5B
s q Even and Odd Numbers
q
q even number
w odd number
5B
w
e 10, 66, 0, 704
r 39, 81, 67, 23, 5
e
t odd number
y even number
r
u6
i1
o 13
!0 24, 1
d w Multiples and Common Multiples
f w Multiples and Common Multiples
q
q
q
Multiples
of 2
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
q 20, 40, 60
Multiples
of 5
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
w 20
w 10, 20
w
w
e 4, 8, 12
r 9, 18, 27
e
e 18
r 39
t 20
y 24
u 24
i 30
t 15, 30, 45
y 14, 28, 42
e
u 40, 80, 120
i 30, 60, 90
o 12D, 24D, 36D
o 12, 24, 36
!0 25, 50, 75
r
!0 8:36 A.M.
―1―
5B
g e Factors and Common Factors
h e Factors and Common Factors
q
q
q
Factors
of 16
0 1 2 3 4 5 6 7 8 9 10111213141516171819202122232425
q 1, 2, 4, 8
Factors
of 24
0 1 2 3 4 5 6 7 8 9 10111213141516171819202122232425
w8
w 1, 2, 4, 8
w
w
e 1, 2, 3, 6
r 1, 3, 5, 15
e 1, 2, 3, 6
r6
t4
y 12
e
e
t 1, 2, 4, 8
y 1, 3
u 4D
u 1, 2, 4
i 1, 2, 3, 6
i 6 squares
o 1, 2, 4, 8, 16
!0 1
pj 8. Characteristics of Whole Numbers
k q Average
q
q
q 1, 2, 3, 4, 6, 9, 12, 18, 36
q the sum of the quantities,
w 50, 100, 150
the number of quantities
e 1, 2, 4, 8
w
w
w k58a64a61lf3g61
r 33
t1
e
y 21
u7
e k12a9a15a8lf4g11
i 60
o4
r 11D
e
!0 24D
t k20a18a15a21a16lf5
g18
y 18X
u k37a39a40a35a44a42lf6
g39.5
i 39.5H
―2―
5B
l q Average
Z/ q Average
q
q
q 4a2a0a5a3g14
q 19.2f30g0.64
w 14 students
w 0.64S
e 14f5g2.8
e 0.64d750g480
r 2.8 students
r 480S
w
w
t k500a300a0a600a800
t 35d7g245
a700a600lf7g500
y 500V
y 245 pages
e
e
u 12f0.3g40
u 16f5g3.2
i 40 apples
i 3.2 books
Zz w Per Unit Quantity
Zx w Per Unit Quantity
q
q
q North Garden
q A:110f22g5,
w South Garden
e North Garden:30f6g5
South Garden:28f4g7
B:160f40g4
w A:5B/H, B:4B/H
e Vegetable garden A produced a
r South Garden
better yield.
w
w
t East Park :40f500g0.08
West Park:60f600g0.1
y East Park is less crowded.
u East Park :500f40g12.5
West Park:600f60g10
i East Park is less crowded.
r 625f5g125, 520f4g130
t One that costs 520yen for 4
notebooks is more expensive.
e
y CarA:232f20g11.6
CarB :375f30g12.5
u Car B has better gas mileage.
