Mathematics-MYP1-1

6:06 Foundation Worksheet

Name: Multiplication of Fractions

Class:

Simple rules to follow when multiplying fractions.
• Write each part as a fraction.
• Simplify by cancelling or dividing top and bottom.
• Multiply numerators and denominators.

Examples 2 5 × --3--- 3 1-- × 2-- 4 1-- × 1----8- 5 1-- × -1---2-

1 4 × 1-- 20 73 6 20 3 16

7 = 1 -5- × --3--- = --2--- = -1- × -1---8- 3 = 1-- × 1----2- 4 1

= 4-- × 1-- 1 20 4 21 1 6 20 1 3 16 4

17 = -3- = --3--- = 1--

= 4-- 4 20 4

7

1 a 2 × -1- b -2- × -1- Exercise d -5- × --1---1--- e -2- × 3

4 14 c 5 × --1---1--- 1 100 9

f 4 × --1--- g 5 × --3--- 100 i 4 × --5--- j 10 × --7---

16 20 h ----7---- × 10 24 80

k 2 × 1----9- l --8--- × 3 100 n 1----3- × 4 o 7 × --8---

40 27 m 6 × --1--- 60 77

2 a 1-- × 4-- b 1-- × 1----2- 30 d -1- × --6--- e 1-- × --8---

28 2 15 c -1- × -1---0- 2 10 4 11

f 1-- × --9--- g -1- × 1----2- 2 20 i --1--- × -4---0- j -1- × 1----5-

3 10 6 20 h 1-- × -1---5- 10 45 3 18

k -1---8- × -1- l --8--- × -1- 5 16 n 1-- × -2---0- o 1-- × --2---8---

24 2 16 4 m 1-- × -2---4- 5 31 4 100

3 a -1- × -1- b 1-- × 1-- 8 25 d 1-- × --1--- e -1- × 1--

23 43 c --1--- × -1- 2 10 35

f --1--- × 1-- g --1--- × --1--- 10 7 i -1- × 1-- j 1-- × --1---

16 2 10 10 h -1- × -1- 65 4 25

44

Fun Spot 6:06 | Teacher: ‘You missed school yesterday, didn’t you?’

Match the letters with the answer below.

C 1-- × -1---0- D -1- × --3--- E 5 × --1--- H 3-- × 2 M 1-- × 1----8- N -2- × 1--

5 15 3 10 30 8 6 20 92

O 1-- × 1-- R -1- × -1- S 1-- × 8 T -1- × 4 U 1-- × --8--- V --1--- × -2---0- Y --8--- × 1--

36 22 4 8 4 16 10 25 11 8

:‘ .’

2 -1- -1- --1--- -1- -1- 1-- -1- --1--- -1- --2--- 1-- -1- --1--- --3--- 1-- --2--- 3--
9 18 2 25 6 4 11 20 8 15 4
2 8 10 6 9 2

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6:07 Foundation Worksheet

Name: Division Involving Fractions

Class:

Examples Divisions ask ‘how many?’

1 Note that 1----2- is shaded. • 10 ÷ 2 means how many 2s in 10.

15 • 6 ÷ -1- means how many -1- s in 6.

How many --3--- in -1---2- ? 4. 44

15 15 • -1---5- ÷ --3--- means how many --3--- s
20 20 20
Then 1----2- ÷ --3--- = 4.
in 1----5- .
15 15
20
2 -1---5- is shaded.
3 1----0- is shaded.
20
12
How many --5--- in 1----5- ? 3.
How many --5--- in 1----0- ? 2.
20 20
12 12
Then -1---5- ÷ --5--- = 3.
Then 1----0- ÷ --5--- = 2.
20 20
12 12

Exercise

1 a How many --1--- in --8--- ? 2 a How many --2--- in 1----8- ?

12 12 25 25
∴ --8--- ÷ --1--- = ∴ 1----8- ÷ --2--- =
12 12 25 25

b How many --2--- in --8--- ? b How many --9--- in 1----8- ?

12 12 25 25

∴ --8--- ÷ --2--- = ∴ -1---8- ÷ --9--- =

12 12 25 25

3 a How many --3--- in --6--- ? 4 a How many --4--- in -1---6- ?

10 10 20 20

∴ --6--- ÷ --3--- = ∴ 1----6- ÷ --4--- =

10 10 20 20

b How many --2--- in --6--- ? b How many --8--- in -1---6- ?

10 10 20 20

∴ --6--- ÷ --2--- = ∴ 1----6- ÷ --8--- =

10 10 20 20

5 1----4- is shaded. 6 1----2- is shaded.

21 16

a 1----4- ÷ --7--- = a 1----2- ÷ --4--- =

21 21 16 16

b 1----4- ÷ --2--- = b 1----2- ÷ --3--- =

21 21 16 16

When the denominators are the same, just divide the numerators.

7 a 6-- ÷ -2- b 1----5- ÷ --3--- c 2----0- ÷ -1---0- d -2---0- ÷ --4--- e -5- ÷ -1-

99 17 17 27 27 27 27 88

f --4---0--- ÷ ----8---- g --2---7--- ÷ ----9---- h 2----1- ÷ --7--- i --7--- ÷ --1--- j --4--- ÷ --4---

100 100 100 100 40 40 19 19 11 11

k 1----8- ÷ --6--- l -3---0- ÷ -1---0- m 3----0- ÷ --5--- n -3---3- ÷ --3--- o -2---4- ÷ -1---2-

25 25 31 31 47 47 40 40 35 35

p 2----4- ÷ --8--- q -1---8- ÷ --2--- r 1----3- ÷ 1----3- s 4----4- ÷ -1---1- t -5---0- ÷ 2----5-

35 35 20 20 18 18 51 51 57 57

INTERNATIONAL MATHEMATICS 1 FOUNDATION WORKSHEETS 22 © Pearson Education Australia 2007.
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6:08 Foundation Worksheet

Name: Fractions of Quantities

Class:

Examples 2 Find -1- of 40 m 3 Find -3- of 35 L 4 Find -5- of $200

1 Find 1-- of $60 5 5 8

3 -1- of 40 m 1-- of 35 L 1-- of $200

-1- of $60 5 5 8

3 = 40 m ÷ 5 = 35 L ÷ 5 = $200 ÷ 8
=7L = $25
= $60 ÷ 3 =8m
= $20 ∴ 3-- of 35 L ∴ -5- of $200

Fractions are divisions. 5 8

=3×7L = 5 × $25
= 21 L = $125

Exercise

1 a 1-- of 20 min b -1- of 6 kg c 1-- of $20 d -1- of 90 m

2 2 4 3

e --1--- of 70 mm f 1-- of $24 g ----1---- of $5000 h 1-- of 36 km

10 8 100 4

i -1- of 66 t j 1-- of 75 kg k --1--- of 180 L l -1- of $180

6 5 10 3

m 1-- of 44 mm n -1- of 960 t o -1- of 48 h p -1- of 555 min

2 8 4 5

2 a -1- of 40 3 88888 a --1--- of $80 4 6 a -1- of $30

10 10 4 88888 10 5

10 10 b 2-- of 40 b --3--- of $80 6 b -2- of $30

4 10 65

c -3- of 40 c --7--- of $80 6 c -3- of $30

4 10 5
6

5 a -3- of $20 b --3--- of 70 mm c 5-- of $24 d ----7---- of $5000

4 10 8 100

e --7--- of 44 t f -2- of 75 kg g -2- of $180 h 3-- of 555 min

11 5 3 5

i -5- of 24 cm j --7--- of 50 L k 5-- of 27 kg l --3--- of 200 h

6 10 9 50

m -3- of 48 m n -4- of $60 o -1---9- of $75 p --5--- of 36 cm

8 5 25 12

Fun Spot 6:08 | Do you know this book?

Calculate each and place each letter above its answer below.

A 1-- of 18 B 1-- of 28 E --1--- of 200 G -1- of 48 I 1-- of 60 L --1--- of 80

3 4 10 6 5 20

M 4-- of 20 N -2- of 60 S -7- of 16 T --7--- of 60 U -5- of 27 Y 3-- of 32

5 3 8 20 9 4

‘’ .

