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Fractions
4Chapter
Contents: A
B
C
D
E
Manipulating fractions
Operations with fractions
Problem solving
The unitary method withfractions
Square roots of fractions
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OPENING PROBLEM
78 FRACTIONS (Chapter 4)
In previous years we have seen how fractions are obtained when we divide a whole into
equal portions.
In general, the division a¥ b can be written as the fractiona
b.
a
bmeans we divide a whole into b equal portions, and then consider a of them.
a
b
the numerator is the number of portions considered
the bar indicates division
the denominator is the number of portions we divide a whole into.
The denominator cannot be zero, as we cannot divide a whole into zero pieces.
A scallop fisherman has a daily catch
limit. One day in the first hour he catches15
of his limit, in the second hour 14
, and
in the third hour 13
.
1 What fraction of his limit has he caught so far?
2 What fraction of his limit is he yet to catch?
3 If he can catch a further 40 kg without exceeding
his limit, what is his limit?
The fraction four sevenths can be represented in a number of different ways:
Words four sevenths
Diagram as a shaded region or as pieces of a pie
Number line
Symbol4
7
numerator
bar
denominator
A fraction written in symbolic form with a bar is called a common fraction.
MANIPULATING FRACTIONSA
0 1
four sevenths
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Y:\HAESE\IB_MYP2\IB_MYP2_04\078IB_MYP2_04.CDR Tuesday, 5 August 2008 11:57:51 AM PETER
FRACTIONS (Chapter 4) 79
PROPER AND IMPROPER FRACTIONS
A fraction which has numerator less than its denominator is called a proper fraction.
A fraction which has numerator greater than its denominator is called an improper fraction.
For example, 14
is a proper fraction.
74
is an improper fraction.
When an improper fraction is written as a whole number and a fraction, it is called a mixed
number.
For example, 74
can be written as the mixed number 134
. We can see this in the diagram
above as there is one whole square shaded plus three quarters of another square.
RATIONAL NUMBERS
A rational number is a number which can be written in the forma
bwhere a and b are
both integers and b 6= 0.
We can see that rational numbers are another special
type of fraction. Most of the fractions we deal with
in this course are rational numbers.
NEGATIVE FRACTIONS
Since the bar of a fraction indicates division, the fraction
¡12
means (¡1)
negative
¥ 2
positive
= ¡12
negative
Also, 1¡2
means 1
positive
¥ (¡2)
negative
= ¡12
negative
So, ¡12
= 1¡2
= ¡12
, and in general¡a
b=
a
¡b= ¡a
b
Integers arewhole
numbers.
In we saw that whenever we divided a positive by a negative,or a negative by a positive, the result is a negative.
Chapter 3
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80 FRACTIONS (Chapter 4)
SIMPLIFYING FRACTIONS
When a fraction is written as a rational number with the smallest possible denominator, we
say it is in lowest terms.
Simplify: a 721
b ¡24
a 721
= 1£73£7
= 13
b ¡24
= ¡24
= ¡1£22£2
= ¡12
The division line of fractions behaves like a set of brackets. This means that using the
BEDMAS rule, the numerator and denominator must be found before doing the division.
Simplify: a3¡ 9
22 + 4b
4£ 5
7¡ 18¥ 2
a3¡ 9
22 + 4
=¡6
4 + 4
= ¡68
= ¡3£24£2
= ¡34
fsimplify numerator and
denominator firstg
fcancel common factorg
b4£ 5
7¡ 18¥ 2
=20
7¡ 9
= 20¡2
= ¡10£22
= ¡10
Two fractions are equal or equivalent if they can be written in the same lowest terms.
We can convert a fraction to an equivalent fraction by multiplying or dividing both the
numerator and denominator by the same non-zero number.
Express: a 34
with denominator 32 b 2545
with numerator 15
Example 3 Self Tutor
Example 2 Self Tutor
Example 1 Self Tutor
1
1
1
1
1
11
1
We can a fraction by cancelling in the numerator and denominator.simplify common factors
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FRACTIONS (Chapter 4) 81
a To convert the denominator to 32 we need to multiply by 8. We must therefore
multiply the numerator by 8 also.
