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Mathematics
5
Book 2
Authors:
Cindi Mitchell & Lori Fowler
Editor:
Alan Christopherson
Graphic Design:
Chris Burkholder
Mark Aguilar
Brian Ring
JoAnn Cumming
Keith Piccolo
Marybeth Graville
Annette Walker
Lisa Kelly
Alpha Omega Publications, Inc.
Rock Rapids, IA
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All rights reserved. No part of this publication may be reproduced, stored in an electronic
retrieval system, or transmitted, in any form or by any means, electronic, mechanical,
photocopying, recording, or otherwise, without the prior written permission of the publisher.
Brief quotations may be used in literary review.
Printed in the United States of America
ISBN 978-1-58095-998-8
© MCMXCVIIII Alpha Omega Publications, Inc.
Horizons Mathematics 5, Student Workbook 2
804 N. 2nd Ave. E., Rock Rapids, IA 51246-1759
© MCMXCVIII by Alpha Omega Publications, Inc.® All rights reserved.
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Lesson 101
Addition of Unlike Fractions
1
Katherine and George hiked !4 of a mile to the creek and another
campsite. How far did they hike in all?
1
!
3
of a mile to the
Since we want to find the total amount hiked, we add.
STEP 1
STEP 2
Look at the
denominators.
STEP 3
Find the least common
denominator.
The denominators Multiples of 4: 4, 8, 12
are NOT the same. Multiples of 3: 3, 6, 9, 12
Write equivalent
fractions with the
same denominator.
1
!
4
1
!
3
+
Katherine and George hiked
1
!
4
=
3
!
12
1
!
3
=
4
!
12
3
!
12
+
4
!
12
7
!
12
of a mile.
+
1
!
2
=
+
=
+
=
1 !
1
!
3 + 6 =
1
2
!
!
10 + 5 =
1
3 !
!
4 + 8 =
Label and find the sum.
_________________
→
34 + 2 =
21 + 45 =
15 + 9 =
4 + 24 =
→
© MCMXCVIII Alpha Omega Publications, Inc.
1
!
4
Add the fractions.
Write the sum. Rename in lowest terms, if possible.
1
2
7
!
12
STEP 4
_________________
Horizons Math 5, Student Workbook 2 65
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3
Draw the lines of symmetry on each shape.
4
Find the perimeter, area, and volume of this shape.
5 cm
5 cm
15 cm
Perimeter of front panel = ______________
______________
Volume of entire box =
______________
Color the products to the following problems.
x
75
80
x
54
40
210
x 50
x
47
30
x
2,100
5,800
6,000
4,510
8,120
1,300
2,160
6,370
6,000
11,000
2,000
4,010
10,500
1,210
3,350
10,000
3,700
1,410
5,600
42,000
66 Horizons Math 5, Student Workbook 2
91
70
200
x 30
© MCMXCVIII Alpha Omega Publications, Inc.
5
Area of front panel =
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Order each row from largest to smallest.
6,489
6,491
6,487
6,495
435,900
436,900
456,900
436,090
Answer using these diagrams.
Which lines are parallel (||)?
a
•M
•N
•P
Name two pairs of perpendicular lines (#).
•O
Name the point where line c and line a
intersect.
© MCMXCVIII Alpha Omega Publications, Inc.
b
Name the point where line d and line b
intersect.
c
d
Name a line segment which is contained
in line d.
Horizons Math 5, Student Workbook 2 67
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Lesson 102
Subtraction of Unlike Fractions
1
2
Lori had !3 yards of material. She used !2 yard to make a pair of shorts for her son.
How much material did she have left over?
Since you are looking for the left over amount or difference, you subtract.
STEP 1
Look at the
denominators.
STEP 2
Find the least common
denominator.
STEP 3
STEP 4
Write equivalent Subtract the fractions.
fractions with the
same denominator.
The denominators Multiples of 3: 3, 6, 12
are NOT the same. Multiples of 2: 2, 4, 6
2
!
3
2
!
3
1
!
2
There will be
1
1
!
6
=
4
!
6
4
!
6
3
!