―3―
5B
Zc w Per Unit Quantity
Zv w Per Unit Quantity
q
q
q Gkor square milesl
q 150d5g750
w the number of people
w 750V
w
e 1200f150g8
200
e 6,056,000f5157g1174.…
r 1200 people per G
00
t 8,791,000f2416g3638.…
y 3600 people per G
e
r 8H
w
t 0.9d4.5g4.05
y 4.05B
40
u 87,463f162g539.…
i 540 people per G
r
00
o 29,541f21g1406.…
!0 1400 people per G
Zb e Speed
Zn e Speed
q
q
q Bill
q SpeedgDistancefTime
w Jenny
w 92f2g46
e Jenny:120f25g4.8
Bill
:100f20g5
Jenny:4.8S
Bill
:5S
r Bill
w
t A:2250f15g150
B :3800f25g152
y Bicycle B
w
e 2700f15g180
r 180S per minute
t 60f8g7.5
y 7.5S per second
e
u 2880f3g960
i 960A per hour
o 960f60g16
!0 16A per minute
―4―
5B
Zm e Speed
Z, e Speed
q
q
q DistancegSpeeddTime
q 4.8Ag4800S
w 35d3g105
4800f600g8
w 8 minutes
w
e 68d25g1700
w
r 1700S
e 135f45g3
t 340d8g2720
r 3 hours
y 2720S
e
t 3Ag3000S
e
u 200d60d2g24,000
24,000Sg24A
3000f150g20
y 20 minutes
i 24A
Z. e Speed
pX/ 9. Per Unit Quantity
q
q
q k65a82a73a80a75lf5g75
w 75 points
e k14a8a17a24a11a13lf6g14.5
r 14.5X
t k7a5a0a6a8lf5g5.2
y 5.2B
w
u 530d9g4770
4770Ng4B770N
i 4B770N
e
o A:k40a45a50a65a55a60lf6g52.5
B:k45a35a55a65a65lf5g53
!0 Group B
q 4200f60g70
w 70 sheets
e 480f8g60
r 60 sheets
t Machine A
w
y A:2000f8g250
B:3120f12g260
u Bicycle B
e
i A:525f35g15
B:810f45g18
o Pump B
―5―
5B
Fractions and
Xx q Simplifying
Finding Common Denominators
pXz 9. Per Unit Quantity
q
q
q A:252f35g7.2
B:425f50g8.5
w Vegetable garden B
w
90
e 92,458f134g689.…
r 690 people per G
e
t 0.3d180g54
y 54B
r
u 1200f8g150
i 150S per minute
o 1200f200g6
!0 6 minutes
3d 5
15
3
q 4 g 4d5 g 20
4
8f2
8
g
w 10 g
10f 2
5
w
5
2
1
e 6 g g 15
3
1
6
3
t 18 g g 3
9
3
1
5
u 20 g g 12
4
4
8
2
o 28 g g 14
7
Fractions and
Xc q Simplifying
Finding Common Denominators
9
6
3
r 10 g g 15
5
q common
4d4
4
16
w 5 g 5d4 g 20
w
3
1
t 24 g
8
2
18
y 45 g 5
e
2
u 9
2
o 15
3
i 25
6
!0 2 7
9
3
1
8
Fractions and
Xv q Simplifying
Finding Common Denominators
q simplitying a fraction
2
36 36f18
r 54 g 54f18 g
3
2
12
2
!0 24 g g 16
4
q
18
6
36
2
g
g
g
e 54
27
9
3
4
i 36 g g 4
12
q
w GCF
8
y 24 g g 6
12
3d5
3
15
e 4 g 4d5 g 20
4
r 5
w
5
6
14
t k 15 , 15 l
y k 21 ,
5
4
28
u k 16 , 16 l
i k 30 ,
15 18 25
o k 30 , 30 , 30 l
45 18 25
!0 k 60 , 60 , 60 l
―6―
15
21 l
9
30 l
5B
Xb w Addition and Subtraction of Fractions
Xn w Addition and Subtraction of Fractions
q
q
w
5
2
27
9
1
25
w 10 s 15 g 30 s 30 g 30 g 6
6
4
1
2 1
3
g 6
q 3s2g 6 s
6
7
w 10
35
r 36
1
y 8
13
i 72
7
!0 24
5
9
5
1
1
3
10
q 12 a 4 g 12 a 12 g 12 g 6
6
5
7
e 8
17
t 18
4
u 15
