8)
5. 18.45 - 10.88 + 18
6. 127.41 - 100 + 17.99
7. 1.45 - 1.08 - 0.18
8. 0.45 - 0.11 - 0.18
9. 70.16 - (60.5 - 50.9)
10. 112 - (80.1 - 79.3)
11. 92.17 + 19 - (41.4 + 30.3)
12. 10 + 50.56 - (49 - 30.7)
13. 130 - 89 - (57.3 - 56)
14. 88.1 - 78.22 - (0.7 - 0.6)
15. 38.2 - (18.1 + 17.3 - 3.3)
16. 57.1 - (19.1 - 12.4 + 3.6)
17. $22.40 + $18.44 + $400.98 - ($15.00 + $25.88 + 22.05 + $55.69)
18. $34.66 + $19.03 + $510.89 - ($25.00 + $34.77 + 52.06 + $51.22)
Making Sense of Numbers
Unit 3 Decimals
99
NAME
CLASS
DATE
Multiplying Decimals
UNIT 3
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.
Multiply: 6.33 X 7
EXAMPLE 1
Soluti n
6.33
7
44.31
two decimal places
X
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.
FINIMIN-MILLMO
I 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.
L 12 X 8.5
2. 6.3 X 9
3. 12 X 3 6
4. 125 X 4.8
5. 124 X 3.1
6. 256 X 8 4
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 © by Holt, Rinehartand Winston. Allrightsreserved.
4.25
X 3.6
255
1275
15.300
DATE
CLASS
NAME
V
dung 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
b. 11.96 ± 2.3
Solution
12.1
a. 7)84.7
7
14
14
7
7
5.2
b. 2.3)11.96 --> 23)119.6
115
46
46
0
Copyright ©by Ho lt, Rinehart andWinston. Al l rights reserved.
So, 84.7 ± 7 = 12.1.
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
Grade Answer Key
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.
yt)A4,m
pa A,“)otohi
142)\-\t-el-vay,
CHAPTER 1 Order of Operations
1. 18
2. 24
3. 29
4. 12
5. 12
6. 30
7. 96
8. 4
9. 23
10. 32
11. 4
12. 70
13. 26
14. 36
15. 20
16. 78
17. 40
18. 10
1. 351
2. 232
3. 38
4. 122
5. 256
6. 864
7. 1000
8. 9261
1. 9
2. 116
3. 4
4. 410
5. 72
6. 9
7. 165
8. 2
9. 35
10. 18
11. 129
12. 44
13. 24
14. 160
15. 53
16. 51
17. 107
18. 28
19. 16
20. 17
CHAPTER 3 Fraction Fundamentals
2. 31.
12
= To
2 4
=
3 12
A
Ft. -4 =
13
7 _ 28
5' 3 -12
9 18
6. .3 =
10
6
3
7' 7 = 14
& 65=20
24
20
- 35
9 _ 63
10.
- 56
13 _ 78
11.
•
54
15 _ 120
12.
▪ - •48
6 = 78
13.
7 91
11 _ 132
14.
8 -•96
17 _85
15. Ti - 60
6
=
4
1
-=
12
9 3
3'12 = i
4 2
4. .17 =
20_S
164
15
6. 30 _
84
36_6
9'
54 6
=
36
32 16
11.
= -171
u.
24 8
yo60
36 3
13. Ti =i
12.
14.
15'
U.
81_9
71.3
6
51 - 6
110
10
=T
175 _ 7
-36-
CHAPTER 4 Addition of Fractions and Mixed Numbers
9
2. 11
11. 1
3
3. -4
5. 34
4
12. , or 11
3
3
8
13. 9
2
9
14. 7, or 17
2
U. 3
15. 2
2
4. 3
7. 11
2
9.
2
1
-24
IT o r 2 7
1
4
17. 3, or 13
8. 1
5
16.
2
3, or 13
18.
11
23
11 . T)
3.
29
12. 45
3
1
13. 1, or 11-
13
15
9
1
2. -, or 113-
or
10.
3
1.
5
or tg
-67-, or 1,1g
4
5
5. 7
12
12
6. -.
31
, 11
14. y, or iyo.)
17
1
15.
5
7. i -9-
17.
4
8. 1-5-
41
18. N
5
9. 29
Ti, or ,IN
19.
119, or 1T-9-0
7._ 1
4_, or _14
1
20.
h5, or 1-i
j
4.