4 6 21 20 6 8 6 12 40 7 24 16 12 14 21 24 7 15 14 14

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6:09 Foundation Worksheet

Name: Review of Percentages

Class:

Examples If possible simplify fractions by cancelling.

A percentage is a fraction over 100 or a decimal with 2 places.

1 9% = ----9---- 2 73% = --7---3--- 3 60% = --6---0--- = -3- 4 45% = --4---5--- = --9---

100 100 100 5 100 20

= 0⋅09 = 0⋅73 = 0⋅60 = 0⋅6 = 0⋅45

Exercise

1 a What percentage 2 a What percentage
is coloured? is coloured?

b What percentage b What percentage
is not coloured? is not coloured?

c What fraction is c What fraction is
coloured? coloured?

d What fraction is d What fraction is
not coloured? not coloured?

3 Write as a fraction and as a decimal.

a 3% b 17% c 63% d 99% e 27% f 20% g 5%
k 25% l 50% m 18% n 62%
h 6% i 15% j 44% r 46% s 77% t 1%
f 0⋅20
o 55% p 36% q 83% l 0⋅45
r --2---8---
4 Write as a percentage.
100
a ----7---- b 0⋅07 c --2---3--- d --7---8--- e 0⋅52
h 0⋅75 k 0⋅35
100 100 100 q 0⋅61

g --3---9--- i --9---0--- j --1---6---

100 100 100

m 0⋅02 n --5---8--- o 0⋅50 p --4---7---

100 100

Fun Spot 6:09 | Do you know this book?

Write each as a simplified fraction. Match each letter with the answer below.

A 10% B 19% D 40% E 75% H 30% I 16%

L 35% O 42% R 51% S 50% T 4% Y 85%

‘ ’

--3--- 2----1- --7--- --4--- -2- --1--- -1---7- --1--- --5---1--- 3-- --1--- --1---
10 50 20 25 5 10 20 25 100 4 10 25

.

--1---9--- 1----7- --5---1--- --3--- -2---1- 2-- --1--- --3--- -2---1- --5---1--- 1-- -3-
100 20 100 10 50 5 10 10 50 100 2 4

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6:10 Foundation Worksheet

Changing Fractions and
Decimals to Percentages

Name: Class:

Examples To change to a percentage, multiply by 100.

1 --2---7--- = --2---7--- × -1---0---0- 1 • For a fraction this means × 1----0---0-- .
100 1100 1 1
%
• For a decimal, move the point 2 places to the right.

= 27%

2 0⋅42 3 3-- = 3-- × 1----0---0- 20 4 0⋅03 5 0⋅7
= 0⋅42 × 100% 5 15 1 = 0⋅03 × 100% = 0⋅7 × 100%
%
= 42% = 3% = 70%
= 60%

Exercise

1 Write as percentages.

a --1---5--- b ----2---- c --4---7--- d --9---3--- e --7---2---

100 100 100 100 100

f --3--- g 1-- h -1- i ----1---- j --3---3---

50 4 5 100 100

k --1--- l --8---4--- m --9--- n --9--- o --6---

20 100 10 20 25

p -1- q -1---1- r -3- s 1----2- t --1---

2 50 4 25 10

u --7---7--- v 4----1- w --7--- x -1---9- y --1---9---

100 50 10 20 100

2 Write as percentages. c 0⋅64 d 0⋅99 e 0⋅02
h 0⋅85 i 0⋅80 j 0⋅18
a 0⋅14 b 0⋅07 m 0⋅53 n 0⋅23 o 0⋅01
r 0⋅9 s 0⋅25 t 0⋅58
f 0⋅31 g 0⋅30
k 0⋅44 l 0⋅4

p 0⋅29 q 0⋅71

Fun Spot 6:10 | Have you heard of this book?

Place these in order from largest (1st) to smallest (11th). Match the letters with

the order below to complete the title.

A 0⋅74 B --4---1--- D --7---8--- E 0⋅7 G 0⋅08 H 0⋅8 I 3-- M 0⋅88 N 4----1- T 40% Y 85%
100 100 4 50

‘’

10th 4th 8th 9th 6th 11th 9th 7th 3rd 11th

.

9th 2nd 5th 6th 3rd 7th 4th 1st 6th 10th 8th

INTERNATIONAL MATHEMATICS 1 FOUNDATION WORKSHEETS 25 © Pearson Education Australia 2007.
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6:12 Foundation Worksheet

Name: Finding a Percentage of
a Quantity

Class:

Examples

Change the percentage to a decimal or fraction and multiply.
Usually it is easier to change to a decimal, but there are some
fractions that are easier than decimals.

1 4% of 200 kg 2 60% of $700 3 10% of 40 4 50% of 148 L 5 25% of 64 t
= 0⋅04 × 200 kg = 0⋅6 × $700 = --1--- × 40 = 1-- of 148 L = -1- of 64 t

= 8 kg = $42 10 2 4

=4 = 74 L = 16 t

Exercise

1 a 50% of $30 b 10% of 80 g c 25% of 40 kg d 50% of 60 m
e 25% of 16 f 25% of 36 L g 10% of $200 h 10% of 150 cm
i 50% of 28 t j 25% of 48 g k 10% of 90 l 25% of 88 m
m 50% of 50 h n 50% of 422 t o 25% of 120 kg p 10% of $450

2 a 20% of $20 b 70% of $50 c 3% of 600 t d 5% of 700 kg
e 40% of 400 m f 6% of 900 g g 30% of 200 h 20% of 120 s
i 80% of $50 j 2% of 1200 km k 60% of 90 d l 90% of $20
m 8% of 3000 m n 30% of 180 cm o 20% of 800 g p 4% of $5000
q 11% of 300 t r 40% of $70 s 60% of 500 L t 15% of 200

Fun Spot 6:12 | Teacher: ‘What came after the Stone Age and the Bronze Age?’

Change each decimal to a percentage. Match the letters with the answers below.

A 0⋅05 D 0⋅35 E 0⋅3 G 0⋅53 H 0⋅50

N 0⋅01 S 0⋅15 T 0⋅1 U 0⋅26

:

15% 10% 26% 35% 30% 1% 10%

‘ - .’

10% 50% 30% 15% 5% 26% 15% 5% 53% 30%

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6:13 Foundation Worksheet

Name: One Quantiy as a Percentage
of Another

Class:

Examples Three simple steps:
• Check that units are the same (eg both $, cm, g).
• Make them into a fraction in the order given.
• Multiply by 100 to make a percentage.

What percentage are the following?

1 20c of 50c 2 18 g of 100 g 3 14 L of 25 L 4 $10 of $40

= 2----0- = --1---8--- = 1----4- = -1---0-
50 100 25 40

= -2---0- × 1----0---0- % = --1---8--- × -1---0---0- % = -1---4- × 1----0---0- % = -1---0- × -1---0---0- %
50 1 100 1 25 1 40 1

= 40% = 18% = 56% = 25%

Exercise

1 What fraction are the following?

a 10 g of 20 g b 20 m of 100 m c $7 of $100 d 15c of 30c
g 33 kg of 100 kg h 150 of 300
e 20 t of 80 t f 10 min of 50 min k 20 mm of 25 mm l 50c of 100c
o 14 g of 20 g p 10 h of 24 h
i $120 of $200 j 90 L of 100 L

m 66 km of 99 km n 80 kg of 240 kg

2 What percentage are the following?

a 10 g of 20 g b 20 m of 100 m c $7 of $100 d 15c of 30c
g 33 kg of 100 kg h 150 of 300
e 20 t of 80 t f 10 min of 50 min k 20 mm of 25 mm l 50c of 100c
o 89 L of 100 L p $1 of $50
i $120 of $200 j 90 L of 100 L s 50 s of 200 s t 30 t of 40 t

m 7 mL of 10 mL n 8 cm of 25 cm

q 4 g of 25 g r 9 min of 50 min

Fun Spot 6:13 | Teacher: ‘If you multiplied 395 by 246 what would you get?’

Match the letter for each question with the simplified fraction below.

A 1----5- D 1----0- E 2----0- G --2---0--- H -1---6- N -2---4-

25 40 24 100 20 50

O --4--- R -5---0- S 2----0- T -4---5- U --3---5--- W 1----6-

12 90 30 60 100 18

: ‘ ’.

