Answers
Chapter 7
Worksheet 1
1. Nine parts are shaded.
As a fraction, we say 9 out of 10 parts are
shaded.
9.
We write it as —
10
2.
7 ; 0.7; seven tenths
—
10
3.
4 ; 0.4; four tenths
—
10
8 ; 0.8; eight tenths
—
10
1; 2; 1.2
2; 3; 2.3
1; 1; 1.1
4.
5.
6.
7.
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8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
10 —
5 —
15
—
10
10
10
15 tenths
15 tenths 1 one 5 tenths
1.5
10 _
2
—
10
10
1 one 2 tenths
1.2
20 —
6
—
10
10
2 ones 6 tenths
2.6
9
9 ; 9; 0.9; —
9; —
10
10
7 ; 7; 0.7; —
7
7; —
10
10
9 ; 9; 0.9; —
9 ; 2; 2
2; 9; 2; —
10
10
9 ; 5; 5; 3; 30
9 ; 9; 0.9; —
3; 5; 9; 30; 5; —
10
10
2 ; 2; 3; 60
6; 3; 2; 60; 3; —
10
4 ; 4; 9; 10
1; 9; 4; 10; 9; —
10
7 ; 7; 2; 50
5; 2; 7; 50; 2; —
10
Worksheet 2
4
1. 4; 4; 100; ——
100
7
2. 7; 7; 100; _
100
6 ; 0.06; 6 hundredths
3. ——
100
9 ; 0.09; 9 hundredths
4. ——
100
5. 0.02; 0; 0; 2
6. 0.08; 0; 0; 8
7. 0.62; 0; 6; 2
8. 0.58; 0; 5; 8
9. 2.38; 2; 3; 8
10. 3.15; 3; 1; 5
11. 60
12. 90
13. 30
14. 50
15. 2; 6
16. 3; 2
17. 1; 2
18. 6; 3
19. 0.28; 28; 28; 20; 8; 2; 8; 0.2; 0.08; 0.28
20. 50; 2; 5; 2; 0.5; 0.02; 0.52
21. 1.13
Ones
Tenths
Hundredths
1
1
3
1; 1; 3; 1; 0.1; 0.03; 1.13
22. 2.26
23.
24.
25.
26.
Ones
Tenths
Hundredths
2
2
6
2; 2; 6; 2; 0.2; 0.06; 2.26
3; 4; 1; 3; 0.4; 0.01; 3.41
4; 2; 7; 4; 0.2; 0.07; 4.27
1.42; 100; 42; 1; 42; 1; 4; 2; 1; 0.4; 0.02,
1.42
2 ; ——
4
2; 4; —
10 100
Ones
Tenths
Hundredths
0
2
4
2 ; 4; 0.04; ——
4
2; 0.2; —
10
100
Reteach 4B
MS_Reteach 4B_ANS_171-185.indd 171
171
11/10/09 9:34:01 AM
5 ; ——
4
27. 5; 4; —
10 100
Tenths
Hundredths
0
5
4
No
So,
is greater
than
.
We write
⬎
Yes
Next, compare
the tenths.
No
Are they the
same?
5 ; 4; 0.04; ——
4
5; 0.5; —
10
100
2 ; ——
7
28. 1; 2; 7; 1; —
10 100
Ones
1
Tenths
2
Next,
compare the
hundredths.
Are they the
same?