25
1
16. ri, or 2E
.
31
,1
t-j, or I-55
11. 13
2. 4
3
3. 54
1
4. 93
12. 8
13. 7
2
5
4. 107
17
5. 35.
13
6. 430
4
14. 7T3
2
15. 18-5
5
16. 173
7. 31
8
17. 16
8. 53
18. 157
5
9. 10
19. 113
7
10. 5
7
12. 215
13' 5-118
2
14. 745
7
15. 1412
13
16' 540
17.
' 30
18. 1018.
2103
5
19. 158
1
20. 162
7
21. 510
7
22. 188
4
23. 165
1
2
24. 12-
CHAPTER 5 Subtraction of Fractions and Mixed Numbers
19
10. 1
-6
13
10. -4-i
'
2
4.
5.
3.
12. To-
4.
1.
3
14. 2
1
15. 3
5
5. .1-47
6. T8-
14.
16. 0
• 1
17.
3
18. To
7. 13
• 1
& 24
5
7
1
6. 3
7. 3
U. 7
31
11. 12:
1.1
20
4
7
5' 3-8
1
6. 4-i
9. 35-
1
18. 9-4
1
3
15. -4
1
16. -§
2
17. 3
1& 15
CHAPTER 6 Multiplication of Fractions and Mixed Numbers
21
1. -43
5
2. -6-
12. 35
1
24
6
3.
55
8
4.
21
13.
2.
5.
6.
7.
a.
9.
10.
11.
1
1
2
15. 5
5
16. 9
7
17. 70
6
18. 33
9 45
1 . 3;
5
1
20. 1., or 21
40
19
21. IT, or 1H
136
6
29
12
12.
107
13. yes
2.
3.
3
14
1
12
1
50
9
21.
22.
49
1
49
1
15
3
14. T5, or
15. 7
1,
- or 3i
16. 28
MO
17. 3-, or 335
8. .2
18. 144
9. 28
19. 40
1
.1 10
5
21
27
23. 1
3. 2
4. 1
15. no
19
1
24. T, or 65
3
25. B-
1
5. 3
6. 200
16. yes
26. 1
6. 3
7. none
17. no
27. 13
1
'7. 3
4.
5.
8. 1
7
9.
15
10. 46
14. yes
18. no
19. 1
20. 4
1
7. 3
10. 48
2..
1
13. -i, or 83
CHAPTER 7 Division of Fractions and Mixed Numbers
11.
1
12. -T, or 455
3. -89-, or 1-g1
21
1
4. iTy or 2Tr)
5. -34-, or , 1
8
2
6. 5, or 25
14. yi
9
3
8
1
9
1
16
3
To
2
35
10
33
63
11. T, or 3172-
11
or 27176
3
7
3
8. 7
4, or 1-4
5
1
9. -,or22
2
6
1
10. 3, or 1-5-
12.
6
15
T, or 1-87
13.
8
14. 1
36
15. 3
17,1
16. 5
49
17.
12
1
18.
18
19. 12
32
2
20.
or 10'
CHAPTER 8 Decimal Fundamentals
1. 123.45
2. 123.5
3. 0.3
4. 0.54
5. 20
6. 8
7. 3.14
8. 1.4
9. 0.005
10. 0.1
11. 18
12. 4
CHAPTER 9 Addition and Subtraction of Decimals
1. 31.7
2. 16
3. 43.4
4. 65.8
5. 44.34
6. 22.08
7. 95.45
8. 50.95
9. 60.9
10. 202.34
11. 64.57
12. 102.74
13. 108.4
14. 169.65
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
3.3
0.1
0.05
17.9
1.56
4.08
1.69
1.38
1
0.02
0.27
4.1
9-9
1. 27.2
2. 11.68
3. 3.3
4. 154.2
5. 25.57
6. 45.4
7. 0.19
8. 0.16
9. 60.56
10. 111.2
11. 39.47
12. 42.26
13. 39.7
14. 9.78
15. 6.1
16. 46.8
17. $323.20
18. $401.53_
CHAPTER 10 Multiplication of Decimals
•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
11-2
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
8.5
12.03
23.7
66.3
422.3
372.7
7.1
3.7 •
12.4
10.4
18.1
20.9
1.7
14.2
5.3
13.8
12.6
14.5
110.3
33.6
21.
22.
23.
24.
66.2
22.9
36.5
55.7