-2- -3- --7--- 1-- -5- -1---2- 3-- -3- 4-- -5- 8-- 5-- -1- 1----2- -1- -3- -1---2- -2- 8-- 5-- -5-
3 4 20 4 6 25 4 456 9 9 3 25 5 5 25 3 9 6 9

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Foundation Worksheet

8:03 Patterns and Rules

Name: Class:

Examples

1 Complete this pattern. 2 Complete the table. 3 Complete the rule.
6, 12, 18, . . . , . . .
The rule is ‘add 6’, so Top 1 234 Top 0 123
the pattern becomes Bottom 4 8 12 Bottom 8 9 10 11
6, 12, 18, 24, 30
The bottom is 4 times the Bottom = top + . . .
top number, so the missing 8 is added each time,
number is 4 × 4 = 16 so bottom = top + 8

1 Complete these patterns. Exercise c 20, 18, 16, . . . , . . .
a 5, 10, 15, . . . , . . . f 2, 4, 8, . . . , . . .
d 3, 6, 12, . . . , . . . b 4, 6, 8, . . . , . . .
e 20, 30, 40, . . . , . . .

2 Complete these tables.

a Top 1234 b Top 1234 c Top 1234

Bottom 2 4 6 Bottom 11 12 13 Bottom 5 10 15

d Top 0123 e Top 3456 f Top 1234

Bottom 456 Bottom 9 12 15 Bottom 456

3 Complete the rule used in each table below.

a Top 1234 b Top 3456 c Top 0123

Bottom 7 8 9 10 Bottom 4 5 6 7 Bottom 0 7 14 21

Bottom = top + . . . Bottom = top + . . . Bottom = top × . . .

d Top 1234 e Top 10 9 8 7 f Top 123 4
1 5
Bottom 10 20 30 40 Bottom 4 3 2 Bottom 2 3 4

Bottom = top × . . . Bottom = top − . . . Bottom = . . . + top

4 Write the rule for each table in question 2.

a Bottom = . . . × top b Bottom = . . . + top c Bottom = top × . . .
f Bottom =
d Bottom = top + . . . e Bottom =

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9:02 Foundation Worksheet

Name: Making Sense of Algebra

Class:

Examples How many counters are here?

Imagine x is a 1x 2y 3 aa 4 aa
box containing an bb b
unknown number x+4 y+2 2a + 2
of counters . 2a + 3b

Exercise

1 Write the number of counters in each case.

ax by c xxx d ea

f yy gx h y i aa j yyy
yy x a yy

2a y y b xx c xy d xxx e abb
y yy b

fx g aba hx x i xyxx j yyy
x bb x xyx y

k xyx la m aaa nx o mn
bbb bb yy

Fun Spot 9:02 | What’s the difference between a night-watchman and

a butcher?

Each expression can be written in a shorter form.

Match the letters to the abbreviations.

A 6×a D a×3 E 1×a G a×a H a÷2 I a×b K y×x
T m×2 W y×1 Y m ÷ 10
N x÷4 O x×3 R y÷4 S m×m

3x -x- a m2 2m 6a -m---- m2 6a y 6a xy a
4 10

6a -x- 3a 2m -a- a 3x 2m -a- a -y-
4 2 2 4

!

y a ab a2 -a- m2 6a m2 2m a 6a xy
2

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9:03 Foundation Worksheet

Name: Substitution

Class:

Examples To substitute, put a number in
1 Find the value of the pronumeral. place of a letter, then calculate.

a 5a, if a = 6 b m − 6 if m = 4
5a = 5 × a m−6=4−6
=5×6 = −2
= 30

2 Given that x = 8 and y = 5, find the value of these.

a x+y b -x- c 4x + 7 d y2 − 10
x+y=8+5 2 4x + 7 = 4 × x + 7 y2 − 10 = 52 − 10
= 13 -x- =4×8+7 = 25 − 10
2 = x ÷ 2 = 39 = 15

=8÷2

=4

Exercise

1 Find the value of each expression.

a 3x, if x = 12 b 2y, if y = 20 c a + 3, if a = 8 d k − 10, if k = 13

e m2, if m = 3 f t + 11, if t = 4 g d − 2, if d = 2 h 7p, if p = 9

i 18 − c, if c = 10 j 9x, if x = 4 k 10 + w, if w = 7 l 8d, if d = 3
m v2, if v = 1 n r + 6, if r = 0 o -3x-, if x = 12 p -1-a--0- , if a = 50

2 Given that x = 12 and y = 4, find the value of each expression.

a -x- b x−y c 5y d y2 e y−7 f 20 − x g 2x − 5
6 i -x- j x2 − 20 k y2 + 8 l xy m y−x n x − 5y
t 3x − 6 u 15 − 3y
h x + 2y y

o -y- + 5 p 3x + 4y q -x- −7 r 2x − 3y s 10y − x
2 3

Fun Spot 9:03 | What’s the difference between a monster and a biscuit?

Simplify the following. Match the letters to the answers.

A 6×a D 12 × b E 3 × 4 × a I 3 × 8 × a K 10 × 6 × b

M 20b + 6b N 6 × 8a O a×b R b×5 S 4×2×a
T 2 × 3b U 5 × 7b V 8×2×b Y 2×a×b

12a 16b 12a 5b 6b 5b 24a 12a 12b 6b ab 12b 35b 48a 60b 6a

?

26b ab 48a 8a 6b 12a 5b 24a 48a 2ab ab 35b 5b 6b 12a 6a

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9:04 Foundation Worksheet

Simplifying Algebraic
Expressions

Name: Class:

Examples A lot of algebra is just counting letters.

1 4c + 3c = 7c 2 10x − x = 9x 3 3a + 7a + 4 + 5 = 10a + 9 4 3m + 4n + 5m

because as ‘x’ means ‘1x’ because 3a + 7a = 10a = 8m + 4n

4+3=7 and 10 − 1 = 9 and 4 + 5 = 9 because 3m + 5m = 8m

Exercise

1 Simplify the following.

ax xb aa cx x d xy ea

xx yy e 12k − k
j 6t + 10t
2 Simplify the following by counting on or counting back. o 11p + 3p
t 8ab + 4ab
a 2x + 3x b 7a − 3a c 10p + 4p d 8f − 2f

f 4m + 5m g y+y h 6y + y i 4x − 3x

k 20w − 5w l x + 4x m 13d − 6d n 3m − 3m

p 7y − y q f+f r 26c − 4c s 15c + 9c

3 Simplify the following by counting like terms.

a 5a + 3 + 4 b 2x + 3y + 4x c 2a + 5a + 6b d 7 + 8 + 4h
h 10 + 3c + c
e 7c − 3c + 1 f 10t + 8 − 3 g 6m + 7 + 3m l 15 − 4 + 7a
p 4b + 3c + 5b
i 6 + 5x − 3x j 3x − x + 4y k 10m − 3m + 2n t 8 + 3y + 4

m 5x + 10x + 3y n 12x + 2y + x o 4b + 3b + 5c

q 10t − 5t + 6u r 4w + 7w + 9 s 8x − x + 4

Fun Spot 9:04 | Which band member is really great at algebra?

Simplify each expression, then match its letter with the answers below.

A 3a + 4a B 7a + a C 6b − b D 9b − 3b

E 2b + b G 13c − 10c H 5c + 2d + 3d I 6a − 2a + 5c

L 2c + 12a − 8a M 6d − 4d + 12 R 3 + 9d + 2 S 2a + 3a + 4a

T 3a + 5b + 5a U 7d + 3c − 2c W 3d + 9 + 8d Y 7 − 2 + 7b

.’

8a + 5b
5c + 5d

3b
6b
9d + 5
c + 7d
2d + 12
2d + 12
3b
9d + 5
5c + 5d
3b
9a

!

3c
9d + 5

3b
7a
8a + 5b
11d + 9
4a + 5c
8a + 5b
5c + 5d
5b
7b + 5
2d + 12
8a
7a
4a + 2c
9a

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9:05 Foundation Worksheet

Name: Grouping Symbols

Class:

To expand or remove grouping symbols, multiply each
term inside the bracket by the term outside.