6
–
3
!
6
1
!
6
of a yard left.
Find the difference. Reduce the answer to lowest terms.
1
!
2
1
!
5
2
Find the sum.
+
1
!
5
1
!
10
68 Horizons Math 5, Student Workbook 2
–
3
!
8
1
!
4
+
7
!
8
2
!
16
–
2
!
3
1
!
6
+
3
!
4
2
!
8
–
1
!
3
1
!
9
+
1
!
6
3
!
8
© MCMXCVIII Alpha Omega Publications, Inc.
–
1
!
2
=
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Find the least common denominator for each set of fractions. Find the answers
in the puzzle below and color them brown.
1
!
2
2
!
5
2
!
3
5
!
10
4
!
10
1
!
5
1
!
20
2
!
6
5
!
6
7
!
8
1
!
12
1
!
5
3
!
8
© MCMXCVIII Alpha Omega Publications, Inc.
5
!
12
4
Match.
____________ Ray
____________ Right angle
•
B
A
____________ Acute angle
____________ Obtuse angle
C
D
Horizons Math 5, Student Workbook 2 69
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Find the product.
45
x 12
32
x 11
98
x 50
6
61
x 45
45
x 26
Estimate. Answer the questions.
Round to the nearest 10.
15
– 10
89
– 25
171
– 43
The number 171 is called the:
a. minuend
b. difference
c. subtrahend
Round to the nearest 100.
255
– 109
356
– 233
1,487
– 891
a. minuend
b. difference
c. subtrahend
Round to the nearest 1,000.
1,546
– 1,009
–
12,870
5,870
4,603
– 2,119
The answer to the subtraction problem is the:
a. minuend
70 Horizons Math 5, Student Workbook 2
b. difference
c. subtrahend
© MCMXCVIII Alpha Omega Publications, Inc.
The number 891 is called the:
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Lesson 103
Addition of Mixed Numbers
1
1
Mrs. Smith had 4 !2 apple pies and 3 !2 pecan pies left when her restaurant closed
on Monday night. How many total pies were left over?
+
4
1
!
2
3
1
!
2
Step 1: Begin with the fractional part of the problem. Add the
fractions following the steps you have already learned.
1
!
2
3
1
!
2
→
→
+
4
2
!
2
= 1 whole
© MCMXCVIII Alpha Omega Publications, Inc.
Step 2: Add the whole numbers together. Rename (reduce) the
answer to lowest terms, if needed.
→ !1
4 2
→ 1
+
3
!
2
7
2
!
2
= 7 + 1 = 8 whole pies
Mrs. Smith will have 8 pies left over for Tuesday.
Look at this problem:
2
+
3
!
4
4
6
3
!
4
Notice that there is not a fraction with the second addend of
the problem. What do you do? Simply follow the steps given
above.
Step 1: Start with the fractional part of the problem. Since
there is not a fraction with the second addend, you
are adding
3
3
3
! + 0. ! + 0 = ! .
4
4
4
Step 2: Add the whole numbers.
Horizons Math 5, Student Workbook 2 71
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Find the sum. Reduce the answer to lowest terms.
+
2
1
3!
10
2
2!
10
4
7!
6
+
4
21 !
6
1
+ 1!
6
3
+
1
6!
6
2
8!
6
Fill in the missing numbers and solve.
+
N
3 !
!
8 = 8
N
1 !
!
4 = 8
7
7
!
!
10 = 10
1 !
N
!
=
5
N
–
1
N
!=!
12
N
9
3
!
+ !
=
4
N
–
12
3 !
!
=
5
N
1
N
!=!
4
N
Name each triangle by using the indicated letters. Label each one scalene,
equilateral or isosceles. Calculate the measurement of the missing angle. (The
sum of all the angles is 180°.)
N
B
I
3
40°
20°
J
A
60°
60°
C
M 70°
4
O
Find the difference.
–
12
4
45
– 20
–
20
9
21
– 10
72 Horizons Math 5, Student Workbook 2
–
100
50
66
– 33
75
– 25
52
– 32
30
– 30
–
89
9
© MCMXCVIII Alpha Omega Publications, Inc.
