nuMber AnD AlgebrA • real numbers
WorkeD exAMple 11
Draw a diagram to show 2 1 as pieces of circle and then write 2 1 as an improper fraction.
3
3
Think
WriTe
1
Draw two whole circles and 1 of a circle.
2
Divide the whole circles into thirds.
3
Count the number of thirds and write the mixed
number as an improper fraction.
3
213 =
7
3
WorkeD exAMple 12
Express 2 3 as an improper fraction.
4
Think
WriTe
1
Write the mixed number.
23
2
Multiply the whole number with the denominator then
add the numerator. The result becomes the numerator
and the denominator stays the same.
=
2×4+3
4
3
Evaluate the top line of the fraction.
=
8+3
4
4
Write the answer.
= 11
4
4
reMeMber
1. An improper fraction has a numerator that is larger than the denominator.
2. A mixed number is made up of a whole number and a fraction.
3. An improper fraction can be changed to a mixed number by dividing the denominator
into the numerator and writing the remainder over the same denominator.
4. A mixed number can be changed to an improper fraction by first multiplying the whole
number with the denominator then adding the numerator. The denominator stays the
same.
eXerCise
4C
Mixed numbers and improper fractions
fluenCy
1 We9 Draw a diagram to show the following improper fractions as pieces of a circle, then
write each improper fraction as a mixed number.
a
5
2
b
4
3
c
11
6
d
13
8
e
12
4
Chapter 4
f
7
6
rational numbers
103
nuMber AnD AlgebrA • real numbers
inDiViDuAl
PatHWaYs
eBoo
k plus
eBook
2 a Sarah ate
Activity 4-C-2
More mixed numbers
and improper
fractions
doc-1707
Activity 4-C-3
Tricky mixed
numbers and
improper fractions
doc-1708
or 3 halves of an apple. Draw the amount of apple that Sarah ate and express 32
as a mixed number.
b Dean ate
9
4
or 9 quarters of pizza. Draw the amount of pizza that Dean ate and express 49
as a mixed number.
Activity 4-C-1
Mixed numbers and
improper fractions
doc-1706
3
2
3 We10 Express these improper fractions as mixed numbers.
a
7
5
b
11
4
c
21
2
d
39
10
e
51
12
f
92
11
g
29
13
h
23
8
i
100
3
j
25
2
k
20
3
l
10
3
11
2
67
8
d
4 Change these improper fractions to mixed numbers.
a
e
i
8
5
58
7
31
12
27
8
117
10
89
6
b
f
j
c
g
h
61
?
8
7 85
97
9
74
9
5 MC a Which of the following is the same as
a 55
b 6
8
5
8
c
b Which of the following is the same as
3
10
7
10
a 3
b 7
4
5
b 5
5
8
E 9
7
10
d 3
3
10
E 7
5
9
5
9
d 9
3
5
E 9
5
8
73
?
10
c 7
c Which of the following is the same as
a 8
d 8
48
?
5
c 9
4
10
4
9
6 We11 Draw a diagram to show the following mixed numbers as pieces of a circle and then
write each one as an improper fraction.
1
a 1
b 3
c
d
e
8
21
6
51
4
f
3
4
1 16
1 35
7 We12 Express the following mixed numbers as improper fractions.
1
7
4 19
4
5
a 1
b 1
f
g 11
1
2
2
3
37
8
c 2
d 3
e 6
h
i
1
3
7 45
j
5
7
110
11
1
4
9 25
8 Change these mixed numbers to improper fractions.
Digital doc
Spreadsheet
Converting
improper
fractions
to mixed
numbers
doc-1725
104
1
5
5 35
4
5
94
7
9
10
8 65
b 4
c 5
d 6
e 2
f
g
h
i
j
9 a
eBoo
k plus
eBook
1
2
3127
a 3
2
7
MC Which of the following is the same as 10 ?
a
27
10
b
72
10
10
27
c
d
72
7
E
72
2
d
53
6
E
68
5
d
97
11
E
77
9
5
b Which of the following is the same as 8 6 ?
a
85
6
b
58
6
56
8
c
9
c Which of the following is the same as 711 ?
a
86
11
b
99
7
Maths Quest 7 for the Australian Curriculum
c
79
11
nuMber AnD AlgebrA • real numbers
understanding
10 Kim and Carly arrived home from school quite hungry and
cut up some fruit. Kim ate 9 quarters of an apple and Carly
ate 11 quarters. How many apples did they each eat?
11 Daniel was selling pieces of quiche at the school fete. Each
quiche was divided into 8 pieces. If Daniel sold 51 pieces,
how many quiches did Daniel sell?
12 It was Cecilia’s responsibility to supply oranges for her
soccer team at half-time. If 19 players ate 1 orange each, how
4
many oranges were eaten?
13 Insert the appropriate < or > sign between each pair of
fractions to make a true statement.
a
d
g
8
5
15
2
21
3
1 25
b
5 12
e
8
3
h
19
2
33
4
1 16
17
8 12
19
4
35
17
c
f
i
33
32
1
77
4 83
3
132
65
7
36
8
14 a Amy made apple pies for her Grandma’s 80th birthday party. She divided each pie into
6 pieces, and after the party she noted that 4 16 pies had been eaten. How many pieces
had been eaten?
b Amy’s cousin Ria provided cordial for the same party, and calculated that she could make
20 drinks from each bottle. At the end of the party 3 17
bottles had been used. How many
20
drinks had been consumed?
15 A catering company provided 12 quiches which
refleCTion
were each cut into 8 pieces for a luncheon. At the
What strategies will you use to
end of the function there were 12 pieces of quiche
write an improper fraction as a
left over. How many whole quiches were eaten?
mixed number?
4D
eBoo
k plus
eBook
Interactivity
Adding and
subtracting
fractions
int-2357
Adding and subtracting rational
numbers
Adding and subtracting proper fractions
■
■
Fractions can be added and subtracted if they have the same denominator.
Remember to simplify your answer if possible.
WorkeD exAMple 13
Find 59 + 19 .
Think
WriTe
1
9
1
Write the question.
5
9
2
Add the numerators since the denominators are the
same.
=
6
9
=
6
3
9
3
Simplify the answer if possible by cancelling the
highest common factor (6 ó 3 = 2, 9 ó 3 = 3).
+
2
= 23
Chapter 4
rational numbers
105