Examples 2 3(x + 5) 3 10(2y − 3)
=3×x+3×5 = 10 × 2y − 10 × 3
1 4(a − 7) = 3x + 15 = 20y − 30
=4×a−4×7
= 4a − 28 5 5(4 − 3y)
= 5 × 4 − 5 × 3y
4 6(4y − 1) = 20 − 15y
= 6 × 4y − 6 × 1
= 24y − 6

Exercise

1 Remove grouping symbols.

a 2(x + 3) b 5(a − 4) c 3(p + 2) d 8(c − 1)
g 7(2 − h) h 2(4 + d)
e 10(m + 5) f 4(y + 8) k 6(3 − x) l 4(y + 5)
o 20(a + 5) p 2(10 − x)
i 5(x + 6) j 9(4 − b) s 3(c − 4) t 6(f + 9)

m 7(3 + t) n 11(c − 3) d 4(3x + 1)
h 6(2x + 1)
q 1(y + 8) r 10(x − 7) l 11(1 − 4c)
p 6(7y + 4)
2 Expand. b 2(2x + 5) c 7(3 + 2x) t 8(2x − 6)
a 3(5m − 1) f 1(7x − 8) g 5(4x − 7)
e 10(2p + 9) j 2(3 − 7x) k 3(8c − 5)
i 8(2 − 7a) n 4(9 + 5t) o 4(3d + 1)
m 9(2y + 3) r 5(3x + 10) s 2(11p − 2)
q 3(7 − 5x)

Fun Spot 9:05 | What is the best cure for dandruff ?

Expand each of these. Match each letter to the answers below.

A 5(3x + 2) B 2(7x + 3) D 3(5x + 4) E 8(2x + 1)

L 6(3x + 2) N 4(4x + 3) S 3(6x + 5)

14x + 6 15x + 10 18x + 12 15x + 12 16x + 12 16x + 8 18x + 15 18x + 15

INTERNATIONAL MATHEMATICS 1 FOUNDATION WORKSHEETS 32 © Pearson Education Australia 2007.
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9:08 Foundation Worksheet

Name: Directed Numbers

Class:

Examples Substitute directed
numbers (positives
1 Evaluate, if a = 5 and b = 6. or negatives) before
you evaluate each
a a−b b ab c 2a + 7 expression.
=5−6 =5×6 =2×5+7
= −1 = 30 = 17

2 If x = −8 and y = 2, find c x−y
b -x- = −8 − 2
a x+3 y = −10

= −8 + 3 = –----8-
= −5 2

= −4

Exercise

1 Evaluate, if x = 7 and y = 3.

a 2x b x+3 c x−y d x+y e 5y
h 3x + 4 i 2y − 5 j 4x + 2y
f x + 3y g y−3
d y−x e 5x
2 If x = −2 and y = 3, find the following. i 3x − 4 j x÷2
n x + 4y o 2x + 3y
a x+1 b x+y c x−y
d 3b e b+5
f y−7 g x−5 h −2y i 3b + 1 j a + 4b
n 10b o 3ab
k x2 l 4x + y m xy

3 If a = 8 and b = −2, find the following.

a a+b b a−b c b−a

f 2a + 3b g ab h b−6

k a÷b l 10 ÷ b m a − 2b

Fun Spot 9:08 | Why doesn’t your sister like peanuts?

Evaluate using m = −10 and n = 4. Match each letter with the answers below.

A m+5 E m+n H 2m I mn K 3n

L m−n N m−2 O n−4 P n−m R 3m + 5

S −m T −n U 2n − 3 V 4m + 10 Y 5n − 4

−20 −5 −30 −6 16 0 5 −6 −30 −6 −25 10 −6 −6 −12

−5 10 12 −40 −12 −12 16 ?

−6 −14 −6 14 −20 −5 −12 −4

INTERNATIONAL MATHEMATICS 1 FOUNDATION WORKSHEETS 33 © Pearson Education Australia 2007.
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9:09 Foundation Worksheet

Simplifying Expressions with
Directed Numbers

Name: Class:

Examples 2 −2a + 5a The rules for directed
= 3a because numbers are the same
1 4x − 10x −2 + 5 = 3 in algebra.
= −6x because
4 − 10 = −6 4 2f − (−5f) 5 −7 × (−3y) 6 −8t ÷ 2
= 7f because = 21y because = −4t because
3 −3 × 2c 2 − (−5) = 7 −7 × (−3) = 21 −8 ÷ 2 = −4
= −6c because
−3 × 2 = −6

1 Simplify. b 2−6 Exercise d −8 + 3 e −6 + 11
a −3 − 2 g −8 − 6 i −5 − (−4) j −7 − 7
f 7 − 13 c 4 − (−7)
b −2 × 3x h −2 + 7 d −5 × − (7x) e −12 ÷ 3
2 Simplify. g 15y ÷ (−3) i −18t ÷ 6 j −7 × 3m
a −4 × 5 l −4 × 9b c −3 × (−4) n −24y ÷ (−8) o −4 × 10x
f 6 × (−2a) h −10 × 2k
k −20 ÷ (−5) b 2y − 7y m 6 × (−5n) d −2m + 5m e −3h − 7h
g −5y + y i x − 7x j 4x − 10x
3 Simplify. l d − (−d) c 5a − 6a n −4x − (−7x) o 3y − 5y
a −2x − x h 10p − (−p)
f 7c − (−3c) m −8w + 8w
k −4t + 9t

Fun Spot 9:09 | What happened to the thief who was caught in the

rubber factory?

Simplify each expression. Match each letter with the answers below to answer

the riddle.

A 4a − 6a C −3 × 2a E −3a + 5a G −10a ÷ 2 H 2a − (−a)

I −5a − 2a L −7 × 2a N 3a − 6a O −20a ÷ (−5) R 9a ÷ (−9)

S 6a − (−2a) T a − 9a V 5 × (−3a) W −4a × 4

3a 2a −16a −2a 8a −5a −7a −15a 2a −3a −2a

−14a 4a −3a −5a .

8a −8a −a 2a −8a −6a 3a

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9:10 Foundation Worksheet

Name: Algebraic Sentences

Class:

Examples To find the number that makes the equation true
• read the sentence to yourself, thinking ‘what

number . . .’
• thinking in reverse can be a help.

1 +5=9 2 3 × = 24
(What number add 5 gives 9?) (3 times what number gives 24?)
=4 =8

In reverse [What number goes into 24 three times?]

3 a−9=7 4 -c- = 3
(What number take away 9 gives 7?) 5
a = 16 (What number divided by 5 gives 3?)
c = 15
[What number is 9 more than 7?]
In reverse

Exercise

Find the number that makes the equation true.

1 a + 3 = 10 b 4 × = 20 c + 9 = 11 d × 3 = 12 e 10 × = 70
f 5 + x = 11 g x + 8 = 12 h 8x = 40 i 2a = 18 j 4 + a = 13
k 6m = 18 l y + 11 = 18 m 6k = 6 n 7w = 56 o x + 9 = 30
p p + 11 = 33 q b + 5 = 32 r 7t = 42 s 4y = 36 t 20 + h = 21
c -c- = 12
2 a x−2=7 b a÷2=9 d y − 9 = 10 e m − 13 = 18
g -c- = 2 4
f h−5=6 h x − 12 = 3 i a−7=0 j --x--- = 3
4 n x÷6=8 10
l k − 6 = 14 m h − 8 = 15 s m−8=8
k a÷3=6 q c − 20 = 10 r p − 15 = 5 o x÷7=9

p -n- = 6 t -a- = 1
5 7

Fun Spot 9:10 | What do you get when you cross a galaxy with a toad?

Solve each equation and match each letter with the answers below.

A 3x = 12 R x + 7 = 12 S x − 9 = 5 T x ÷ 6 = 2 W 7 + x = 10

14 12 4 5 !

3 4 5 12 14

INTERNATIONAL MATHEMATICS 1 FOUNDATION WORKSHEETS 35 © Pearson Education Australia 2007.
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9:11 Foundation Worksheet

Name: Solving Problems Using Algebra

Class:

Examples

1 The total of 5, 9, 13 and a number is 45. 2 The product of a number and 21 is 273.

What is the missing number? Find the number.
Let n = number. Let x = number.
∴ n + 5 + 9 + 13 = 45
21 × x = 273
n + 27 = 45 x = 273 ÷ 21
n = 18 Subtract 27 x = 13

∴ number is 18. ∴ number is 13.