7
7
7; 7; 7; 0.07; 0.07; ——
100
2
2; 2; 2; 0.2; 0.2; —
10
1; 1; 1; 1
29. 10; 27; 1.27
30. 8; 40; 8.40
31. 30; 26; 30.26
Worksheet 3
1. 0.6
2. 1.3
3. 0.06 4. 0.32
5. 1.21 6. 1.5
7. 2.9
8. 0.05
9. 0.56 10. 2.83
11. 0.6; 0.7; 0.6; 0.7; 0.6; 0.7; 0.6; 0.7
12. 4.3; 4.5; 4.3; 4.5; 4.3; 4.5; 4.3; 4.5
13. 1.15; 1.16; 1.15; 1.16; 1.15; 1.16; 1.15; 1.16
14. 4.33; 4.36; 4.33; 4.36; 4.33; 4.36; 4.33; 4.36
15. 8.5; 8.52; 8.5; 8.52; 8.5; 8.52; 8.5; 8.52
16. 7.77; 7.81; 7.77; 7.81; 7.77; 7.81; 7.77; 7.81
17. 2.2; 2.1; 2.2; 2.1; 2.2; 2.1; 2.2; 2.1
18. 11.3; 11.1; 11.3; 11.1; 11.3; 11.1; 11.3; 11.1
19. 8.09; 8.06; 8.09; 8.06; 8.09; 8.06; 8.09; 8.06
20. 3.37; 3.35; 3.37; 3.35; 3.37; 3.35; 3.37; 3.35
21. 2.4; 3.6
22. 1.6; 1.3
23. 0.28; 0.22
24.
Ones Tenths
Hundredths
0
4
3
0
3
4
172
Yes
Hundredths
Which is greater?
.
Which is greater?
4 tenths
So, 0.43 is greater
than 0.34.
We write 0.43 ⬎
0.34.
Which is greater?
No
So,
is greater
.
than
We write
⬎
.
Yes
The two decimals
are the same!
25.
Ones
0
0
Tenths
3
6
Compare the
ones. Are they
the same?
Hundredths
5
2
Which is less?
No
Yes
Next, compare
the tenths.
No
Are they the
same?
Yes
Next, compare
the hundredths.
No
Are they the
same?
Yes
So,
is less than
.
We write
⬍
.
Which is less?
3 tenths
So, 0.35 is less
than 0.62.
We write 0.35 ⬍
0.62.
Which is less?
So,
than
We write
is less
.
⬍
.
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Ones
Compare the
ones. Are they
the same?
The two decimals
are the same!
Answers
MS_Reteach 4B_ANS_171-185.indd 172
10/2/09 10:25:51 AM
26.
Ones
1
1
2
Tenths
3
2
5
Hundredths
9
2
0
1.22, 1.39, 2.5
27.
Ones
5
8
6
Tenths
4
5
2
Worksheet 5
7 ; 0.7; seven tenths
1. —
10
9 ; 0.9; nine tenths
2. —
10
3.
Hundredths
3
0
5
5
5 ; 0.5
0.5; —
10
1
_
2
5
4.
2
8 ; 0.8
0.8; —
10
4
_
5
Ones
9
9
9
Tenths
3
2
3
Hundredths
4
0
2
5.
4 ; 0.4
—
10
2
2
_
5
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1.74,
4.45,
4.54,
3.58,
8.89,
3.57,
0.95,
1.76,
7.32,
7.84,
2.35, 3.57
5.31, 5.5
5.3, 5.5
4.25, 4.26
9.88, 9.98
2.35, 1.74
0.05, 0.03
1.74, 1.73
6.39, 3.57
7.49, 7
Worksheet 4
1. 20
3. 50
5. 18
7. 5.1
9. 24.2
11. 3; 2.6
13. 2; 1.9
15. 1.74; 1.7
17. 1.55; 1.6
4
_
10
2
3
_
4
6.
75 ; 0.75
——
100
7.
50 ; 0.5
——
100
2
_
4
8.
55 ; 0.55
_
100
11
20
9.2, 9.32, 9.34
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
8
_
10
2
5.43, 6.25, 8.5
28.
5
_
10
25
75
_
100
25
25
50
_
100
25
5
55
100
5
5
9.
3—
15
_
2
10
3
_
2
15
_
10
5
2.
4.
6.
8.
10.
12.
14.
16.
