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Mixed Numbers
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Quick Review
Tyla arranged 7 trapezoids.
Her arrangement shows 7
haivesofahexagon:Z
H
It also shows 3 whole
hexagonspiusi 3j
and 3.- represent the same amount.
They are equivalent.
f
=
3
-}
An improper fraction shows an amount greater than 1 whole.
is an improper fraction.
C
A mixed number has a whole number part and a fraction part.
isa mixed number.
Try These
a a
a a a
a
a a
a a
•
a •
a •.
• .
• •
a
a
a . a
a
a
a a
a a
a
1. Write an improper fraction and a mixed number for each picture.
b)
c)
58
AAAA
ØOOQOOO
a
a a
•
•
a
a
___
___
___
Converting between
Mixed Numbers and
Improper Fractions
These plates have
) These plates have 1+ sandwiches.
--
--
sandwiches.
-
----1and4 reprsentthesameannount.
---
is a mixed number.
* is an improper fraction.
2 X 8 = 16
16 + 7 = 23
> To write 2-- as an improper fraction,
multiply the whole number by the
denominator and add the numerator.
=
13 ÷ 2
as a mixed number, divide
the numerator by the denominator.
> To write
7
23
SO,T
-
6 Ri
=
13
1
So,6j-
2-
=
T
\
Try These
.
.
.
1. Write each mixed number as an improper fraction.
7
a) 3=
3
b) 4=
6
C)
=
1
7y
d)
19
12O
2. Write each improper fraction as a mixed number.
8
a)=
60
39
b)--=
48
-=
c)9
16
d)—-=
J
Comparing Mixed
Numbers and Improper
Fractions
Quick Review
You can compare and order mixed numbers and improper fractions.
I
3
39
> Order 1,ä-,and
I
1
0
114
from least to greatest.
I
Use numberlinesof
I I I I
I
1
equal length.
8
I
I
I
I
I
A
V
I
I
I
I
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‘
I
0
The order frofl1 least to
933
greatest is --,-j-, lij-.
‘T’
I
i
+
I
I
I
A
1
3
2
I
I
I
2
I
2
Compare 3and-.
3
15
.
.
Write 3 as an improper fraction: -iWrite
-
15
45
4
12
I
as an equivalent fraction with denominator 12:
17
17 45
45
Compareand-j-j--
> -j
17
3
So,3>
.
.
.
.
,
.
.
,
.
.
.
.
.
1
1. Use these number lines to order
II
II
I
II
I
.
.
I
.
.
.
and
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
4 from least to greatest.
I
1
0
I,llllllllIlI
0
1
2
I
I
I
1
2. Write>,<,or=
7
a)1
62
7
b)
4
13
4
c)-
5
3
.
.
.
.
.
.
_____
Exploring Ratios
Quick Review
A
ratio is a comparison of 2 quantities with the same unit.
Here are 3 squares and 5 circles.
LI LI L100 00 0
Here are some ways to compare the shapes.
-
>
-
Part-to-PartRatios
squares to circles is 3 to 5 or 3 : 5.
•
circles to squares is 5 to 3 or 5 :3.
-
Thenumbers3and5are
the terms of the ratio.
-
-
>
Part-to-Whole Ratios
squares to shapes is 3 to 8 or 3 :8 or
circles to shapes is 5 to 8 or 5 :8 or
Try These
. .
.
.
,
,
S
1. Write each ratio in as many ways as you can.
a) balls to bats
—
b) batstoballs_
c) balls to all toys
d) bats to all toys
64
You can write a part-to-whole
ratio as a fraction.
--.
. .
—
•
S
•
S
S
S
• •
S
I
•
S
S
I
S
S
S
S
_____
_____
_____
_____
_____
_____
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Equivalent Ratios
4
Quick Review
-____
> The ratio 3 :2 means that for every 3 apples there are 2 pears.
The ratio 6 :4 means that for every 6 apples there are 4 pears.
3 :2 and 6:4 are equal. 3 :2 and 6 :4 are equivalent ratios.
ii
) You can use a table and patterns
to find equivalent ratios.
The numbers in the Apples
column are multiples of 3.
The numbers in the Pears
column are multiples of 2.
The ratios of apples to pears are:
3:2,6:4,9:6,12:8,15:10,
Apples
Pears
Ratio
3
2
3:2
6
4
6:4
9
6
9:6
12
8
12:8
15
10
15:10
j
Try These
WI
t
I
F
4•W*P
I
I
W
I
I
I
IllS
,
I
S
I
IIII
IS
ISa
1. Write 2 equivalent ratios for each ratio.
66
a) 5 :3
b)7:4
c)3:9
d)4:11
e)2:6
f) 8:5
I
Exploring Percents
/
_%
Quick Review
This hundredths grid has 100 small squares.
of the grid.
Each square represents
Twenty-seven squares are shaded.
You can describe the shaded part of the grid.
)‘ 27 out of 100 squares are shaded.
.
) 0.27 of the grid is shaded.
27% of the grid is shaded.
Percent means “per hundred” or “out of 100.”
This is a percent symbol. You read 27% as 27 percent.
Try These
. .
. .
.
. a
*
t
a a a •
b
a a • • a • • • • •
I
• • • •
I
I
I
•
1. Write a fraction with hundredths, a decimal, and a percent to describe the•
shaded part of each grid.
a)
f
b)_
C)
d)fWWW
2. Write a fraction with hundredths, a decimal, and a percent to describe the
unshaded part of each grid in question 1.
a)
68
b)
c)
d)
I
Relating Fractions,
Decimals, and Percents
1’
Quick Review
‘F
27
100
Fractions, decimals, and
percents are 3ways to
describe parts of a whole.