3 Find the side a if the perimeter is 80. 20

a + 20 + 11 + 17 + 25 = 80 a 11 • Form an equation.
17 • Solve this equation to
a + 73 = 80 (-73)
answer the problem.
a=7
∴ side is 7. 25

Exercise

1 Solve each equation.

a x + 9 = 10 b 5x = 30 c y − 4 = 11 d t ÷ 3 = 6 e 13 + m = 20
h p + 18 + 13 + 6 = 45 i -c- = 10
f a + 5 + 7 = 30 g 15x = 120
6

2 Form an equation, then solve it.

a Perimeter = 18 b Perimeter is 24. c 7 Perimeter = 50

3 Find y. x Find x.

Find x. 18

x

6 y
x

d The sum of two numbers is 40. If one is 18, what is the other?

e If two numbers multiply to give 40 and one number is 8, what is the other?

f The difference between a number and 12 is 13, what is the number?

g Five copies of a CD cost me $74.50. Form an equation, then find the cost, c.

h Three sisters shared $100. If Tina got $30, and Janet got $24, how much did Helen receive?

i An amount of money is divided evenly between 6 people. If they each get $22, how much was

the original amount?

j 17 Perimeter = 70 k Area = 180. l Perimeter = 85

Find x. Find x. Find a.

x 30 20 a

x

m A box of 144 apples is shared evenly. If each person gets 9 apples, how many people are there?
n Duncan starts shopping with $120. If he ends up with $84, how much did he spend?

INTERNATIONAL MATHEMATICS 1 FOUNDATION WORKSHEETS 36 © Pearson Education Australia 2007.
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Foundation Worksheet

11:04 Finding the Size of an Angle

Name: Class:

Examples

Find the value of each pronumeral.

1 A right angle = 90°. 2 A straight angle = 180°. 3 A revolution = 360°.

67° 134° y° 60°
x° a°
y = 180 − 134
x = 90 − 67 = 46 a = 360 − 90 − 60
= 23 = 210

4 The angle sum of a triangle is 180°. 5 The angles in a quadrilateral total 360°.

134° 116° 65°
x° 80°
18°

x = 180 − 134 − 18 x°
= 28
x = 360 − 80 − 116 − 65
= 99

Find the value of each pronumeral. Exercise d 74°
ab
c d°
a° 140° b° 85°
30° c°
e 120° 32° h 62° h° 37°
f
e° 235° g l
85° f °
152° g° l° 73°
40°
i 124° 111° j j° p
k
62° 102°
80° p°

i° 65° k° 40° t
x°
m 137° n o 128° t°
122°
q q° m° 60° n° 50° 16°
80° 160°
130° s s°
70° r
68°
70°

70° r°

INTERNATIONAL MATHEMATICS 1 FOUNDATION WORKSHEETS 37 © Pearson Education Australia 2007.
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Foundation Worksheet

12:01 Measuring Instruments

Name: Class:

Exercise

1 Measure each length in centimetres. b c
a
d e g
f i
h d

2 What time is shown? c 11 12 1 PM 11:02

5:00a b 11 12 1 10 2 h AM 1:29
10 2 93
l 11 12 1
93 84
84 76 5 10 2
76 5 93
g 11 12 1
e 11 12 1 f AM 10:10 84
10 2 76 5
10 2 93

93 84
76 5
84
76 5

i 7:01 j 11 12 1 k AM 3:20

PM 10 2

93

84
76 5

Fun Spot 12:01 | Dad: ‘How did you find your maths test?’

Put these times in order, left to right, from earliest to latest in the day, in the
boxes below to find the code. Some have been done for you. Use the code to
answer the question.

(earliest) 9 11 48 10 (latest)

A E F I L NO R S T UWY

1 8 pm 2 10:15 am 3 7 o’clock at night 4 noon

5 quarter to seven in the morning 6 1:30 pm 7 6:15 am

8 half past three in the afternoon 9 ten minutes past midnight

10 quarter past nine at night 11 4:36 am

12 two in the afternoon 13 twenty past six in the evening

S N: ‘ N NA E Y

864 3 4 7 6 12 13 3 4 9 13 11 2 10

5 13 ASN S !’
1 9 8 4 13
2 6 8 13

INTERNATIONAL MATHEMATICS 1 FOUNDATION WORKSHEETS 38 © Pearson Education Australia 2007.
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Foundation Worksheet Class:

12:02 Units of Length

Name:

Examples • When converting or changing to a smaller unit, multiply.
• When converting to a larger unit, divide.
1 5 m = . . . cm
m is larger unit, 2 80 mm = . . . cm 10 mm = 1 cm
multiply by 100 mm is smaller unit, 100 cm = 1 m
5 × 100 = 500 cm divide by 10 1000 mm = 1 m
80 ÷ 10 = 8 cm 1000 m = 1 km
3 2 min = . . . s
min is larger unit, 4 360 min = . . . h 1 h = 60 min, 1 min = 60 s
2 × 60 = 120 s min is smaller unit,
360 ÷ 60 = 6 h

Exercise

1 Write down the length of each interval to the nearest centimetre.

0 1 2 3 4 5 6 7 8 9 10 11 12

cm c de f

ab

2 a 8 cm = . . . mm b 300 cm = . . . m c 90 mm = . . . cm d 8000 mm = . . . m
e 7 km = . . . m f 9 m = . . . cm g 3 m = . . . mm h 12 cm = . . . mm
i 5000 m = . . . km j 1500 cm = . . . m k 2 km = . . . m l 11 m = . . . mm

m 50 mm = . . . cm n 10 km = . . . m o 8000 m = . . . km p 600 cm = . . . m
q 12 000 mm = . . . m r 20 cm = . . . mm s 62 000 m = . . . km t 6 m = . . . mm

3 a 3 min = . . . s b 2 h = . . . min c 120 s = . . . min d 600 min = . . . h
e 5 min = . . . s f 480 s = . . . min g 24 h = . . . min h 300 min = . . . h
i 20 min = . . . s j 30 min = . . . h k 900 s = . . . min l 7 h = . . . min
m 12 h = . . . min n 10 min = . . . s o 4 h = . . . min p 15 min = . . . h

Fun Spot 12:02 | What do bees do if they want to catch public transport?

Fill in the gaps for each question. Match the letters with the answers below.

A 75 cm = . . . mm B 5 m = . . . mm I 5 m = . . . cm

O 500 cm = . . . m P 570 mm = . . . cm S 7 m = . . . mm

T 7 cm = . . . mm U 70 mm = . . . cm W 75 m = . . . cm Z 5 cm = . . . mm

.

7500 750 500 70 750 70 750 5000 7 50 50 7000 70 5 57

INTERNATIONAL MATHEMATICS 1 FOUNDATION WORKSHEETS 39 © Pearson Education Australia 2007.
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Foundation Worksheet

12:03 Measuring Length

Name: Class:

Examples • Measuring is rounding off.
• Write the measurement it is closest to.
1
2
012345
cm 012345

mm — AW W09.003 —

This measures 3 cm to the nearest cm, This measures 37 mm to the nearest mm,
since it is only a bit more than 3 cm since the ruler is marked in mm. (It would
long. measure 4 cm to the nearest cm.)

Exercise cd
h
1 Measure these lengths correct to the nearest centimetre.
ab d
e

f g j
c
i b
2 Measure these lengths in millimetres. f
h
a
e
g

Fun Spot 12:03 | What’s the easiest way to get a day off school?

Put these lengths in order from shortest to longest in the boxes below to find the
code. (Change to mm first.) Use the code to solve the riddle.