27°
H
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Solve the problems and find the path through the maze.
848
x 120
600
x 390
273
x 115
928
x 245
603
x 339
109
x 169
721
x 451
271
x 605
564
x 502
START
→
243,001
234,000
31,395
79,564
189,781
98,653
546,849
32,551
227,360
283,128
229,452
661,239
213,551
894,255
45,281
213,447
204,417
18,421
12,879
97,245
78,521
31,894
21,580
325,171
54,212
31,110
110,877
45,612
213,450
163,955
→
101,760
354,894
101,894
34,562
564,897
78,409
6
778
© MCMXCVIII Alpha Omega Publications, Inc.
END
Round to the nearest 10.
12,894
212
Round to the nearest 100.
31,894
1,284
569
Round to the nearest 1,000.
781,258
451,894
14,523
Horizons Math 5, Student Workbook 2 73
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Lesson 104
Addition and Subtraction of Mixed Numbers
1
1
!
Kathryn ran 5 !
2 miles on Saturday and only 1 6 miles on Sunday. How much further
did she run on Saturday than Sunday?
Step 1: Begin with the fractional part of the problem. Subtract or add the
fractions following the steps you have learned when adding or
subtracting fractions with unlike denominators.
STEP 1
STEP 2
STEP 3
STEP 4
Look at the
Add or subtract the
Find the least common Write equivalent
denominators denominator
fractions with the
fraction (rename to
same denominator lowest terms if needed)
–
5
1
!
2
=5
3
!
6
1
1
!
6
=1
1
!
6
2
!
6
=
1
!
3
Step 2: Subtract the whole numbers. Rename (reduce) the answer to
proper lowest terms, if needed.
–
1
2
!
3
1
!
2
=5
3
!
6
1
1
!
6
=1
1
!
6
4
2
!
6
=4
1
!
3
© MCMXCVIII Alpha Omega Publications, Inc.
Kathryn ran 4
5
miles farther on Saturday than Sunday.
Find the sum or difference.
13 !3
2
45 !2
1
18 !5
1
– 14 !5
1
+ 24 !8
+ 2!
12
74 Horizons Math 5, Student Workbook 2
2
20
4
!
8
7!
12
3
– 20 !
16
6
5!
10
3
+ 2 !4
1
– 2!
20
9
3
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3
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13
© MCMXCVIII Alpha Omega Publications, Inc.
1!
15
2
1
!
15
3
!
15
0
!
15
7
!
15
1
!
15
2!
15
1
6
!
15
8
!
15
9
!
15
3
!
15
3!
15
1
Two of the problems below are incorrect. Circle them and answer them correctly.
3
3 !
!
=
8
8
4
1
!=!
2
8
7
!
8
7
7
!
!
=
10
10
1
1
!
– !
=
5
10
8
= !
10
+
2
1 !
!
=
6
6
2
2
!=!
3
6
4
!
6
–
2
1 !
!
=
4
8
2
2
!=!
8
8
0
Estimate by rounding 3-digit numbers to the nearest 10 and 4-digit numbers to
the nearest 100.
1,256
x 106
5
Page 75
Which rows total to 3 !
15 ? Color them red.
+
4
3:48 PM
845
x 276
653
x 452
3,209
x 1,504
178
x 144
Solve.
1
1
!
Alex poured 3 !
4 gallons of water into a fish tank. He added another 1 2
gallons and the tank was full. How much water did the tank hold?
Horizons Math 5, Student Workbook 2 75
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Draw a bar graph to show the following information.
Profits from weekly school store sales.
Monday—$45.00 Tuesday—$25.00
Wednesday—$29.00 Thursday—$35.00 Friday—$38.00
Label the following quadrilaterals.
Word Bank
trapezoid
rectangle
parallelogram
rhombus
square
76 Horizons Math 5, Student Workbook 2
© MCMXCVIII Alpha Omega Publications, Inc.
7
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Lesson 105
Improper Fractions to Mixed Numbers
When adding mixed numbers, we sometimes get an improper fraction. An
improper fraction is a fraction where the numerator (top number) is larger than the
denominator (bottom number). Look at the diagram below.