20
6
25
18.1
4; 3.7
4; 4.3
1; 0.9
0.73; 1
5
10 _
—
10
10
1 0.5
1.5
5_
125
10. _
4
100
5
_
4
25
125
_
100
25
100 _
25
_
100
100
1 0.25
1.25
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22. 2.15 2 0.15
15
2 ——
100
15
2——
100
200 _
75
_
100
100
2 0.75
2.75
13
12. 3—
2
3
3.5
5
—
10
0.5
3 2 ——
75
13. 2—
4
100
2 0.75
2.75
45
14. 5—
5
5
5.8
Chapter 8
Worksheet 1
1. 0.6 6 tenths
2.
8
—
10
0.8
Ones
Tenths
0
6
0.1 1 tenth
Ones
Tenths
0
1
3.
0.8 ; 0.8
4.
0.7; 0.7
5.
0.7 0.2
Ones
7 tenths 2 tenths
9 tenths
0.9
25
1 1 ——
15. 1—
4
100
1 0.25
1.25
4
26_
16. 6—
5
10
6 0.4
6.4
7
17. 0.7 7 tenths —
10
2
18. 0.2 2 tenths —
10
25
19. 0.25 25 hundredths ——
100
20. 1.7 1 0.7
7
1—
10
0
6.
7
1—
10
21. 1.27 1 0.27
27
1 ——
100
27
1——
100
174
7.
9.
0.4 0.3
Ones
4 tenths 3 tenths
7 tenths
0.7
0
0.9
0.4
Tenths
9
Tenths
7
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25
275
11
_
_
4
100
25
275
11 _
11. _
4
100
8. 0.8
10. 1.1; 1.1
Answers
MS_Reteach 4B_ANS_171-185.indd 174
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11. 9; 3; 12; 1; 2; 1.2
Ones
25. 0.51
Tenths
Ones Tenths
1
Tenths
Hundredths
One
Tenths
Hundredths
0
5
1
Ones Tenths
1
13. 1.0
15. 1.8
16. 0.08; 0.08
Tenths
2
12. 4; 8; 12; 1; 2; 1.2
One
One
2
26. 0.23
One Tenths Hundredths
14. 1.1
One Tenths Hundredths
17. 0.07; 0.07
0
2
3
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27. 9.41
Ones
18. 4; 4; 8; 0.08
Ones
Tenths
Hundredth
0
0
8
19. 0.07
21. 0.07
Hundredths
Ones
Tenths
1
1
1
1
1
Hundredths
5.63
⫹3 . 7 8
9.41
20. 0.07
22. 0.22; 0.22
Tenths
Hundredths
5.63
⫹3 . 7 8
9.41
24. 0.24; 0.24
9
4
1
Reteach 4B
MS_Reteach 4B_ANS_171-185.indd 175
1
5.63
⫹3 . 7 8
9.41
Ones
23. 0.23; 0.23
Tenths
175
3/25/09 12:09:55 PM
0.4 0.2 0.2
28. 7.62
4.83 2.79 7.62
3 hundredths 9 hundredths 12 hundredths
1 tenth 2 hundredths
8 tenths 7 tenths 1 tenth 16 tenths
1 one 6 tenths
4 ones 2 ones 1 one 7 ones
3.
29. 6.01
3.72 2.29 6.01
2 hundredths 9 hundredths 11 hundredths
1 tenth 1 hundredth
7 tenths 2 tenths 1 tenth 10 tenths
1 one 0 tenths
3 ones 2 ones 1 one 6 ones
4.
30. 8.61
1.65 6.96 8.61
5 hundredths 6 hundredths 11 hundredths
1 tenth 1 hundredth
6 tenths 9 tenths 1 tenth 16 tenths
1 one 6 tenths
1 one 6 ones 1 one 8 ones
5.
7.
9.
31.
32.
33.
34.
35.
36.
37.
38.
10. 0.5; 0.5
Worksheet 2
1. 0.2; 0.2
2.
Tenths
0
2
0.7 0.4 0.3
Ones
Tenths
0
3
0.2
0.4
0.8; 0.8
0.7
0 . 4
0.3
6.