(shortest) 11 (longest)

A D I L N R S T UWY

1 19 mm 2 3 cm 3 28 mm 4 6⋅2 cm 5 6⋅7 cm 6 59 mm
7 1 cm 8 39 mm 9 5 cm 10 42 mm 11 4 mm

A 62913 A A!
4 11 1 9
10 11 9 6 8 7 11 5

INTERNATIONAL MATHEMATICS 1 FOUNDATION WORKSHEETS 40 © Pearson Education Australia 2007.
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Foundation Worksheet Class:

12:05 Perimeter

Name:

Examples • Perimeter is the total length around a shape.
• The same marking on sides mean they have the

same length.
• For a square, P = 4 × side.

For a rectangle, P = 2 × length + 2 × breadth.

1 13 cm 2 3 4m 4

10 m 8m

7 cm 5m 11 mm

16 cm

20 m 3m
6m

P = (7 + 13 + 16) cm P = 2 × 20 + 2 × 10 m P = 4 + 8 + 3 + 6 + 5 m P = 4 × 11 mm

= 36 cm = 60 m = 26 m = 44 mm

Exercise

1 Calculate each perimeter.

a b 8 cm c 10 cm d 10 cm 20 cm
h 23 cm
2 cm 4 cm 5 cm 6 cm 6 cm 15 m

3 cm 12 cm 8 cm 11 cm

e 19 m f 12 m g 7m 8m
8m
8m
20 m
9m 5m
3m

i 7·3 cm j 15·4 m k 8 mm l

5·2 cm 7·3 m 16 m
3·9 cm
13·7 m

12·1 m

mn o p
8·1 m
8 cm 7·5 mm 10 cm

18 cm 3·2 m 15 cm

2 Find the perimeter of the following shapes.

a a square of side length 10 cm

b a rectangle with a length of 16 m and a breadth of 5 m

c a square with a side length of 50 m
d a rectangle with a length of 1⋅9 cm and a width of 1⋅1 cm

e a rectangle with length 37 mm and breadth 30 mm
f a square with sides 3⋅6 cm long

g a square with each side length 110 m
h a rectangle with length 2·5 cm and breadth 1⋅7 cm

i a triangle with sides 17 cm, 24 cm and 36 cm
j a quadrilateral with sides of length 9⋅3 m, 14 m, 16⋅2 m and 20⋅7 m

INTERNATIONAL MATHEMATICS 1 FOUNDATION WORKSHEETS 41 © Pearson Education Australia 2007.
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Foundation Worksheet

12:06 The Calendar and Dates

Name: Class:

Examples 365 days = 1 year 2 weeks = 1 fortnight
7 days = 1 week 12 months = 1 year
1 How many days 2 How many years

in 3 weeks? in 60 months?

3 × 7 = 21 days 60 ÷ 12 = 5 years

3 How many days 4 How many days 5 How many days 6 How many days from
in 2 years? from 8 to from 8 June to 28 April to 17 June?
2 × 365 20 September? 14 July? 28 to 30 April = 2
= 730 days 20 − 8 = 12 days 8 to 30 June = 22 + May = 31
+ 14 in July = 14 + June = 17
Total = 36 days Total = 50 days

Exercise

1 a How many days in 2 weeks? b How many years in 36 months?
c How many days in 3 years? d How many fortnights in 16 weeks?
e How many days in 4 fortnights? f How many months in 4 years?
g How many days in 10 weeks? h How many weeks in 84 days?
i How many (full) weeks in a year? j How many months in 10 years?
k How many weeks in 280 days? l How many years in 72 months?

2 How many days from: b 1 to 24 April?
a 13 to 20 June? d 30 March to 21 April?
c 22 October to 13 November? f 7 April to 7 July?
e 16 February to 16 March? h 3 August to the end of the month?
g 20 October to Christmas Day? j 15 January to 9 February?
i 10 August to 10 October?

Fun Spot 12:06 | What is bigger when it is upside down?

Put each day in order as it comes during the year. The first one has been done for you.

B Christmas Day E April Fool’s Day H Fathers’ Day

I New Year’s Day 1 M Australia Day N Anzac Day

R Mothers’ Day S Boxing Day T New Year’s Eve

U Halloween (31 October) X Valentine’s Day (14 February)
Use the letters to complete the riddle.

.

11 7 4 582946 10 1 3

INTERNATIONAL MATHEMATICS 1 FOUNDATION WORKSHEETS 42 © Pearson Education Australia 2007.
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Foundation Worksheet

12:07 Clocks and Times

Name: Class:

Examples There are
5 minutes
1 How many minutes in the 2 Read the times in ‘minutes between
to’ or ‘minutes past’. numbers.
following times?

a 4 hours b 2 1-- hours a 11 12 1 b 11 12 1
4 × 60
= 240 min 2 10 2 10 2
93 93
2 1-- × 60
84 84
2 76 5 76 5

= 150 min 25 minutes past 3 10 minutes to 6

Exercise

1 How many minutes in the following lengths of time?

a 1 hour b 2 hours c 10 hours d 24 hours e 1-- hour f 1 1-- hours

h 5 1-- hours i 1-- hour j 2 1-- hours 2 2

g 5 hours 24 4 k 11 hours l 7 hours

2 Write each time as ‘minutes to’ or ‘minutes past’.

a 11 12 1 b 11 12 1 c 11 12 1 d 11 12 1 e 11 12 1 f 11 12 1

10 2 10 2 10 2 10 2 10 2 10 2

93 93 93 93 93 93

84 84 84 84 84 84
76 5 76 5 76 5 76 5 76 5 76 5

g h i j k l
11 12 1 11 12 1 11 12 1 11 12 1 11 12 1 11 12 1
10 2 10 2 10 2 10 2 10 2 10 2

93 93 93 93 93 93

84 84 84 84 84 84
76 5 76 5 76 5 76 5 76 5 76 5

Fun Spot 12:07 | Why is a belt like a garbage truck?

Fill in the blanks below, then use the letters to answer the riddle.

A 3 h = . . . min B 2 days = . . . h C 5 min = . . . s D 660 min = . . . h
I 7d=...h
E 30 min = . . . s G 300 min = . . . h H 10 min = . . . s S 6 h = . . . min
N 180 s = . . . min O 30 s = . . . m R -1- day = . . . h

T 120 s = . . . min U 24 h = . . . day 2

W 3-- h = . . . min

4

48 1800 300 180 1 360 1800 168 2 5 -1- 1800 360 180 12 -1- 1 3 11
2 2

.

180 3 11 5 180 2 600 1800 12 360 2 600 1800 45 180 168 360 2

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Foundation Worksheet

12:08 Operating with Time

Name: Class:

Examples 2 Find the difference 3 How long is it from

1 Find 3 h 10 min between 9 am and 8 pm. a 8:15 to 8:55? b 3:30 to 5:45?
plus 4 h 20 min. 9 am to 12 noon = 3 h
3 h 10 min 55 min 5 h 45 min
4 h 20 min noon to 8 pm = 8 h
7 h 30 min ∴ difference = 11 h −15 min −3 h 30 min

40 min 2 h 15 min

Exercise

1 a 2 h + 5 h 30 min b 1 h 20 min + 6 h c 4 h 15 min + 2 h 20 min
d 3 h 25 min + 2 h 15 min e 2 h 55 min + 8 h f 10 h + 4 h 5 min
g 6 h 25 min + 7 h 5 min h 1 h 17 min + 3 h 36 min i 8 h 7 min + 2 h 19 min
j 4 h 15 min + 27 min k 34 min + 2 h 12 min l 3 h 5 min + 2 h 9 min

2 What is the difference between the following times (on the same day)?

a 10 am and 1 pm b 7 pm and 11 pm c 4 am and 10 am

d 8 am and 3 pm e 1 am and noon f 3 am and 2 pm

g 11 am and 6 pm h noon and 5 pm i noon and midnight

j 3 pm and 8 pm k 6 am and 6 pm l 7 am and 4 pm

3 How long is it between the following times?

a 5:35 to 5:50 b 1:20 to 1:42 c 11:10 to 11:40
f 10:15 to 11:35
d 7:05 to 7:30 e 3:10 to 4:30 i 2:16 to 2:50
l 8:27 to 8:50
g 9:05 to 11:35 h 6:30 to 9:45

j 4:30 to 6:50 k 3:25 to 4:30

Fun Spot 12:08 | My sister went on a crash diet.

Put these times in order from the earliest to the latest in the day (1st to 13th).

Then use the letters to complete the punchline below.

