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9.
[Fractions]
Skill 9.1
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Illustrating proper fractions as part of one whole.
numerator - how many parts count
3
5
Q. Shade in
denominator - how many equal parts in one whole
5
(five sixths)
6
⇒
A.
of this hexagon.
5
6
Q. What fraction of this
A.
circle is shaded?
3
4
The hexagon is divided into 6 equal parts.
The numerator tells us to shade 5 parts.
The circle is divided into 4 equal parts, so
the denominator of the fraction is 4.
Only 3 parts of the circle are shaded so the
numerator is 3.
The fraction of the circle that is shaded is
three fourths or 3 .
4
a)
5
Shade in 9 (five nineths)
of this square.
d) What fraction of this
pentagon is shaded?
g) Shade in
square.
page 49
1
of this
4
b) Shade in
1
(one quarter)
4
Shade in 7 (four sevenths)
of this rectangle.
f)
What fraction of this
circle is shaded?
i)
Shade in of this
3
parallelogram.
of this triangle.
e)
What fraction of this
rectangle is shaded?
h) Shade in
hexagon.
1
of this
2
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4
c)
2
© Math’s Mate Yellow/Red Skill Builder 9
Skill 9.2
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MMRed 1 1 2 2 3 3 4 4
Illustrating proper fractions as part of a group.
numerator - how many identical circles in the group count
3
5
denominator - how many identical circles in the group all together
group of identical circles
Hint:
3
can read as “three out of five”, which means three objects out of a total of five are counted.
5
Q. Shade in
7
of this group
10
A.
⇒
of apples.
Q. What fraction of this
A.
group of sunglasses is
shaded?
7
10
The group has 10 identical apples.
The numerator shows to shade 7 apples.
3
4
There are 4 sunglasses in the group all together,
so the denominator of the fraction is 4.
Only 3 sunglasses are shaded so the numerator
is 3.
The fraction of the group of sunglasses that is
shaded is three fourths or 3 .
4
a)
5
Shade in 6 of this group
of butterflies.
d) What fraction of this
group of balloons is
shaded?
page 50
b) Shade in
2
of this group
5
Shade in 3 of this group
of ginger bread men.
f)
What fraction of this
group of lemons is
shaded?
of houses.
e)
What fraction of this
group of stars is
shaded?
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2
c)
© Math’s Mate Yellow/Red Skill Builder 9
Skill 9.3
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Writing 1 as a fraction.
1 whole
circle
shaded
1
1
2
2
=
3
3
=
4
4
=
5
5
=
=
numerator = denominator
Q. Which of the following
fractions = 1
A. A and D
fractions equal 1?
3
A)
3
4
B)
3
2
C)
3
cake was eaten, what
fraction of the cake
remains?
Which of the following
fractions equal 1?
A)
3
3
B)
1
8
C)
8
8
D)
3
8
A)
c)
to 1 that has a
denominator
of 8.
g) Luke has spent one sixth
5
2
B)
2
2
C)
1
2
D)
5
5
Write a fraction equal
to 1 that has a
denominator
of 5.
h) If three fifths of the show
is over, what fraction of
the performance is left?
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Which of the following
fractions equal 1?
A)
and
e)
4
Three thirds make the whole cake. If one
third was eaten, there are two thirds left.
fractions equal 1?
d) Write a fraction equal
page 51
2
3
b) Which of the following
and
of his pocket money.
What fraction of the
money is left?
The only fractions in which the numerator
is the same as the denominator are 3 and 4 .
3
3
= 1 (three thirds make a whole)
3
4
= 1 (four fourths or quarters make a whole)
4
4
D)
4
Q. If one third of the birthday A.
a)
1
1
7
B)
7
7
C)
1
1
D)
7
1
and
f)
Write a fraction equal
to 1 that has a
denominator
of 12.
i)
Three quarters of the
students are girls. What
fraction of the students
are boys?
© Math’s Mate Yellow/Red Skill Builder 9
Skill 9.4
•
•
•
•
Illustrating and converting mixed numbers to improper fractions.
Consider the mixed number as two bits:
A whole number.
A fraction.
Draw and shade both bits.
Count the total parts shaded.
Write this total over the same denominator.
1
2
1 3
5
1 3 = 8 IMPROPER FRACTION
5
5
fraction
denominator - 5 equal parts in one whole
Q. Name the mixed number
A. 3
represented by these
shaded rectangles.
Q. Shade these circles to
2
Name the mixed number
represented by these
shaded squares.
1 + 1 +
1
2
2
to show that 3 =
page 52
15
5
Three whole rectangles are
shaded and one sixth of
another rectangle is shaded.
The total number of rectangles
shaded is three
1
and one sixth, or 3 6 .
1
= 1
3
+
1
+
1
3
3
7
=
3
3
+
3
3
+
1
3
b) Name the mixed number
Shade two whole circles and a
third of the remaining circle.
In total 7 thirds have been
shaded.
This shows that 2 1 = 7
3
1 +
e)
3
c)
Name the mixed number
represented by these
shaded hexagons.
f)
Shade these rectangles
3 8
to show that 1 =
5 5
represented by these
shaded triangles.