/
0.274
N.
[-1j
p27%
of this shape is shaded.
,/P.XlOWN
=
-
I
Iw1i
=
30%
---
=0.30
30% of the shape is shaded.
of the squares are shaded.
,X25
I
----25°/
25% of the squares are shaded.
Try These.
.
.
•t
a
a
a
1. Write each fraction as a percent and as a decimal.
7
9
a)-y
b)
d)
e)-j
4
2. What percent is shaded?
a)
.:
b)
00000
00000
70
c)
a
a
•m
•
S•
S
Exploring Triangles
Quick Review
——___________
We can name triangles by the number of equal sides.
symmetry.
Try These
a
a)A
a
a
a
a
a
A scalene triangle
has no equal sides,
no equal angles,
and no lines of
symmetry.
An isosceles triangle
has 2 equal sides.
It has 2 equal angles.
It has 1 line of
symmetry.
An equilateral triangle
has 3 equal sides.
It has three 60° angles.
It has 3 lines of
a
a
a
a
•
a
a
a
a
a
a
a
• a
j
a a
a
• a
a
a
a
a
a
a
a
a
.
a a
a
1 a Name each triangle as equilateral, isosceles, or scalene.
d)N
72
b)/\
C)
>
ey
j
b
Naming and Sorting
Triangles by Angles
An obtuse triangle
has one angle greater
than 90°.
A right triangle
has one 90° angle.
An acute triangle
has all angles less
than 90°
B
D
AA
E
NF
We can sort triangies in a Venn diagram.
Right Triangles
Isosceles Triangles
Try These
.
4
4
4
4
4
4
4
4
I,
•
4
4
4
4
4
4
4
4
4
4
•
4
4
1. Name each triangle as an acute,a right, or an obtuse triangle.
a)
C)
b)N
2. Which triangle in question 1 is isosceles? How do you know?
74
4
j
44••
_______
Drawing Triangles
/
7-
Quick Review
You can use a ruler and a protractor to construct a triangle.
Construct triangle ABC with these measures
•
AB=3cm
•
•
LA80°
AC=2.5cm
chthetriang(erst
Draw side AB.
Make it
3 cm long.
Measure an
80°angle at A. -
Draw side AC.
Makeit2.5cm
long.
JoinCtoBto
rn:keside BC.
4.
,L.
H
Try These
.
.
e
.
.
.
.
.
.
.
.
.
S
I
S
1. Use a ruler and protractor.
Construct triangle EFG.
Side EF is 7 cm long.
Angle F is 900.
Side FG is 5.3 cm long.
2. What is the measure of:
a) angleE?
3. How long is side EG?
76
b) angleG?
• •
S
I
S
I
•
S
I
S
•
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•
S
• • •
p
a
•
S
•
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UNIT 6
lila
1
Investigating Polygons
Quick Review
line segments.
A polygon is a closed shape with sides that are straight
at the
Exactly 2 sides meet at each vertex. The sides intersect only
vertices.
These shapes are non-polygons.
This shape is a polygon.
>
R
A regular polygon has all sides
and all angles equal.
It also has line symmetry.
0 h.--
An irregular polygon does not
have all sides equal and all
angles equal.
d
A convex polygon has alt angles
less than 1800.
A concave polygon has at least
one angle greater than 180°.
HN
TryThese
1. Circle each polygon.
78
1
UNIT 6
Congruence in Regular
Polygons
Quick Review
Here are 2 ways to show 2 squares are congruent.
Place one square on top of the other.
If they match exactly, they are congruent.
) Compare the side and angle measures.
If all sides are equal and all angles are equal, the squares are
congruent.
H
2cm
2cm
2cm
2 cm
B
2cm
2cm
C
2cm
G
TryThese
,
1. Triangles LMN and QPQ are
congruent.
Write the measure of each
angle and the length of each
side in OPQ.
2cm
.
•1
.
*
0
3
cm
P
Q
2. Which of these polygons are congruent? Explain how you know.
z2
80
c7
;
Perimeters of Polygons
;5;
Quick Review
We can find the perimeter of any polygon by adding the side lengths.
For this pentagon:
2.0 cm
4.0 cm
+
+
2.0
+
2.5
+
2.0
1.5
=
4.0
Perimeter
1.5
The perimeter is 12 cm.
cm
2.0 cm
We can use a formula to find the perimeter of some polygons.
ParaI1eIograh,
Square
-
2c__
2cm
3cm
P=2X(€+s)
P=2X(3+2)
P=sX4
P=2X4
=2X5
=10
The perimeters of the polygons are 8 cm and 10 cm.
=8
Try These
*
I
4
$
4
1. Find the perimeter of each polygon.
a)
b)
2.5 cm
82
5
2.5
cm
5;
UNIT 6
100
Area of a Rectangle
A *
-
(ISSOII
rj
Quick Review
Here is one way to find
the area of a rectangle.
8cm
) Multiply the length by the width.
8 X 4=32
So, the area of the rectangle is
32 cm
.
2
cm
Tà findthe thea of a rectangle, muftiply the length
by the width.
Rule.
Formula:
Area
=
A
=
length X width
exw
Try These
Find the area of each rectangle.
Complete the chart.
Figure
A
7cm
A
6
4mB
B
C
2m
7cm
3m
D
D
5 cm
E
E
20cm
lim
1km
F
F
10km
84
1
Area