3
1!
2 pizzas is:
One whole pizza and
1
!
2
of another 3 pizzas.
1
!
2
1
!
2
1 whole
1+
3
1!
2
1
!
2
a mixed number
1 whole 1 whole
=
3
!
2
=2
1+1+
2
1
!
2
1
!
2
1
!
2
1
!
2
Here are a few other examples:
1
6
© MCMXCVIII Alpha Omega Publications, Inc.
(Think:
6
!
5
1
= 1!
5
1
7
2
7
!
5
= 1!
5
9
!
7!
5 = 85
!
13 !
5 = 14 5
(Think:
1
2
!
13 + 1 !
5 = 14 5 )
7 + 1!
5 =8
8!
9 =9
2
(Think:
2
!
5)
9
!
9
= 1 whole
8 + 1 whole = 9)
Remember: Convert the improper fraction to a mixed number first. Then
add the new mixed number to the whole number already given.
1
Rename each mixed number.
4
N
!
4!
3 =53
3
N
!
6!
2 =72
15
15 !
10 = ?
14
9!
11 = ?
5
N
!
10 !
4 = 11 4
5
8!
3 =?
6
N
!
21 !
4 = 22 4
7
3!
6 =?
Horizons Math 5, Student Workbook 2 77
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Find the sum or difference.
3
11 !
7
1
3!
4
+
1
2!
3
+
3
88 !
5
–
3
2
7!
5
–
1
37 !
5
2
+ 10 !
10
2
21 !
5
1
3!
2
7
15 !
12
1
– 10 !
24
Solve.
n x 15 = 30
4
5
4!
6
n x 20 = 60
n x 4 = 28
n x 4 = 40
Solve.
Mrs. Wardell is cooking a roast for Sunday dinner. If she put the roast in the
1
oven at 9:00 A.M., and it needs to cook for 3 !
2 hours, what time will she need to
take it out?
Mr. Fowler’s gas tank is
1
!
2
full. If he has an 18-gallon tank, how many gallons
of gas does he have in the car when it is
1
!
2
full?
Samantha has a dollar and several quarters. If a soda pop and a candy bar cost
$1.50, does she have enough money to purchase them?
78 Horizons Math 5, Student Workbook 2
© MCMXCVIII Alpha Omega Publications, Inc.
Lisa turned 15 years old today. Write a mixed number to show how old she will
be in 9 months.
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Find all the multiplication facts. Facts may be vertical, horizontal, or diagonal.
Look at the example given.
6
4
24
15
3
5
6
6
3
7
8
2
3
6
0
12
1
9
2
4
36
11
25
3
89
5
10
32
9
2
18
9
3
27
21
5
9
8
6
15
3
40
45
0
2
78
4
14
56
Answer the indicated items.
B
•
Name each part: Chord
________________
Diameter ________________
A•
E
C•
•
________________
•D
•F
Label and find the product.
10 x 7 =
→
7
→
© MCMXCVIII Alpha Omega Publications, Inc.
Radius
6x9=
2x6=
5x8=
8x8=
7x9=
4x1=
3x8=
5x9=
4x7=
3x7=
1x6=
Horizons Math 5, Student Workbook 2 79
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Lesson 106
Renaming Improper Fractions in Sums
3
1
!
Brett rode his bike 2 !
2 miles on Friday and 3 4 miles on Saturday. How far did he ride
over the two days?
1
2
3
3
Step 1: Add or subtract the fractional part of the problem
by converting to like denominators.
Step 2: Add or subtract the whole numbers.
Step 3: If the answer is improper, make it a proper mixed
fraction. If the answer can be renamed (reduced)
to lower terms, do it.
!
2!
2 = 24
!
+ 3!
4 = 34
5
5!
4
5
1
1
!
!
5!
4 = 5 + 14 = 64
1
Brett rode his bike 6 !
4 miles over the two days.
1
Find the sum. Rename any improper answers to mixed numbers.
2
3!
3
+
2
6!
3
+
3
2!