1
o 14
w
1
e 2
15
t 14
1
u 2
11
o 15
3
r 4
1
y 5
1
i 6
19
!0 36
Xm w Addition and Subtraction of Fractions
X, w Addition and Subtraction of Fractions
1
q
1 1
4
3
7
q 3 a 4 g 12 a 12 g 12
7
w 12 S
w
3 21 6 24
e 4 g 28 , 7 g 28
9
q 1 10
2
w 15
1
e 66
1
r 83
1
t 1 12
1
y 2
7
i 15
13
u 1 28
7
o 28
1
!0 2 4
3
24 21
28 s 28 g 28
3
r red ribbon is longer by 28 S
e
1
5
4
25
8
33
3
t 6 a1 15 g 30 a1 30 g1 30 g2 30 g2 10
1
y 2 10 hours
r
13
2
1 1
28 10
5
u 1 5 sk 2 a 4 lg 20 s 20 s 20 g 20
13
i 20 A
―7―
5B
pX. 10. Addition and Subtraction of Fractions
pC/ 10. Addition and Subtraction of Fractions
q
q
5
6
35
9
3
10
q 15 g g 10 w 42 g 6 g
12
5
11
q 12
3
e 4
1
t 29
1
u 12
w
3
8
e 13
r 34
e
5
3
9
t k 12 , 12 l
y k 18 ,
9
10
12
u k1 12 , 2 12 l i k 24 ,
r
2 3
4
5
o 8 , 12 , 16 , 20
t
10
18 l
w
20 15
,
l
5 2 5 4 9
3
1
24 24
o 6 a 3 g 6 a 6 g 6 g1 6 g1 2
1
!0 1 2 X
e
!0 A
1
2 48 40
8
!1 3 5 s2 3 g 15 s 15 g 15
21
7
B: 10 g 30 l
5 25
kA: 6 g 30
2
w 15
8
r 15
3
y 10
1
i 18
8
!2 Jack, 15 B more
Cz Rescue Mission!
Cx 2 Keeping a Park Clean
q
q
1
a2
3
a4
1
s1 2
q 198a12g210
2
3
w
2
s1 3
1
a2
210f5g42
5
a6
42d4s12g156
e s1 1
3
w Larg cranes 42
3
a4
1
a1 2
Small cranes 156
w
5
a1 6
1
s1 2
e 12f0.8g15
2
s1 3
15d1.8g27
3
a1 4
r Potatoes 27B
Onions 15B
q
1
2 1 7 7
3 a 2 g 6 → 6 s1 2 →×
w
2
2 3 17 17
3 a 4 g 12 → 12 s1 3 →×
e
2 5 9 9
1 1 1 3 11 11
2
3 a 6 g 6 → 6 s1 3 g 6 → 6 a 4 g 12 → 12 s1 3 →×
―8―
5B
pCc Check（4）
Cv q Fractions and Division
q
q
q 48
w4
q 3f7g
3
7
w
10 12 14
e k 20 , 20 , 20 l
e
3
1
r 4
t 12
2
5
y 12
u 9
r
w
i 126f6g21
1
y 6 g1f 6
6
w 11
3 8
r 15k5l
13
e 19
45
t 9 k5l
e
o 21 pages
7
u 8 g 7 f8
10
i 7 g 10 f7
t
!0 South Town :52,090f74g703.…
North Town:27,650f43g643.…
19
o 12 g19f 12
!1 South Town
Cb q Fractions and Division
Decimal Numbers,
Cn w Fractions,
and Whole Numbers
q
q
2
q 500f300g1 3
q 4f5g 0.8
2
5
w 1 3 kor 3 l
w
1
e 100f300g 3
1
r 3
w
12
t 12f25g 25
12
y 25
11
3
u 11f8g 8 g1 8
11
3
i 1 8 kor 8 l
1
e 4,
1
r 3,
4
w 4f5g 5
7
8
4
9
e
t 0.75
y 1.2
u 1.375
9
i 10
1
o 25
3
!0 2 100
―9―
5B
Decimal Numbers,
Cm w Fractions,
and Whole Numbers
q
0
0.2
4
5 11.1
q
w
r
pC, 11. Fractions and Decimal Numbers
8
7
4
1
10 2
q
t
w
e
4
q 9
w
e 0.3
r 4.5
5 10
y 1 k 2 ,…l
4
y 5 < 0.81
4
u 0.5 > 9
1
t 25
3
i 4 g 0.75
1
o 0.16 < 6
e
u 0.24
7
!0 8 > 0.87
6 27
w 37k 7 l
8
i 19
r
21
8
o 21f13g 13 g1 13
8 21
!0 1 13 k 13 l
C. q Relative Value and Percentage
V/ q Relative Value and Percentage
q
q
q Relative Value
q;
gCompared QuantityfBase Quantity
w 18f20g0.9
w percentage
w
w
e 3;