3
4=
24
32
b We first notice there is a common factor of 5 in the numerator and denominator.
To convert the numerator to 15 we need to multiply by 3. We must also multiply
the denominator by 3.
5
9=
15
27
COMPARING FRACTIONS
To compare fractions we first convert them to equal fractions with a common denominator
which is the lowest common multiple of the original denominators. This denominator is
called the lowest common denominator or LCD.
For example, consider the fractions 45
and 79
.
The lowest common denominator is 45.
EXERCISE 4A
1 Represent the fraction three fifths using:
a a diagram b a number line c symbol notation.
2 Express with denominator 12:
a 23
b 34
c 56
d 618
e 1545
3 Express with numerator 12:
a 37
b 65
c 49
d 2428
e 1842
4 Express in lowest terms:
a 610
b 618
c 2510
d 1435
e 3377
f 4872
g 78117
h 1251000
5 Simplify:
a 153
b ¡155
c 20¡4
d 22¡2
e 186
f ¡186
g ¡12¡4
h 3¡6
i ¡2¡8
j ¡515
k ¡7¡14
l 4¡8
£8
£8
£3
£3
The fraction baracts like a
division sign!
2545
= 5£59£5
= 59
1
1
45= 4£9
5£9= 36
4579= 7£5
9£5= 35
45
3645
> 3545
, so 45> 7
9:
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82 FRACTIONS (Chapter 4)
6 Simplify:
a32
4¡ 7b
11¡ 3
16¥ 4c
3¡ 7
5 + 3d
7 + 2
4£ 3
e8¡ 2£ 5
4£ 3f
7£ 3¡ 5
22g
¡1 + 8¥ 2
8¡ 5h
32 ¡ 2£ 5
8¡ 32
7 Simplify:
a4£¡3
6b
¡5£¡4
¡10c
5£¡8
4d
24
¡3£¡4
e6¡¡12
¡3f
3 +¡9
¡6g
5¡¡15
6¡ 8h
¡5£¡6
¡11¡ 4
8 Plot each set of fractions on a number line:
a ¡35
, 15
, 75
, 185
b ¡52
, ¡43
, 16
, 23
, 72
9 What fraction is greatest?
a 35
or 47
b 23
or 57
c 16
or 211
d 14
or 310
or 27
10 Place these fractions in ascending order:
a 18
, ¡23
, 311
, ¡16
, ¡34
b 43
, 75
, 57
, ¡34
, ¡ 611
11 Place these fractions in descending order:
a 25
, 37
, 49
, 513
, 610
b ¡58
, ¡12
, ¡47
, ¡ 711
, ¡ 613
In this section we revise rules for operations with fractions that you should have seen in
previous years.
ADDITION AND SUBTRACTION
To add or subtract fractions:
² If necessary, convert the fractions so they have the lowest common denominator.
² Add or subtract the new numerators. The denominator stays the same.
Find: a 38+ 1
2b 3
4¡ 2
3+ 1
2
OPERATIONS WITH FRACTIONSB
Example 4 Self Tutor
Ascending meanssmallest to largest.Descending meanslargest to smallest.
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FRACTIONS (Chapter 4) 83
a 38+ 1
2
= 38+ 1£4
2£4
= 38+ 4
8fLCD = 8g
= 78
fadding numeratorsg
b 34¡ 2
3+ 1
2
= 3£34£3
¡ 2£43£4
+ 1£62£6
= 912
¡ 812
+ 612
fLCD = 12g= 9¡8+6
12
= 712
When adding or subtracting mixed numbers, you can first convert them to improper fractions
and then perform the operation. However you can also add the whole numbers and fractions
separately, then combine the result.