10
5
19 !
6
7
+ 5!
10
9
+ 13 !
12
Write the missing numbers in the circles to complete each problem. Rename to
lowest terms.
11
7!
16
3
1!
5
+
1
!
10
7
!
5 10
80 Horizons Math 5, Student Workbook 2
–
5
4!
6
3!
16
9
25 !
43 !
4
1
!
+
5
19
55 !
20
–
4
!
5
13 !
15
© MCMXCVIII Alpha Omega Publications, Inc.
2
1
27 !
2
4
9 !
5
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Find the quotient.
———
5)25
———
3)18
———
———
2)12
9)63
———
8)64
———
4)36
Complete the table. The first one is done for you.
4
Factors
102
© MCMXCVIII Alpha Omega Publications, Inc.
Page 81
10 x 10
Product
Exponent
Number
of Zeros
100
2
2
103
104
105
106
Horizons Math 5, Student Workbook 2 81
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Page 82
Use the pictures below to help complete these equations.
Remember: 1 pint (pt)
1 quart (qt)
= 2 cups (c)
= 2 pints (pt)
1 gallon (gal) = 4 quarts (qt)
4 qt =
6
__________ gal
6 pts =
__________ cups
1
!
2 gal = __________ qts
8 cups =
__________ pts
5 gals = __________ qts
2 cups =
__________ pt
Label and solve.
→
→
→
35 ÷ 7 = _________
42 ÷ 7 =
54 ÷ 6 =
56 ÷ 8 =
64 ÷ 8 =
63 ÷ 9 =
28 ÷ 7 =
81 ÷ 9 =
82 Horizons Math 5, Student Workbook 2
© MCMXCVIII Alpha Omega Publications, Inc.
40 ÷ 8 =
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Page 83
Lesson 107
Renaming Improper Fractions in Sums
Sarah worked 8
1
!
2
hours on Monday, 7 hours on Wednesday, and 8
1
!
2
hours on
Friday. How many hours did she work in the week?
Remember to add the fractional part of
the problem first.
1
8!
2
7
After adding the fractional part of the
problem, add the whole numbers.
1
8!
2
+
2
23 !
2 =23 + 1 whole = 24 hours
If the answer can be renamed, rename it
and make it a proper mixed number.
Sarah worked a total of 24 hours.
1
Find the sum or difference.
1
4!
2
+
3
1!
4
–
1
9!
3
5
1
3!
4
© MCMXCVIII Alpha Omega Publications, Inc.
+
2
1
21 !
12
12
7
10 !
8
+
3
!
6
4
98 !
5
1
– 54 !
10
14
3!
15
6
5!
10
+
7
Match.
7
13 !
5
1
22 !
2
10
13 !
7
2
14 !
5
12
21 !
8
1
22 !
4
5
21 !
4
3
14 !
7
Horizons Math 5, Student Workbook 2 83
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Page 84
Fill in the sum on the fraction wheel. Reduce.
2
9!
5
1
10 !
2
1
4!
3
2
3!
8
3
15 !
12
4
Find the quotient.
———
5)63
———
6)72
———
———
8)90
3)41
Find the least common multiple for the denominators of each set of fractions.
3
!
4
2
!
9
7
!
10
1
!
5
1
!
8
3
!
4
1
!
16
3
!
7
5
!
12
5
!
4
1
!
2
5
!
6
84 Horizons Math 5, Student Workbook 2
© MCMXCVIII Alpha Omega Publications, Inc.
5
———
4)40
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Page 85
Write a problem for each illustration, then solve.
+
=
+
=
+
© MCMXCVIII Alpha Omega Publications, Inc.
+
–
=
Horizons Math 5, Student Workbook 2 85
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Page 86
Lesson 108
Subtraction of Mixed Numbers
1
If Clayton worked 7 hours on Wednesday, and 5 !2 hours on Friday, how much
longer did he work on Wednesday than he did on Friday?
7
Step 1:
1
5!
2
–
Always begin with the fractional part of the problem.
There is not a fractional part to the minuend. How
can we rename 7 so that it has a fractional part?