r 49;
e 21f30g0.7
t 60;
y 153;
r 0.7
e
t 16f25g0.64
y 0.64
u Timmy
i 0.5
o 1.6
!0 0.007
r
e
i 0.5
u 0.28
o 0.75
!0 1.5
!1 42f50g0.84
!2 84;
― 10 ―
5B
Vz w Problems involving Percentage
Vx w Problems involving Percentage
q
q
q Compared Quantity
q
1.6
d
g56
gBase QuantitydRelative Value
35
g
w
675（students）
0
e 675d0.48
0
0.48
1
Relative
value
g324
w 35
w
r 324 boys
e
d0.72g90
e
0
t 140d1.15
1.6
g56f
w 800d0.3g240
0
140
1 1.15
g90f 0.72
g 125
（D）
Relative
value
g161
y 161D
r 125 pages
Vc e Graphs of Relative Values
Vv e Graphs of Relative Values
q
1
q 45;
w 25;
q 28
1
e 5
w 42
r 3 times
r
e 16
Relative Values of Living Expenses (January)
w
Housing
t 17;
3
y 25
0
t
10
20
Food
30
40
Relative Values of
Living Expenses (January)
100
90
10
Others
80
20
Housing
Utilities
70
40
60
50
― 11 ―
30
Food
50
60
Utilities
70
80
Others
90
100;
5B
pVb 12. Percentage and Graphs
pVn 12. Percentage and Graphs
q
q
q 70.5;
w 200;
e 0.39
r 0.041
w
t 40d0.15g6
y 6 students
w 4 times
w
e 26
r 16
of Amount of Income
Agricultural Produce
t RelativebyValues
e
u
1
q 2
100
90
d0.76g38
10
Others
80
g38f 0.76
g 50
20
Flowers
Rice
70
30
Vegetables
40
60
50
i 50 math problems
Vm q Regular Polygons
V, q Regular Polygons
q
q
q BC, CD, DE, EA
q 72/
w
w 54/
,
,
,
e sides, angles
e isosceles triangle
w
w
r R
r
t×
t
45/
y R
u R
i×
e
o regular hexagon
!0 equilateral triangle
― 12 ―
5B
V. w Circumference
B/ w Circumference
q
q
q PigCircumferencefDiameter
q ngbd3.14
w CircumferencegDiameterdPi
w 6.28
e 9.42
w
e 20d3.14g62.8
r 2, 3, 4 times
r 62.8D
w
t 8d3.14g25.12
t 57f3g19
y 25.12D
y 19D
u 18d3.14g56.52
u 24f3g8
i 56.52D
i 8D
e
o 96f3g32
!0 32D
Bz e Area of Circles
q
q The Area of a Circle
gRadiusdRadiusdPi
w 3d3d3.14g28.26
w
e 8d8d3.14g200.96
r 200.96J
t 10d10d3.14g314
y 314J
u 16d16d3.14g803.84
i 803.84J
Bx e Area of Circles
q
q 6d6d3.14f2g56.52
w 56.52J
e 4d4d3.14f4g12.56
r 12.56J
t 10d10d3.14g314
5d5d3.14g78.5
314s78.5g235.5
y 235.5J
w
u 4d3.14f2g6.28
8d3.14f4g6.28
6.28a6.28a4g16.56
i 16.56D
o 2d2d3.14f2g6.28
4d4d3.14f4g12.56
6.28a12.56g18.84
0
! 18.84J
― 13 ―
5B
pBc 13. Circles and Regular Polygons
q
q
q 7d7d3.14g153.86
w 153.86J
e 6d6g36, 3d3d3.14g28.26
36s28.26g7.74
r 7.74J
t 8d8d3.14f4g50.24
y 50.24J
q regular octagon
w
:45/
:67.5/
w
e 6d3.14g18.84
r 18.84D
t 10d3.14g31.4
y 31.4D
w
u 40d3.14f2g62.8
20d3.14g62.8
62.8a62.8g125.6
i 125.6D
o 20d20d3.14f2s10d10d3.14f2g471
10d10d3.14f2g157
471a157g628
0
! 628J
e
u 72/
i 40/
r
o 42d3.14d60g7912.8
7912.8Dg79.128S
!0 79Sk80Sl
Bb Moo! What should I do?