Find: 213¡ 31
2+ 11
4
213¡ 31
2+ 11
4
= 73¡ 7
2+ 5
4fconverting to improper fractionsg
= 7£43£4
¡ 7£62£6
+ 5£34£3
= 2812
¡ 4212
+ 1512
fLCD = 12g= 28¡42+15
12
= 112
EXERCISE 4B.1
1 Find:
a 23+ 1
3b 3
4¡ 1
4c 2
5+ 4
5d 3
7¡ 5
7
e ¡12+ 5
2f 4
3¡ 7
3g 1
5¡ 3
5+ 1 h ¡1
4+ 3
4¡ 2
2 Find:
a 25+ 1
2b 3
5¡ 1
4c 1
3¡ 1
2d 2
3+ 4
5
e 37¡ 1
2f ¡1
2+ 3
4g ¡2
3¡ 5
6h 1
6+ 3
2
i 110
¡ 45
j 79+ 2
3k 5
8¡ 7
4l ¡5
7+ 11
14
3 Find:
a 123¡ 2 b 33
4¡ 11
2c 3
4¡ 21
2d 12
3+ 31
4
e 413+ 21
6f 22
3¡ 55
6g ¡21
4+ 31
8h 41
5¡ 21
6
4 Find:
a the sum of 13
and 25
b the difference between 14
and 23
c the number 3 less than 23
d the number 23
more than 114
.
Example 5 Self Tutor
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Remember that thenumber on top is the
and thenumber on the bottomis the .
numerator
denominator
84 FRACTIONS (Chapter 4)
5 a What must 15
be increased by to get 23
?
b What number is 34
less than ¡112
?
6 Find:
a 56+ 3
5+ 1
3b 2
5+ 3
8+ 1 c 3
4+ 1
6¡ 1
2d 1
3¡ 2
5+ 1
4
MULTIPLICATION OF FRACTIONS
To multiply two fractions, we multiply the two
numerators to get the new numerator and multiply
the two denominators to get the new denominator.
a
b£ c
d=
a£ c
b£ d
Find: a 23£ ¡¡4
5
¢b 1
3£ ¡2
5
¢2a 2
3£ ¡¡4
5
¢= ¡2£4
3£5f(+)£ (¡) = (¡)g
= ¡ 815
b 13£ ¡2
5
¢2= 1
3£ 2
5£ 2
5
= 1£2£23£5£5
= 475
To help make multiplication easier, we can cancel any common factors in the numerator and
denominator before we multiply.
Find: a 49£ 3
5b 4
9£ 17
8
a 49£ 3
5
= 49£ 3
5
= 415
b 49£ 17
8
= 49£ 15
8
= 56
Example 7 Self Tutor
Example 6 Self Tutor
1
3
1 5
23
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FRACTIONS (Chapter 4) 85
EXERCISE 4B.2
1 Find:
a 12£ 3
5b 1
4of 3
4c¡35
¢2d¡¡1
3
¢£ 25
2 Evaluate, giving your answer in simplest form:
a 34£ 1
3b 2
5£ 3
4c¡¡1
2
¢£ 23
d 47
of 28
e 54£ ¡¡2
3
¢f 4
7£ 21
16g 11
2£ ¡¡1
3
¢h¡¡3
4
¢2i 3
4of 124 j 3
8£ 4
9k¡¡2
3
¢£ ¡¡98
¢l 2
5of ¡65
3 Find the product of 27
and 125
.
RECIPROCALS
Two numbers are reciprocals of each other if their product is one.
For any fractiona
b, we notice that
a
b£ b
a= 1.
So, the reciprocal ofa
bis
b
a.
DIVIDING FRACTIONS
To divide by a number, we multiply by its reciprocal.
Find:
a 54¥ 2
3b 11
3¥ 31
2
a 54¥ 2
3
= 54£ 3
2
= 158
fmultiplying by
reciprocalg
b 113¥ 31
2
= 43¥ 7
2
= 43£ 2
7
= 821
fconverting to
improper fractionsg
Example 8 Self Tutor
Remember touse BEDMAS.