7=6+
2
–
2
!
2
6!
2
Step 2:
Rewrite the problem with the renamed minuend.
1
5!
2
Step 3:
Subtract the problem. Reduce or rename the answer
if needed.
1
1!
2
1
Clayton worked 1 !
2 hours longer on Wednesday than he did on Friday.
1
Find the difference.
40
3
80 !
4
–
10
3
15 !
6
–
–
7
1!
8
2
8!
5
5
!
8
–
Solve the problems to find your way through the maze.
3 !2
1
23 !6
5
31 !4
1
+ 8!
12
10
+ 12 !4
+ 5 !4
3
8 !4
start
1
3 !2
7
32 !3
1
8 !8
!
31 12
15 !9
2
86 Horizons Math 5, Student Workbook 2
7
3
3
1
44 !2
4
3 !5
8
!
37 11
1
6 !2
15 !3
1
– 7 !6
– 10 !5
2
36 !3
43 !4
3
8 !6
1
7 !5
52 !2
7
16 !
10
1
5 !5
1
11 !7
1
3 !3
2
2
1
1
5
9 !6
2
– 6!
12
© MCMXCVIII Alpha Omega Publications, Inc.
2
1
20 !
2
–
10
25
JMS052Mar09(6.5).qxd
3
4
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3:48 PM
Rename each mixed number.
4
10 !
3 = _________
11
256 !
9 = _________
9
45 !
5 = _________
12
34 !
12 = _________
10
2!
8 = _________
4
897 !
3 = _________
8
9!
7 = _________
11
3!
6 = _________
Solve and match to the proper illustration.
———
———
© MCMXCVIII Alpha Omega Publications, Inc.
———
9)$8.01
3)$1.86
5
Page 87
———
4)$24.00
6)$7.50
Complete.
15
32
8
63
9
Horizons Math 5, Student Workbook 2 87
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Page 88
Solve and complete the crossword puzzle.
4.
5.
1.
3.
6.
2.
Across
1.
29 + 79 = ___________
1.
819 + 266 = ___________
2.
295 + 278 = ___________
4.
314 + 273 = ___________
3.
284 + 95 = ___________
5.
761 + 458 = ___________
6.
23 + 54 = ___________
Solve.
3 5 4
+
5 1 7
?
+
2 , 1 8 8
2 1
?
+
9 7 3
5 7
8 7 4
+
?
1 , 2 0 0
88 Horizons Math 5, Student Workbook 2
?
7 3 8
+
?
1 , 3 9 0
© MCMXCVIII Alpha Omega Publications, Inc.
7
Down
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Page 89
Lesson 109
Subtraction With Unlike Denominators
1
It takes 5 !4 packages of string to make the Vacation Bible School wind chime craft
1
project. It takes only 3 !2 packages of string to make the Indian drum craft project. How
much more string does the wind chime project need than the Indian drum project?
–
4
5!
4 =
1
1
!
4
1
2
!
4
3!
2 =
1
5!
4 =
1
!
4
+
4
!
4
Step 1: Always begin with the fractional part of the problem. The
denominators are not the same. Rename them. We
1
2
cannot subtract !4 from !4 . We need to borrow from the
whole number and rename one whole number as a
fraction. Look at the illustration below.
=
5
!
4
5
1
5 !4 and 4 !4 are the same amount. Look at the shaded area.
Step 2: Rewrite the problem with the renamed subtrahend.
5
4!
4
2
© MCMXCVIII Alpha Omega Publications, Inc.
–
3!
4
Step 3: Subtract the problem. Reduce or rename the answer, if
needed.
3
1!
4
3
The wind chime project takes 1 !
4 more string than the Indian drum project.
Find each difference.
1
–
1
9!
6
1
6!
8
1
1!
3
1
3!
4
–
12
–
3
5!
5
1
14 !
5
–
1
8!
3
62
–
9
15 !
11
1
15 !
5
–
1
!
2
Horizons Math 5, Student Workbook 2 89
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Page 90
Find the renamed fractions in the puzzle. Color the pieces containing the
answers red.