A 2:30 pm C noon E 7:20 am H 6:45 pm I 4 am

K 9:16 pm L 11:52 am O 1 am R 3:05 pm S 5:55 am

T 9 pm W 12:30 am Y 11:10 pm

3rd 4th 11th 10th 8th 11th 1st 10th 13th 4th 10th 5th

?

6th 2nd 2nd 12th 4th 8th 1st 9th 5th 7th 12th

INTERNATIONAL MATHEMATICS 1 FOUNDATION WORKSHEETS 44 © Pearson Education Australia 2007.
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13:01 Foundation Worksheet

Name: The Definition of Area

Class:

Examples The area of a figure is measured by counting
the number of square units it covers.
Find the area of each shape
by counting square centimetres. 3

12

Area = 5 cm2 Area = 8 cm2 Area = 7 cm2

Exercise

1 These shapes are drawn on centimetre grid paper. Find their areas.
a bc

d ef

g hi

j

2 a On your own grid paper draw 3 different shapes with an area of 6 cm2.
b Draw shapes with areas of 3 cm2, 5 cm2, 7 cm2, 10 cm2.

INTERNATIONAL MATHEMATICS 1 FOUNDATION WORKSHEETS 45 © Pearson Education Australia 2007.
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Foundation Worksheet

13:02 Area of a Rectangle

Name: Class:

Examples For rectangles, multiply squares across by
squares down: area = length × breadth.
Find the area of each figure.
12 34

Area = 8 unit2 Area = 12 unit2 Area = 9 unit2 Area = 20 unit2
(by counting) (3 squares across (3 squares across (5 across by 4 down)
by 4 squares down) by 3 squares down)

1 Find the area in square units. Exercise d
ab h
c
ef g

2 Find the area in square units. c d
ab
h
e fg i

3 Calculate the area of these rectangles. b length 14 cm, breadth 2 cm
a length 10 cm, breadth 4 cm d length 8 cm, breadth 4 cm
c length and breadth both 10 cm f length 3 cm, breadth 11 cm
e length 5 cm, breadth 9 cm h length and breadth both 8 cm
g length and breadth both 6 cm j length 15 cm, breadth 2 cm
i length 20 cm, breadth 5 cm

INTERNATIONAL MATHEMATICS 1 FOUNDATION WORKSHEETS 46 © Pearson Education Australia 2007.
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Foundation Worksheet

13:03 Area of a Triangle

Name: Class:

Examples

Find the area of these triangles. These two areas 3 The triangle is half the
total 1 square. 6 by 4 rectangle.
1 These two areas 2 ∴ Area = -1- × (6 × 4) cm2

total 1 square. 2

6 cm = 12 cm2

11 1 The triangle is half the
3 by 6 rectangle.
These two areas These two areas 4 4 cm ∴ Area = 1-- × (3 × 6) cm2
total 1 square. give 1 square. 3 cm
2
Area = 4 cm2 Area = 3 cm2
= 9 cm2
Easier than counting is to say each triangle is 6 cm

half the rectangle.

Area = 1-- × (4 × 2) cm2 Area = 1-- × (3 × 2) cm2
22
= 4 cm2 = 3 cm2

Exercise d

1 Use the centimetre grid to find the area of each triangle.
ac

b

2 Calculate the area of each triangle.2 cm cd 5 cm
a 6 cm b 6 cm
6 cm
4 cm 14 cm
8 cm

e 4 cm g h

7 cm f 10 cm

8 cm

4 cm j 8 cm 5 cm 10 cm
7 cm
i 7 cm k l
6 cm
10 cm 12 cm 15 cm

20 cm 6 cm

INTERNATIONAL MATHEMATICS 1 FOUNDATION WORKSHEETS 47 © Pearson Education Australia 2007.
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Foundation Worksheet

13:06 Volume of a Rectangular Prism

Name: Class:

Examples To find the volume of a rectangular prism,
count (or imagine) the number of cubes in
1 the box. It’s helpful to count layer by layer.

23

This prism has 2 layers This prism has 2 layers This prism has 3 layers
each with 3 × 3 cubes. each with 4 × 2 cubes. with 4 × 5 cubes.
∴ Volume = (3 × 3) × 2 ∴ Volume = (4 × 2) × 2 ∴ Volume = 4 × 5 × 3

= 18 cm3 = 16 cm3 = 60 cm3

1 Find the volume in cm3. Exercise d
ab
c

2 Find the volume of each prism in cm3.

a 2 cm b c 2 cm
f 2 cm
4 cm 4 cm
3 cm
8 cm

6 cm

6 cm 2 cm
3 cm
de

5 cm

5 cm 6 cm

4 cm 2 cm
1 cm
4 cm 3 cm
10 cm
g 4 cm h i

3 cm 2 cm

4 cm

7 cm 8 cm 6 cm

INTERNATIONAL MATHEMATICS 1 FOUNDATION WORKSHEETS 48 © Pearson Education Australia 2007.
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Foundation Worksheet Class:

13:07 Capacity

Name:

Capacity is the volume of liquids. It is measured using the litre (L) as the basic unit.

• 1 litre (L) = 1000 millilitres (mL) • 1000 L = 1 kilolitre (kL)

Volume and capacity are connected: • 1000 cm3 = 1 L
• 1 cm3 = 1 mL

Examples

Complete these conversions.

1 5 L = . . . mL 2 8000 L = . . . kL 3 25 mL = . . . cm3 4 2 L = . . . cm3

L is larger unit L is smaller unit equal units L is larger unit

∴ × 1000 ∴ ÷ 1000 ∴ 25 mL = 25 cm3 ∴ × 1000

5 L = 5000 mL 8000 L = 8 kL 2 L = 2000 cm3

Exercise

Complete. b 7 L = . . . mL c 4000 mL = . . . L d 11 000 mL = . . . L
1 a 2 L = . . . mL f 6 L = . . . mL g 5000 mL = . . . L h 14 000 mL = . . . L
j 8 L = . . . mL k -1- L = . . . mL l 20 000 mL = . . . L
e 3000 mL = . . . L
2 d 6000 L = . . . kL
i 10 L = . . . mL h 10 000 L = . . . kL
c 9 kL = . . . L l 4000 L = . . . kL
2 a 3 kL = . . . L b 2000 L = . . . kL g 7 kL = . . . L
e 5000 L = . . . kL f 25 kL = . . . L k 700 L = . . . kL d 4000 cm3 = . . . L
i 0⋅5 kL = . . . L j 0⋅4 kL = . . . L h 750 mL = . . . cm3
c 100 mL = . . . cm3 l 1500 cm3 = . . . L
3 a 3 cm3 = . . . mL b 15 cm3 = . . . mL g -1- L = . . . cm3
e 400 cm3 = . . . mL f 8 L = . . . cm3
2
i 0⋅1 L = . . . cm3 j 5000 cm3 = . . . L
k 3000 cm3 = . . . mL

Fun Spot 13:07 | Why did the girl plant birdseed?

Complete the following, then match the letters with the answers below.

A 35 mL = . . . cm3 B 35 L = . . . mL C 3500 mL = . . . L

D 300 L = . . . kL E 5 L = . . . mL H 350 cm3 = . . . mL I 2⋅5 L = . . . mL

N 0⋅5 kL = . . . L O 6 mL = . . . cm3 R 4000 L = . . . kL S 5⋅5 L = . . . mL

T 3000 mL = . . . L U 50 cm3 = . . . mL W 3 L = . . . cm3

35 000 5000 3⋅5 35 50 5500 5000 5500 350 5000 3000 35 500 3 5000 0⋅3

.

36 4 35 2500 5500 5000 3⋅5 35 500 35 4 2500 5000 5500

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Challenge Worksheet

Extension 1:09 Solving Puzzles

Name: Class:

Examples 16 42 28

Complete this magic square. 3 120 38 14 40 26 2
You can see from the bottom line 1 that the 1 120
total is 120. Each row, column and diagonal 24 0
must have a sum of 120, the magic number.
You find the 26 from column 2. 46 22 34
Then find the 40 from row 3.
Then move to column 4 to fill in the empty 20 6 32 18 44
box, and so on until completed.
42
120 120

Exercise

1 Find the missing numbers in these giant magic squares.

a 6 32 18 44 30 b 6 19 15 c 3 10 17 26

16 42 28 18 1 14 22 22

14 26 38 5 13 21 9 11 20

48 24 36 12 8 16 25 7 9 16

34 20 46 73 14 23 5 12

2 A carpenter has two lengths of timber, each with
a square cross section of 100 mm by 100 mm.
He saws one length into 3 pieces in six minutes.
At this rate of sawing how long would it take him
to saw the second length into 6 pieces?