pBn Check（5）
q
q 0.875
w 2.6
2
23
e 25
r 15
w
t 21f60g0.35
y 35;
4S
Shed
10S
6S
3
10d10d3.14d 4 g235.5
6d6d3.14f4g28.26
4d4d3.14f4g12.56
235.5a28.26a12.56g276.32
Answer
pBv 13. Circles and Regular Polygons
276.32H
e
u 30d3.14f2g47.1
20d3.14f2g31.4
47.1a31.4a10g88.5
i 88.5D
o 15d15d3.14f2g353.25
10d10d3.14f2g157
353.25a157g510.25
!0 510.25J
― 14 ―
5B
pBm 5th Grade Review
pB, 5th Grade Review
q
q
q 7, 4, 6, 3
q 1, 2, 4, 8
w 5.087
w 1, 2, 3, 6
w
e 6, 12, 18
w
e 537.2
r 30.72
y 0.721
u 0.440
t 1.19
20
i 1.96
r 40, 80, 120
e
t odd numbers y even numbers
e
r
o 25f4.5g5 R 2.5
5
u 1 12
5
i 56
5
o 16
3
!0 2 4
!0 5 people
2.5S will be left
pB. 5th Grade Review
pN/ 5th Grade Review
q
q
q 9d8f2g36
w 36J
e k5a8.2ld7f2g46.2
r 46.2J
t 10d10d3.14f2s5d5d3.14
f2g117.75
5d5d3.14f2g39.25
117.75a39.25g157
y 157J
u 10d10d3.14f4s5d5d3.14
f2g39.25
i 39.25J
91
q 100
7
w 3 25
e 0.75
r 0.625
w
t 8:45A.M.
y 5 times
k8:00, 8:45, 9:30, 10:15, 11:00l
e
1 3
5
12 17
u 4 a 5 g 20 a 20 g 20
17
i 20
r
3 6 6 3 3
o 4g8 8s8g8
3
!0 8 X
w
o 25.12f3.14f2g4
4d4d3.14g50.24
0
! 50.24J
― 15 ―
5B
pNz 5th Grade Review
pNx 5th Grade Review
q
q 5d12d6g360
w 360+
e 7d8d6a7d6d4g504
r 504+
w
t 0.4d0.6d0.5g0.12, 0.12Lg120X
120f15g8
y 8 minutes
e
u 340d7g2380, 2380Sg2.38A
i 2.38A
r
o 12f4g3, 12f6g2
3a2g5
!0 5 hours
q
q 52/
w 38/
e 50/
r 90/
t 100/
w
y k6a3ld2d3.14s6d2d3.14
g18d3.14s12d3.14
g6d3.14g18.84
u 18.84D
e
i regular hexagon
o equilateral triangle
!0 equilateral triangle
pNc 5th Grade Review
pNv 5th Grade Review
q
q
q 15f8g1.875
21f12g1.75
w garden at Mike's house
w
e 12f150g0.08, 0.08g8;
100s8g92
r 92;
e
t 84f1.12g75
y 75B
r
u 1.20dba0.40g10
bgk10s0.40lf1.20g8
i 8 cakes
q 25
w 9.8
e 21
r 105
w
t 19;
y 0.215
u 0.703
i 1000;
e
9
o 0.9, 10
1
!0 0.125, 8
r
!1 76f80g0.95,
0.95
!2 512f320g1.6,
160;
― 16 ―