4 Find:
a 23£ 1
4£ 3
5b 3
8£ ¡¡4
3
¢£ ¡¡25
¢c 2
3+ 3
4£ 2
3d 3
5¡ 5
2£ 4
3
e 35£ 1
3+ 2
3£ 1
4f 4
3£ 1
2¡ 1
6£ 2
3
g¡23
¢2 ¡ 34£ 12
3h 4£ 11
3¡ 5£ 2
7
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86 FRACTIONS (Chapter 4)
EXERCISE 4B.3
1 State the reciprocal of:
a 34
b 27
c 4 d ¡12
e ¡2 f 58
g ¡52
h ¡1
2 Find:
a 23¥ 1
6b 5
7¥ 1
3c 3
4¥ ¡¡1
2
¢d 4
5¥ 3
e 14¥ 12
3f 23
4¥ 2
3g 11
2¥ ¡¡3
4
¢h 31
5¥ 11
3
3 Find:
a 23¡ 3
2¥ 4
5b 5
3¥ 1
2+ 4
3c 1
2£ 2
5¡ 3
4¥ 6
5d 2
5¥ ¡¡1
2
¢+ 3
4£ 2
5
4 Find:
EVALUATING FRACTIONS USING A CALCULATOR
When we enter operations into a calculator, it automatically uses the BEDMAS rules.
However, we need to be careful with more complicated fractions because we need to divide
the whole of the numerator by the whole of the denominator. To make sure the calculator
knows what we mean, we insert brackets around the numerator and the denominator.
For example, consider the expression5 + 6
3¡ 1.
If we type in 5 + 6 ¥ 3 ¡ 1, the calculator will think we want 5+ 63¡ 1, and so
it will give us the wrong answer.
We need to insert brackets around both the numerator and denominator, giving(5 + 6)
(3¡ 1).
We type in ( 5 + 6 ) ¥ ( 3 ¡ 1 ) .
Find the value of: a15¡ 33
17¡ 7£ 3b
15 + 3£ 52
11¡ 25¥ 2
a15¡ 33
17¡ 7£ 3=
(15¡ 33)
(17¡ 7£ 3)= 41
2
Calculator: ( 15 ¡ 33 ) ¥ ( 17 ¡ 7 £ 3 ) =
b15 + 3£ 52
11¡ 25¥ 2=
(15 + 3£ 52)
(11¡ 25¥ 2)= ¡60
Calculator: ( 15 + 3 £ 5 x2 ) ¥ ( 11 ¡ 25 ¥ 2 ) =
Example 9 Self Tutor
a the average of 14
and 34
b the number midway between ¡12
and 23
c the average of 12
, 23
and 34
d the quotient of 13
and 34
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FRACTIONS (Chapter 4) 87
EXERCISE 4B.4
Simplify: a2 + 1
3
2¡ 13
b23+ 3
423¡ 3
4
c13+ 1
4
1¡ 15
a2 + 1
3
2¡ 13
=
Ã2 + 1
3
2¡ 13
!3
3fLCD = 3g
=6 + 1
6¡ 1
= 75
b23+ 3
423¡ 3
4
=
Ã23+ 3
423¡ 3
4
!12
12fLCD = 12g
=8 + 9
8¡ 9
= 17¡1
= ¡17
c13+ 1
4
1¡ 15
=
Ã13+ 1
4
1¡ 15
!60
60fLCD = 60g
=20 + 15
60¡ 12
= 3548
Example 10 Self Tutor
1 Use a calculator to find the value of:
a 5 + 105
b5 + 10
5c 3¡ 9
6
d3¡ 9
6e 15¡ 8¥ 4 + 10 f
15¡ 8
4 + 10
g4 + 82
11¡ 35h
(4 + 8)2
11¡ 35i
4 +82
24¡ 13
j18¡ 22
18¡ 8£ 2k
¡4¡ 11
12¡ 9¥ 2l
22 + 11¥ 2
23¡ 3£ 4
FRACTIONS WITHIN FRACTIONS
When faced with fractions such as2 + 1
3
2¡ 13
, it may be very tempting to reach for a calculator.
However, this fraction can actually be simplified easily by hand.
We multiply the fraction top and bottom by the lowest common denominator (LCD) of the
little fractions within it. We are really just multiplying by 1, so the value of the fraction is
not changed.