8.
0.2
0.3
11. 0.8; 0.8
14 tenths 6 tenths 8 tenths; 0.8
12. 0.8; 0.8
11 tenths 3 tenths 8 tenths; 0.8
13.
15.
17.
18.
1.5
2.7
0.8
0.09; 0.09
0.2; 0.2
19. 0.05; 0.05
176
0.4
0 . 2
0.2
14. 2.6
16. 1.8
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6.47
16.6
22.41
7.26
7.22
10.36
11
13.11
Ones
Answers
MS_Reteach 4B_ANS_171-185.indd 176
3/20/09 8:30:46 PM
20. 0.26; 0.26
21. 1.14; 1.14
22. 1.38; 1.38
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23. 1.08; 1.08
24. 5.65 ⫺ 2.38 ⫽ 3.27
Regroup the tenths and hundredths
5 ones 6 tenths 5 hundredths
⫽ 5 ones 5 tenths 15 hundredths
Subtract the hundredths
15 hundredths ⫺ 8 hundredths ⫽ 7 hundredths
Subtract the tenths
5 tenths ⫺ 3 tenths ⫽ 2 tenths
Subtract the ones
5 ones ⫺ 2 ones ⫽ 3 ones
25. 6 ⫺ 4.57 ⫽ 1.43
Regroup the ones and tenths
6 ones ⫽ 5 ones 10 tenths
Regroup the tenths and hundredths
5 ones 10 tenths ⫽ 5 ones 9 tenths 10 hundredths
Subtract the hundredths
10 hundredths ⫺ 7 hundredths ⫽ 3 hundredths
Subtract the tenths
9 tenths ⫺ 5 tenths ⫽ 4 tenths
Subtract the ones
5 ones ⫺ 4 ones ⫽ 1 one
26. 3 ⫺ 2.74 ⫽ 0.26
Regroup the tenths
3 ones ⫽ 2 ones 10 tenths
Regroup the hundredths
2 ones 10 tenths ⫽ 2 ones 9 tenths
10 hundredths
Subtract the hundredths
10 hundredths ⫺ 4 hundredths ⫽ 6 hundredths
Subtract the tenths
9 tenths ⫺ 7 tenths ⫽ 2 tenths
Subtract the ones
2 ones ⫺ 2 ones ⫽ 0 ones
27. 2 ⫺ 0.74 ⫽ 1.26
Regroup the tenths
2 ones ⫽ 1 one 10 tenths
Regroup the hundredths
1 one 10 tenths ⫽ 1 one 9 tenths
10 hundredths
Subtract the hundredths
10 hundredths ⫺ 4 hundredths ⫽ 6 hundredths
Subtract the tenths
9 tenths ⫺ 7 tenths ⫽ 2 tenths
Subtract the ones
1 one ⫺ 0 ones ⫽ 1 one
28.
29.
30.
31.
32.
33.
34.
1.08; 1.08; 1.08
1.14; 1.14; 1.14
0.36
2.06
2.16
2.17
0.52
Worksheet 3
1. $2.40 ⫺ $0.85 ⫽ $1.55
Helen has $1.55 left.
2. 1.5 ⫹ 1.85 ⫽ 3.35
3.35 liters of water are in the pail now.
3. 1.25 ⫹ 0.75 ⫽ 2
The longer ribbon is 2 meters long.
1.25 ⫹ 2 ⫽ 3.25
The total length of the two ribbons is
3.25 meters.
Reteach 4B
MS_Reteach 4B_ANS_171-185.indd 177
177
11/6/09 12:17:17 PM
5.
6.
1.45 ⫹ 0.5 ⫽ 1.95
Pedro jogs 1.95 kilometers on Tuesday.
1.45 ⫹ 1.95 ⫽ 3.4
Pedro jogs 3.4 kilometers during both days.
2.35 ⫺ 1.3 ⫽ 1.05
The papaya has a mass of 1.05 kilograms.