12 = __________
DATA BANK
11 = __________
13 = __________
76 = __________
24 = __________
6 = __________
9
3 !4
5
11 !2
75
1
23 !1
8
12 !8
2
7 !2
7
13 !7
3
10 !3
2
44 !5
4
6
!
6
6
43 !6
7
!
5 !4 8 7
5
26
7
40 !5
9
!
9
40 !7
2
3
3
!
3
9
74 !9
Find your way through the maze by following the prime numbers.
Start →
1
5
11
8
4
9
15
10
12
32
13
42
20
60
10
95
25
16
29
3
2
40
33
80
70
12
30
90
23
55
77
65
28
36
2
8
19
9
35
4
86
50
66
18
41
17
37
29
15
10
14
40
32
25
24
1
30
6
85
92
69
58
38
3
→ End
Find the sum.
+
5
4!
6
1
1!
2
3
19 !
5
1
5!
4
1
!
5 12
1
3!
3
1
3!
2
1
6!
2
1
2!
3
90 Horizons Math 5, Student Workbook 2
+
8
!
6
+
1
!
5
+
1
!
8
© MCMXCVIII Alpha Omega Publications, Inc.
4
9 = __________
4
6 !9
8
1 !8
45 = __________
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Page 91
Find the sum.
64,392
+ 14,208
3,186
+ 1,209
4,361
+ 5,691
6
178,093
+ 104,351
+
30,756
4,613
Complete.
© MCMXCVIII Alpha Omega Publications, Inc.
5,219,304,786
7
__________ is in the hundreds’ place
__________ is in the hundred millions’ place
__________ is in the millions’ place
__________ is in the ten thousands’ place
__________ is in the ones’ place
__________ is in the billions’ place
Solve.
15 + n = 21
25 + n = 60
n + 40 = 70
n + 1 = 99
Horizons Math 5, Student Workbook 2 91
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Page 92
Lesson 110
Working With Mixed Numbers
Remember three basic steps when working with mixed numbers:
Add or subtract the fractional part Add or subtract the
of the number FIRST! Rename
whole number part.
with a common denominator, if
necessary. Borrow from the whole
number, if necessary.
Rename the answer,
if necessary.
Look at these examples:
+
8!
2 =
1
2
!
4
1
1
!
4
4!
4 =
12
1
14
_
3
!
4
1
2
!
6
5!
2 =
1
3
!
6
9
5
!
6
+
6
!
6
=
11
8
!
6
–
5
12 !
5 =
5
!
5
4
3!
5
1
8!
5
Solve.
11
25 !
12
1
8!
2
+
1
3!
3
+
3
15 !
6
65
–
7
31 !
8
–
1
23 !
2
Borrow from the whole number and rename each mixed number.
7
9!
12 = __________
3
14 !
2 = __________
2
8!
3 = __________
6
61 !
5 = __________
1
13 !
5 = __________
8
3!
5 = __________
4
5!
10 = __________
6
7!
4 = __________
92 Horizons Math 5, Student Workbook 2
9
!
10
1
42 !
4
+
1
6!
5
© MCMXCVIII Alpha Omega Publications, Inc.
2
15 !
3 =
JMS052Mar09(6.5).qxd
3
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Find the sum.
21
10
+ 18
4
Page 93
56
7
+ 12
78
14
+ 22
90
8
+ 31
15
3
+ 45
Find the “length” of the word by using the “word ruler”.
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
0
1
2
3
4
5
6
Examples:
A
T
→
→
→
H
→
M
© MCMXCVIII Alpha Omega Publications, Inc.
1
3
3
6
2
!
!
!
!
3 + 0 + 4!
+
1
=
8
=
9
=
9
4
4
4
4
2
5
G
O
D
3
1
1
3
!
!
!
1!
2 + 32 + 4 = 54
JESUS =
______________________________________________
BIBLE =
______________________________________________
SIN =
______________________________________________
GRACE =
______________________________________________
SALVATION =
______________________________________________
Complete.
Write a number with a 7 in the millions’ place.
_____________________________
Write a number with a 5 in the ones’ place.