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INVESTIGATION 1 DIVISION BY ZERO
88 FRACTIONS (Chapter 4)
EXERCISE 4B.5
1 Simplify:
a1 + 1
2
1¡ 12
b2¡ 1
4
2 + 14
c1 + 2
3
2¡ 13
d12+ 3
434¡ 1
2
e12+ 1
512¡ 1
5
f13+ 1
413¡ 1
4
g12+ 1
313¡ 1
4
h1¡ 1
312¡ 2
5
i1 + 1
4¡ 1
3
1¡ 12+ 1
5
What to do:
1 a Copy and complete: i Since 62= 3, 2£ 3 = ::::::
ii Since 205= 4, 5£ 4 = ::::::
iii Since 20= a, 0£ a = ::::::
b In iii above, we are saying that if 20
is equal to some number a, then 0 = 2.
Do you agree with this deduction?
c What can we conclude from b?
2 a Evaluate the following:
i 1¥ 12
ii 1¥ 15
iii 1¥ 120
iv 1¥ 11000
v 1¥ 11 000 000
b Copy and complete: As the number we are dividing 1 by gets smaller and
smaller, the answer gets ...... .
In this section we see how fractions are applied to the real world. They can describe a part
of a quantity or a group of objects.
For example, 34
of 12 coins is 9 coins
and 34£ 12 = 3
4£ 12
1= 9
Examples like this one tell us that ‘of’ is replaced by £.
PROBLEM SOLVINGC
55 55 55 55 55 55
55 55 55 55 55 55
We have already indicated that division by zero (0) is not permitted. In fact,
numbers like 20
are excluded from being rational numbers because 20
is
not real and cannot be placed on a number line.
3
1
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FRACTIONS (Chapter 4) 89
Find 35
of E85. 35
of E85
= 35£ E
851
= E51
EXERCISE 4C
1 Find 23
of $213:
2 Find 37
of $434:
3 Julie owes Gigi 35
of E1336:25. How much does she owe Gigi?
4 Millie calculated that her bicycle cost 183
of the cost of her father’s car. If the car cost
$38 014, what did her bicycle cost?
5 The price of a shirt is 213
of the cost of a suit. If the suit costs E292:50, find the cost of
the shirt.
Rob eats 13
of a watermelon one day and 38
of it the next day.
What fraction of the watermelon remains?
6 Pam uses 58
of a cabbage for the evening meal. What fraction remains?
7 Phong eats 13
of a chocolate bar in the morning and 58
of it in the afternoon. What
fraction remains?
8 Over three successive days Colin builds 13
, 15
and 14
of the brickwork of his new garage.
What fraction must he complete on the fourth and final day?
9 200 kg of sugar must be poured into packets so there is 25
kg of sugar per packet. How
many packets will be filled?
10 2400 kg of icecream is put into plastic containers which hold 34
kg each. How many
plastic containers are needed?
Example 12 Self Tutor
Example 11 Self TutorRemember that ‘of ’
means multiply.
1
17
The fraction remaining
= 1¡ 13¡ 3
8ffrom the whole we subtract the fractions eateng
= 2424
¡ 1£83£8
¡ 3£38£3
fLCD = 24g= 24¡8¡9
24
= 724
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90 FRACTIONS (Chapter 4)
11 Jon says that his income is now 312
times what it was 20 years ago. If his current annual
income is E63 000, what was his income 20 years ago?
12 Silvia owns 13
of a bakery, 25
of a grocers shop and 16
of a clothing store. The profits
from these stores last year were $215 610, $436 215, and $313 200 respectively. How
much profit did Silvia make from the three businesses last year?
If 47
of an amount of money is $480, then
17
of the amount = $480¥ 4 = $120.
Thus 67
of the amount = 6£ $120 = $720.
and 77
is the whole amount which is 7£ $120 = $840.
So, given the value of a number of parts of a quantity we can find one part of the quantity
and then the whole quantity or another fraction of the quantity. This is called the unitary
method.
If 38
of a shipping container holds 2100 identical cartons, how many cartons will fit
into:
a 58
of the container b
38
of the container holds 2100 cartons.