1.05 ⫹ 0.25 ⫽ 1.3
The mass of the pumpkin is 1.3 kilograms.
1.56 ⫺ 0.25 ⫽ 1.31
Pamela is 1.31 meters tall.
1.31 ⫹ 0.47 ⫽ 1.78
Luther is 1.78 meters tall.
Chapter 9
Worksheet 1
1. ray
2. line
3. vertex
4. line segment
5. point
6. the same as
7. smaller than
8. larger than
9. JKL ; LKJ
10. PSR; RSP
11. WZY ; YZW
12. XWZ ; ZWX
WXY ; YXW
XYZ ; ZYX
WZY ; YZW
13. BAD ; DAB
ABC ; CBA
BCD ; DCB
ADC ; CDA
14. inner scale; 75°
15. outer scale; 45°
16. inner scale; 155°
17. outer scale; 135°
18. inner scale; 175°
19. outer scale; 100°
20. inner scale; 80°
178
Worksheet 2
1.
2.
3.
4.
5.
acute
6.
obtuse
Worksheet 3
1. 180
3. 360
5. 3; 270°
7. 2; 180°
2.
4.
6.
270
4; 360°
1; 90°
Chapter 10
Worksheet 1
1. perpendicular
2. parallel
3. Draw a horizontal line segment with one end
beginning on line segment GH.
Sample:
G
D
S
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4.
H
Answers
MS_Reteach 4B_ANS_171-185.indd 178
11/6/09 12:17:31 PM
4.
Draw a perpendicular line segment with one end
beginning on line segment LM.
Sample:
10.
U
X
M
V
11.
J
Y
M
P
N
Q
L
5.
K
Draw a vertical line segment with one end
beginning from line segment TU.
T
R
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R
E
W
O
U
S
6.
Worksheet 2
1. Sample:
2.
Sample:
P
S
H
M
L
7.
X
D
R
G
S
8.
3.
R
Sample:
K
F
I
T
9.
G
K
L
J
J
U
L
Reteach 4B
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179
3/20/09 8:30:50 PM
4.
Sample:
R
Chapter 11
F
Worksheet 1
1.
5.
G
2.
Sample:
G
3.
X
4.
K
Z
6.
5.
Sample:
P
O
6.
M
L
7.
Solution: Answers vary.
Sample:
8.
Solution: Answers vary.
Sample:
9.
Solution: Answers vary.
Sample:
Sample:
C
D
F
D
G
R
Q
P
T
180
Rectangle
✔
✔
✔
✔
✔
✔
✔
✔
E
F
Worksheet 3
1. vertical
2. vertical
3. horizontal
C
4.
5.
7.
Square
10.
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T
Property
All sides are of
equal length.
Not all angles
measure 90o.
All angles measure
90o.
has exactly two
pairs of parallel
sides
has exactly two
pairs of parallel
sides of different
lengths
has four sides
Answers
MS_Reteach 4B_ANS_171-185.indd 180
10/2/09 10:26:49 AM
11.
12.
13. No shading.
14. No shading.
15.
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16. No shading.
17.
18. No shading.
19. No shading.
20. No shading.
21.
22. No shading.
23. No shading.
Worksheet 2
1. Measure of ⬔b 90° 67°
23°
2. Measure of ⬔c 90° 73°
17°
3. Measure of ⬔d 90° 52°
38°
4. 2
5. 9
6. 5
7. 4
8. 6
9. 3
Chapter 12
Worksheet 1
1. 15
2. 12
3. 12
4. There are 3 rows of 4 one-centimeter
squares.
3 4 12
Area 12 cm2
5. There are 4 rows of 3 one-centimeter
squares.
4 3 12
Area 12 cm2
6. There are 5 rows of 2 one-centimeter
squares.