1
2
d) Shade these pentagons
1
6
A.
1 7
show that 2 =
3 3
a)
8
numerator - 8 parts count
MIXED NUMBER
whole
number
3
6
7
5
4
MMYellow 1 1 2 2 3 3 4 4
MMRed 1 1 2 2 3 3 4 4
3
4
Shade these circles
2 8
to show that 2 =
3 3
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© Math’s Mate Yellow/Red Skill Builder 9
Skill 9.5
•
•
MMYellow 1 1 2 2 3 3 4 4
MMRed 1 1 2 2 3 3 4 4
Comparing fractions.
First illustrate each fraction by shading the appropriate proportion of the identical shapes.
Then compare the size of the shaded areas to decide which is largest or smallest.
Hint:
3
6
<
same
numerator
largest numerator
= largest fraction
5
6
BUT
1
7
same
denominator
Q. Which fraction is larger?
1
or 1
3
4
A.
1
3
3
Q. Shade this diagram to
2
5
compare and .
3
9
A.
2
3
2
3
5
9
Which fraction is larger?
Which fraction is larger?
2
3
or
5
5
2
5
3
5
4
Shade two thirds of the first rectangle.
Shade five ninths of the second
rectangle.
The fractions are close in value
however 2 is slightly greater than 5 .
b) Which fraction is larger?
3
3
or
4
5
3
c)
9
Which fraction is larger?
4
4
or
7
9
3
5
d) Which fraction is smaller? e)
1
3
or
6
6
g) Shade this diagram to
2
1
compare and .
5
3
Which fraction is smaller?
page 53
smallest denominator
= largest fraction
The shaded area corresponding to 1 is
3
bigger than the area shaded for 1 ,
4
which means that 1 is larger than 1 .
1
3
1
4
a)
1
4
<
Which fraction is smaller? f)
2
2
or
5
7
h) Shade this diagram to
2
7
compare and .
5
8
Which fraction is larger?
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i)
Which fraction is smaller?
2
2
or
3
5
Shade this diagram to
3
5
compare and .
4
6
Which fraction is smaller?
© Math’s Mate Yellow/Red Skill Builder 9
Skill 9.6
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MMRed 1 1 2 2 3 3 4 4
Illustrating and finding equivalent fractions.
same
area
shaded
1
2
=
2
4
3
6
=
4
8
=
different
fraction names
equal value
(equivalent fractions)
Q. Shade this diagram to
A.
Shade three fourths inside the first
square.
Shade six eighths inside the second
square.
The same area of each square has been
shaded. This shows that 3 = 6
=
show the equivalent
3 6
fractions: =
4 8
=
4
Q. Complete to form
A.
equivalent fractions:
1 3
=
4 12
The rectangle on the left has
4 equal parts. Shade one part.
The rectangle on the right has 12
equal parts. Shade the same area
as in the first rectangle. Three out
of twelve parts have been shaded.
One fourth is the same as three
twelfths.
1
3 are equivalent fractions.
=
=
1
=
4
12
4
a)
Shade this diagram to
show the equivalent
2 4
fractions: =
3 6
b) Shade this diagram to
c)
equivalent fractions:
e)
Complete to form
equivalent fractions:
g) Complete to form
equivalent fractions:
2
6
=
3
f)
Complete to form
equivalent fractions:
4 16
=
5
i)
Complete to form
equivalent fractions:
3
9
=
10
6
=
2
12
1
=
3
9
h) Complete to form
equivalent fractions:
2
1
=
8
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Shade this diagram to
show the equivalent
fractions: 3 = 12
4 16
=
=
d) Complete to form
page 54
12
show the equivalent
fractions: 4 = 8
5 10
=
8
© Math’s Mate Yellow/Red Skill Builder 9
Skill 9.7
•
Adding and subtracting fractions with the same denominators.
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Add or subtract the numerators (top numbers of the fractions).
Don’t add or subtract the denominators (bottom numbers of the fractions).
Q. 1 + 3 =
9
A.
9
4
9
Add the fractions:
One ninth plus three ninths is four ninths.
Add only the top numbers.
+
=
one ninth + three ninths = four ninths
1
9
Q. 4 − 2 =
7
A.
7
2
7
+
3
9
=
4
9
Subtract the fractions:
Four sevenths minus two sevenths is two
sevenths. Subtract only the top numbers.
four sevenths − two sevenths = two sevenths
4
7
a)
1+1 =
3 3
+
2
3
−
2
7
b)
2+3 =
7 7
c)
2+2 =
5 5
2
7
=
d)
3+2 =
8 8
e)
3 + 4 =
10 10
f)
5 + 6 =
12 12
g)
2−1 =
3 3
h)
4−1=
5 5
i)
6−2 =
9 9
j)
3−2 =
5 5
k)
9 − 6 =
10 10
l)
8 − 3 =
12 12
m)
1+4 =
6 6
n)
6−3 =
7 7
o)
7 − 2 =
11 11
page 55
=
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© Math’s Mate Yellow/Red Skill Builder 9
Skill 9.8
•
MMYellow 1 1 2 2 3 3 4 4
MMRed 1 1 2 2 3 3 4 4
Simplifying fractions.