) 18
of the container holds 2100¥ 3 = 700 cartons.
a So, 58
holds 700£ 5
= 3500 cartons
b The whole is 88
which is 700£ 8
= 5600 cartons
EXERCISE 4D
1 23
of an amount of money is $519. Find:
a 13
of the money b the whole amount.
2 45
of a soy bean crop is 2104 tonnes. Find the weight of:
a 15
of the crop b the whole crop.
3 211
of Jo’s weekly earnings are paid as income tax. She has $666 remaining after tax.
What is her total weekly pay?
4 313
of a field was searched for truffles and 39 were found. How many truffles would we
expect to find in the remainder of the field?
Example 13 Self Tutor
D THE UNITARY METHODWITH FRACTIONS
the whole container?
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magentacyan yellow black
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Y:\HAESE\IB_MYP2\IB_MYP2_04\090IB_MYP2_04.CDR Tuesday, 29 July 2008 3:37:29 PM PETER
FRACTIONS (Chapter 4) 91
5
6 Alfredo sent 25
of his potato crop to market last
week. This week he sent 23
of the remainder.
a What fraction of his crop has now gone to
market?
b If he has 860 kg remaining, what was the
original weight of the crop?
7 Annika pays 225
of her weekly income into
a retirement fund. If she pays $42 into the
retirement fund, what is her:
a weekly income b annual income?
8 Jamil spent 14
of his weekly salary on rent, 15
on food, and 16
on clothing and
entertainment. The remaining money was banked.
a What fraction of Jamil’s money was banked?
b If he banked $138:00, what is his weekly salary?
c How much did Jamil spend on food?
9 In autumn a tree starts to shed its leaves. 25
of the leaves fall off in the first week, 12
of those remaining fall off in the second week, and 23
of those remaining fall off in the
third week. 85 leaves now remain.
a What fraction of leaves have fallen off at the end of:
i the second week ii the third week?
b How many leaves did the tree have to start with?
ra
b=
papb
for positive numbers a and b.
SQUARE ROOTS OF FRACTIONSE
We have seen previously how 32 = 9 indicates thatp9 = 3.
In the same way,¡25
¢2= 4
25indicates that
q425
= 25
.
However,p4p25
= 25
also.
So, we observe that
Last week we picked 13
of our grapes and this
week we picked 14
of them. So far we have
picked 3682 kg of grapes. What is the total
weight of grapes we expect to pick?
IB MYP_2
magentacyan yellow black
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75
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Y:\HAESE\IB_MYP2\IB_MYP2_04\091IB_MYP2_04.CDR Monday, 18 August 2008 3:47:10 PM PETER
INVESTIGATION 2 CONTINUED FRACTIONS
92 FRACTIONS (Chapter 4)
Find a
q49
b
q214
EXERCISE 4E
1 Copy and complete:
a Since¡12
¢2= 1
2£ 1
2= 1
4,q
14= ::::::
b Since¡23
¢2= :::::: = ::::::,
p:::::: = 2
3
c Since¡37
¢2= :::::: = ::::::,
p:::::: = ::::::
2 Find:
aq
19
bq
116
cq
1121
dq
425
eq
916
fq
1649
g
q259
h
q254
i
q81100
j
q10049
k
q9
121l
q36169
3 Find:
a
q614
b
q179
c
q1 916
d
q549
e
q3 116
f
q111
9
In this investigation you will need to find the reciprocals of fractions using
your calculator. To do this you can use the function marked or x-1 .
What to do:
1
a 1 + 2 1 + 2 = and keep this
answer in display.
b 1 + 2
1 + 2
then £ 2 + 1 = and keep this
answer in display.
Example 14 Self Tutor Before finding thesquare root, convertmixed numbers toimproper fractions.
1x
1x
Use your calculator to find the decimal values of the followingfractions. Give all answers using the full display of your calculator.
a
q49
=p4p9
= 23
b
q214
=q
94
=p9p4
= 32
= 112
IB MYP_2
magentacyan yellow black
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25
75
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50
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Y:\HAESE\IB_MYP2\IB_MYP2_04\092IB_MYP2_04.CDR Tuesday, 29 July 2008 3:40:27 PM PETER
REVIEW SET 4A
c 1 + 2
1 + 2
1 + 2
then £ 2 + 1 =
d 1 + 2
1 + 2
1 + 2
1 + 2
e Continue this process until it is obvious not to proceed any further.