5 2 10
Area 10 cm2
7. 9; 4; 9 4 36; 36
8. 7; 5; 7 5 35; 35
9. 12; 9; 12 9 108; 108
10. 6
11. 12
12. 15
13. 19
Worksheet 2
1. 16
2. 14
3. 12
4. 9 4 9 4; 26
5. 12 9 12 9; 42
6. 24; 12; 12; 3; 9
7. 42; 21; 21; 12; 9
8. 38; 19; 19; 17; 2
9. 10 10 10 10; 40; 40
10. 1 1 1 1; 4; 4
11. 20; 5
12. 48; 12
13. 7; 7; 49
Reteach 4B
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4; 4; 16
60; 5; 12
36; 12; 3
6; 6; 6; 6; 24
8; 8; 8; 8; 32
9; 9; 9; 9; 36
Worksheet 3
1. 12; 12; 12
12 12 12 12; 48
2. 11; 9 7 2; 9 5 4; 7
11 2 7 4 7 5 11 7; 54
3. Perimeter AB BC CD DE EF FG
GH HI IJ JK KL LA
422458522
2 4 6 46 cm
4. 11; 9 7 2; 9 5 4; 7
7 4; 28
11 7; 77
28 77; 105
5. Area of small rectangle AL LK
6 4 24 cm2
Area of square CD DI
2
2 2 4 cm
Area of big rectangle FG HG
8 5 40 cm2
24 4 40 68 cm2
Worksheet 4
1. 90 35 3,150; 3,150
2. 30; 25
30 25 30 25; 110; 110
3. 35; 15
35 15 35 15; 100; 100
4. 120 40 22 18 12 14; 14; 14
5. 18
6. 13–14
7. 4; 4 4, 16; 16 15 240; 240
8. 15; 19
10; 14
19 14 266; 266
182
Chapter 13
Worksheet 1
1.
2.
Symmetric objects:
3.
5.
7.
9.
✗
4. ✗
✔
6. ✗
✔
8. ✗
Place 9 checks (✔) for the following;
A; B; C; D; E; H; M
10.
11.
12.
13.
Worksheet 2
1.
2.
3.
4.
Yes
6.
8.
No
Yes
5.
7.
Yes
No
© 2009 Marshall Cavendish International (Singapore) Private Limited. Copying is permitted; see page ii.
14.
15.
16.
17.
18.
19.
Answers
MS_Reteach 4B_ANS_171-185.indd 182
11/6/09 12:17:55 PM
Worksheet 3
1. ✗
2.
4. ✗
5.
7. ✔
8.
10. ✔
11.
13. ✗
14.
✔
✗
✔
✔
3.
6.
9.
12.
✗
✗
✔
✔
Chapter 14
Worksheet 1
1.
2.
15.
3.
16.
4.
17.
5.
© 2009 Marshall Cavendish International (Singapore) Private Limited. Copying is permitted; see page ii.
6.
18.
7.
8.
19.
9.
20.
10.
21.
22.
23.
24.
25.
The
The
The
The
The
figure
figure
figure
figure
figure
has rotational symmetry.
has rotational symmetry.
does not have rotational symmetry.
does not have rotational symmetry.
does not have rotational symmetry.
Reteach 4B
MS_Reteach 4B_ANS_171-185.indd 183
183
3/20/09 8:30:57 PM
11.
16. Answers vary.
Sample:
12.
17. Answers vary.
Sample:
18. ✔
20. ✔
14.
Worksheet 2
1. Answers vary.
Sample:
15. Answers vary.
Sample:
184
19. ✔
21. ✗
© 2009 Marshall Cavendish International (Singapore) Private Limited. Copying is permitted; see page ii.
13.
Answers
MS_Reteach 4B_ANS_171-185.indd 184
3/25/09 10:10:32 AM
Answers vary.
Sample:
3.
Answers vary.
Sample:
4.
Answers vary.
Sample:
5.
Answers vary
Sample:
© 2009 Marshall Cavendish International (Singapore) Private Limited. Copying is permitted; see page ii.
2.
Reteach 4B
MS_Reteach 4B_ANS_171-185.indd 185
185
11/6/09 3:33:08 PM