Decide if the fraction can be simplified.
If both numbers, top (numerator) and bottom (denominator), can be divided by the same
number then the fraction can be simplified.
Hint: If the numbers are both even then you can start with dividing by 2.
6
8
•
numerator
(even)
denominator
(even)
Always divide both the numerator and the denominator by the same number.
6
8
÷2
÷2
= 3
4
Q. Simplify:
6
10
A.
Simplify:
12
18
b) Simplify:
÷2
÷3
a)
6
=
10
6 ÷2 3
=
=
10 ÷ 2 5
12
=6 =
18
9 ÷3
÷2
....................................................
2
3
4
20
d) Simplify:
Both 6 and 10 are even numbers.
They can be divided by 2.
The fraction can be simplified.
4
6
c)
....................................................
e)
....................................................
10
25
Simplify:
9
12
Simplify:
f)
....................................................
....................................................
g) Which of the following
h) Which of the following
20
70
Simplify:
....................................................
fractions cannot be
simplified?
A) 3 B) 4 C) 5 D) 13
fractions cannot be
simplified?
A) 5 B) 6 C) 7 D) 9
Which of the following
fractions cannot be
simplified?
A) 7 B) 9 C) 12 D) 17
......................................................................
......................................................................
......................................................................
15
15
15
15
B and D
page 56
10
10
10
and
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10
i)
18
18
18
18
and
© Math’s Mate Yellow/Red Skill Builder 9
Skill 9.9
•
•
MMYellow 1 1 2 2 3 3 4 4
MMRed 1 1 2 2 3 3 4 4
Adding and subtracting mixed numbers.
Add or subtract the whole numbers first.
Hint: For subtractions you may need to convert 1 whole number to an equivalent fraction.
5
Example: 1 =
one whole equals five fifths
5
Then add or subtract the numerators (top numbers of the fractions).
Don’t add or subtract the denominators (bottom numbers of the fractions).
Q. 1
1
2
+2 =
4
4
A. 3
3
4
Add the whole numbers first: 1 + 2 = 3
Add the fractions:
One fourth plus two fourths is three
fourths. Add only the top numbers.
+
11
4
Q. 2 −
5
=
6
A. 1
1
6
=
22
4
+
33
4
=
The two can be seen as one whole and six
sixths.
Six sixths minus five sixths is one sixth.
6 5 1
− =
6 6 6
2−
a)
3
3
2 +3 =
7
7
d) 4
1
4
+1 =
6
6
5
6
7
2
5
+1 =
8
8
c)
2
2
1
3 +1 =
5
5
f)
2
3
2 +4 =
9
9
b) 2
e)
5
= 11
6
6
3
4
+2 =
10
10
g) 2 −
1
=
3
h) 4 −
1
=
2
i)
3−
2
=
7
2−
1
=
4
k)
4−
2
=
3
l)
9−
5
=
9
m) 1 −
3
=
5
n) 5 −
3
=
4
o) 6 −
5
=
6
j)
page 57
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© Math’s Mate Yellow/Red Skill Builder 9
Skill 9.10
•
•
MMYellow 1 1 2 2 3 3 4 4
MMRed 1 1 2 2 3 3 4 4
Finding a fraction of a number.
First find one fraction of the number by dividing by the denominator.
Then multiply the number of fractions you need by the result.
Example: Three fifths of 10?
First find one fifth of 10 by dividing 10 by 5.
10 ÷ 5 = 2
Then find three fifths of 10 by multiplying 3 by 2.
2+2+2=3×2=6
So three fifths of 10 is 6.
Q. Eric kicked two thirds of
A. 8
his team’s 12 goals. How
many goals did he kick?
a)
Three fourths of the 28 students in the
class are boys. How many boys are in
the class?
b) Two fifths of the 50 children at the
day care had the flu. How many
children were ill?
one
fourth of 28 = 28 ÷ 4 = 7
....................................................................................................................
three
fourths of 28 = 3 × 7 =
..............................................................................................
c)
one
fifth of 50 =
....................................................................................................................
21
Ian scored five eighths of the 40 points
on the test. How many points did he
score?
two
fifths of 50 =
..............................................................................................
d) Of the 24 students in a class, one third
are chosen for the school play.
How many students are chosen for the
play?
one
eighth of 40 =
....................................................................................................................
one third of 24 =
..............................................................................................
five
eighths of 40 =
..............................................................................................
e)
Find one third of 12 ⇒
divide 12 by 3
12 ÷ 3 = 4
Find two thirds of 12 ⇒
multiply 2 by 4
2×4=8
Of the 100 cakes at a party, seven
tenths were eaten in the first hour.
How many cakes were eaten in the
first hour?
f)
Five sixths of the 30 horses in the race
jumped over the first hurdle.
How many horses passed the first
hurdle?
....................................................................................................................
....................................................................................................................
..............................................................................................
..............................................................................................
page 58
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© Math’s Mate Yellow/Red Skill Builder 9