2 Make up other continued fractions of your own choosing. For example,
2 + 3, 2 + 3
2 + 3
, 2 + 3
2 + 3
2 + 3
, ......
Evaluate each fraction and record your observations.
3 Use your skills in adding and dividing fractions to explain the results above.
1x
FRACTIONS (Chapter 4) 93
² common fraction ² denominator ² fraction
² improper fraction ² integer ² lowest common denominator
² lowest terms ² mixed number ² number line
² numerator ² proper fraction ² rational number
² reciprocal
1 Simplify:
a¡24
8b
¡3
¡9c
4¡ 7
11 + 22d
6¡ 3¥ 3
2 + 10¥ 2
2 Plot the fractions ¡13
, 23
, 113
and 223
on a number line.
3 Write in ascending order: ¡34
, 114
, 23
, ¡112
and 45
.
4 Find:
a 37+ 5
14b 2
3¡ 4
5c ¡11
4+¡2
3d 1
4¡ 3
5¡ 1
2
5 What number is 34
more than 23
?
6 Find:
a 23£ 11
2b ¡2
3¥ 1
2c ¡3£ ¡¡2
3
¢2d 4
7of $630
7 Find the number which is midway between 34
and ¡1.
8 Simplify: a2 + 1
3
1 + 23
b34¡ 2
5
1 + 35
KEY WORDS USED IN THIS CHAPTER
IB MYP_2
magentacyan yellow black
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Y:\HAESE\IB_MYP2\IB_MYP2_04\093IB_MYP2_04.CDR Thursday, 31 July 2008 12:23:26 PM PETER
REVIEW SET 4B
94 FRACTIONS (Chapter 4)
9 Ken spent 14
of his money on Monday and 25
of it on Tuesday. What fraction of his
money remains?
10 200 kg of brass is melted down and cast into ornamental frogs each weighing 320
kg.
How many frogs are made?
11 29
of Freda’s income is used to pay rent. If her rent is E115 per week, what is her
weekly income?
12 Fong’s family bought a large sack of rice. They consumed 720
last month and 811
of
the remainder this month. What fraction of rice:
a has been consumed b remains?
13 Find: a¡23
¢2b
¡212
¢2cq614
1 Plot 34
, ¡112
, 114
and 3 on a number line.
2 Simplify:
a¡12
¡4b
5
¡25c
6 + 22
6¡ 23d
12 + 8¥ 2
12¡ 8£ 2
3 What number is 23
less than 112
?
4 Find: a¡112
¢2b
¡23
¢3c
5 Write in descending order: ¡45
, ¡113
, 12
, ¡ 110
, 56
.
6 Find:
a 13¡ 2
5b 21
3¡ 11
2c 3
5¥ (¡2) d 1
10¡ 2
3+ 1
2
7 Find:
a ¡34£ 2 b 3
5¥¡1
2c 3
4of $84 d 12£ ¡¡1
2
¢38 Find the average of 2, 3
4and 1
2.
9 Simplify: a1¡ 3
4
2 + 14
b12+ 1
3¡ 1
6112
¡ 14
10 What must ¡13
be increased by to get 45
?
11 What fraction of material is left if 15
, 14
and 16
are used to make dresses?
12 Jacob’s business investments have been bad this year. He has lost a 13
share in $45 000
and a 25
share in $65 000. How much has he lost from these two investments?
13 325
of Jim’s income is used to pay for health insurance and superannuation. If this
amounts to $105 per week, find Jim’s:
a weekly income b annual income.
q279
IB MYP_2
magentacyan yellow black
0 05 5
25
25
75
75
50
50
95
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100
100 0 05 5
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25
75
75
50
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Y:\HAESE\IB_MYP2\IB_MYP2_04\094IB_MYP2_04.CDR Monday, 18 August 2008 3:48:09 PM PETER