_____________________________
Write a number with a 2 in the thousands’ place.
_____________________________
Write a number with a 0 in the ten thousands’ place. _____________________________
Write a number with a 9 in the billions’ place.
_____________________________
Horizons Math 5, Student Workbook 2 93
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Page 94
Solve.
Tom ordered a BBQ beef sandwich, an order of onion rings, and a large soda.
How much did he spend?
Who spent more? Kimberly or Tom? How much more did he/she spend?
A family of four ordered two small chopped pork plates, two large chopped pork
plates, two large lemonades, and two medium milks. How much change did
they receive from a $50.00 bill when paying for dinner?
Which meal would cost less: a jumbo beef sandwich, fries, and a large drink, or
half a chicken plate and a small drink?
94 Horizons Math 5, Student Workbook 2
© MCMXCVIII Alpha Omega Publications, Inc.
Kimberly ordered a small chopped pork plate and a large tea. How much did she
spend for lunch?
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Page 95
Test 11
1
Find the sum or difference. Be sure the fractions are in lowest terms. 6 pts.
3 !
2
1. !
+
9
9 =_____
2
4
!
2. !
+
12
12 =______
4
4
! = ______
3. !
+
18
18
11 !
4
4. !
21 – 21 = _____
14 !
4
5. !
25 – 25 = _____
15
35 !
6. !
40 – 40 = ______
2
Change each mixed fraction to an improper fraction. 8 pts.
1
7!
4 = ________
2
5!
3 = ________
1
3!
4 = ________
1
7!
2 = ________
4
9!
9 = ________
2
8!
5 = ________
2
11 !
7 = ________
3
15 !
4 = ________
Change each improper fraction to a whole number or mixed fraction. Reduce the
answer to lowest terms. 8 pts.
© MCMXCVIII Alpha Omega Publications, Inc.
3
18
!
3 = ________
24
!
4 = ________
17
!
2 = ________
19
! = ________
7
27
!
10 = ________
85
!
9 = ________
10
!
4 = ________
78
!
9 = ________
4
5
Find the least common denominator of the two numbers. 4 pts.
1
!:
6
5
!:
6
2
!:
3
3
!:
4
1
!:
3
1
!:
2
1
!:
4
1
!:
7
Use the problem solving strategy, make it simpler, to help you solve these word
problems. 2 pts.
1. There was $14.00 worth of quarters in the giant gumball machine. If each gumball
costs $0.25, how many gumballs were purchased?
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Page 96
2. Pam sent 3,956 flyers to computer companies in the northeastern United States
advertising software. If each letter costs $0.32 in postage, how much did Pam have
to pay for postage for all of the flyers?
6
Write the sum. 4 pts.
1
1
!
!
7 + 2 = ______
7
2
1
!
!
3 + 9 = ______
3
2
!
!
10 + 5 = ______
1
1
!
!
4 + 2 = ______
Find the difference. Reduce the answers to lowest terms. 4 pts.
2
1
! – ! = ______
3
5
8
5
1
! – ! = ______
8
4
2
2
! – ! = ______
3
9
1
7
! – ! = ______
7
2
Find the sum. Reduce the answer to lowest terms. 4 pts.
1
7 !
6
4
13 !
9
2
+ 11 !
6
1
+ 3!
9
1
16 !
9
1
!
7
2
+ 9 !
9
+
Find the sum or difference. 4 pts.
10
1
7 !
3
1
10 !
2
2
8 !
5
4
11 !
5
1
+ 2 !
4
1
– 4 !
3
3
+ 2!
10
1
– 2 !
3
Rename each mixed number. Reduce the answer to lowest terms. 8 pts.
5
N
!
7 !
3 = 8 3
7
11 !
5 =?
96 Horizons Math 5, Student Workbook 2
3
N
!
16 !
2 = 17 2
9
6 !
7 = ?
7
N
!
1 !
4 =2 4
N
6
!
3 !
5 =4 5
4
8 !
3 = ?
9
13 !
6 = ?
52 points Total
© MCMXCVIII Alpha Omega Publications, Inc.
9
4
15 !
7