3 Here are six different views of the same
cube. What letter is on the opposite face
To F? To E? To C?
(Hint: Make a cube.)

4 How would you place the numbers
1, 2, 3, 4, 5 and 6

in the circles so that the sum of the numbers on
each side of the triangle is 10?

INTERNATIONAL MATHEMATICS 1 FOUNDATION WORKSHEETS 50 © Pearson Education Australia 2007.
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Challenge Worksheet

Extension 3:06 HCF and LCM by Prime
Factors

Name: Class:

• HCF is the highest factor common to both numbers and must
contain all the common prime factors.

• LCM is the lowest number both numbers divide into and may be
found by listing the factors of the bigger number and including
factors of the smaller number not yet included.

Examples

Find the HCF and LCM of the following.

1 80 and 112 80 112

2 × 40 2 × 56

2 × 2 × 20 2 × 2 × 28

2 × 2 × 2 × 10 2 × 2 × 2 × 14

2 × 2 × 2 × 2× 5 2 × 2 × 2 × 2× 7

∴ 80 = 2 × 2 × 2 × 2 × 5 ∴ 112 = 2 × 2 × 2 × 2 × 7

HCF= 2 × 2 × 2 × 2 = 16 (all the factors that are common to both)

LCM= 2 × 2 × 2 × 2 × 7 × 5 = 560 (the factors of 112 and the 5 not included from 80)

2 84 and 156 84 156

2 × 42 2 × 78

2 × 2 × 21 2 × 2 × 39

2 × 2 × 3 ×7 2 × 2 × 3 × 13

∴ 84 = 2 × 2 × 3 × 7 ∴ 156 = 2 × 2 × 3 × 13
HCF= 2 × 2 × 3 = 12 (all the factors that are common to both)
LCM= 2 × 2 × 3 × 13 × 7 = 1092 (the factors of 156 and the 7 not included from 84)

Exercise

Find the HCF and LCM of the following pairs of numbers.

1 16 and 24 2 18 and 24 3 36 and 100
6 48 and 72
4 80 and 140 5 81 and 108 9 90 and 135
12 70 and 98
7 30 and 75 8 36 and 54
© Pearson Education Australia 2007.
10 60 and 84 11 50 and 75 This page may be photocopied for classroom use.

INTERNATIONAL MATHEMATICS 1 FOUNDATION WORKSHEETS 51

Challenge Worksheet

Extension 8:02 Describing Number
Patterns

Name: Class:

1 This table of values gives the Exercise 2
number of small squares in each
figure. 1

3 4

Height of figure 12 3 45 6 7 8

Number of small squares 2 6 12 20

Hint: 1 × 2 2 × 3 3 × 4 4 × 5
a What rule links the number of small squares to the height of each figure?
b Complete the table for heights up to 8.

2 a Write down the number pattern that these matches represent.

b Write the next two numbers in the pattern.
3

a Complete this table. Diagonals Drawn from One Vertex
Number of sides (s) 3 4 5 6 7 8 9 10
Number of diagonals (d)

b The pattern in words is . . . .
c Write the rule using s, d.

4 Find the rule connecting the top row number with the bottom row number. (B = . . .)
What would the tenth bottom number be?

a Top (T) 1234 b Top (T) 1 2 3 4
10 9 8
Bottom (B) 1 4 9 16 Bottom (B) 11

5 Find the pattern, then write the next two numbers.

a 5, 9, 13, 17, . . . , . . . . b 8, 4, 2, 1, . . . , . . . .

c 20, 15, 10, 5, . . . , . . . . d 400, 4000, 40 000, 400 000, . . . , . . . .

6 Write the first four numbers in the pattern with these rules.

a 3n + 2 b 6−n c 2n − 7 d n2 + 5

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Foundation Worksheets

Answers

1:03 Know Your Tables 2 9, 3, 6, 10, 2, 5, 8, 1, 4, 7
1 7, 8, 11, 10, 14, 9, 15, 13, 12, 16 4 12, 24, 8, 28, 32, 4, 16, 36, 20, 40, 0, 44
3 0, 14, 7, 35, 70, 21, 49, 28, 56, 42, 63, 77 6 6, 1, 2, 5, 8, 3, 0, 7, 9, 4
5 9, 12, 8, 11, 5, 6, 10, 14, 13, 15 8 13, 14, 10, 12, 16, 8, 15, 11, 17, 9
7 24, 12, 18, 27, 21, 15, 6, 3, 0, 33, 9, 30 10 9, 8, 12, 5, 7, 10, 3, 13, 6, 11
9 42, 12, 24, 60, 36, 48, 54, 18, 66, 6, 0, 30 12 1, 10, 4, 2, 7, 6, 9, 3, 0, 5
11 9, 27, 72, 99, 18, 81, 90, 0, 36, 63, 54, 45

1:06 Powers of Numbers

1 a 16 b 64 c9 d1 e 81 f4 g 25 h 100
l1 m 125 n 27 o 1000 h 16
i 49 j 36 k8 h 43
d 64 e4 f1 g 36
2 a 49 b 100 c 25 l8 m 64 n 1000 o 216
d 72 e 54 f 95 g 84
i9 j 81 k 27

3 a 103 b 62 c 26
i 105

1:07 Rounding Numbers

1 a 370 b 80 c 40 d 140 e 570 f 6080 g 590 h 8020
l 210 e 6600 f 900 g 2800 h 200
i 40 j 880 k 60
d 500
2 a 8700 b 1200 c 300 l 300

i 500 j 9900 k 7000

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2:01 Problem Solving

1 $35 2 $55.40 3 $65.50 4 33 5 $10.32, $10.30
8 20 000 000 9 24 10 $840
6 344, 86 7 54

INTERNATIONAL MATHEMATICS 1 FOUNDATION WORKSHEETS 2 © Pearson Education Australia 2007.
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3:01A Grouping Symbols

1 a 50 b 42 c9 d 30 e 49 f 28
c2 d 20 e 30 f 16
2 a 18 b4 c5 d2 e7 f0

3a 3 b2

3:03 Language and Symbols

1a F bT cT dF eT fT
c 12 − 5 = 7 d 4×3Ͼ7 e 10 ≠ 4 × 3 f 6+3
2 a 5Ͻ6 b 10 Ͼ 4

3:07 Divisibility Tests b 1, 3, 5, 7, 9, 11, 13, 15, 17, 19
1 a 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
b 3, 6, 9, 12, 15, 18, 21, 24, 27, 30
c 5, 10, 15, 20, 25, 30, 35
2 a 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 d 10, 20, 30, 40, 50, 60, 70, 80, 90, 100

c 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 f 7, 14, 21, 28, 35, 42, 49, 56, 63, 70
e 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
g 8, 16, 24, 32, 40, 48, 56, 64, 72, 80 h 9, 18, 27, 36, 45, 54, 63, 72, 81, 90
3 a 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28
4 a 15, 54 321 b 3, 6, 9, 12, 15, 18, 21, 24, 27 c 10, 20
c 12, 201, 54 321, 12 345
b 40, 125, 100 000

d 24, 42, 66, 888

3:08 Square Roots

1a 4 b2 c5 d9 e 11 f 20
c 10 d 12 e1 f 15
2a 7 b8 c4 d9
c8 d 30
3a 5 b3

4a 6 b2

INTERNATIONAL MATHEMATICS 1 FOUNDATION WORKSHEETS 3 © Pearson Education Australia 2007.
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4:01 Review of Decimals

1 a 0⋅3 b 0⋅07 c 0⋅93 d 0⋅6 e 0⋅004 f 0⋅133
g 0⋅1 h 0⋅73 i 0⋅43 j 0⋅024 k 0⋅92 l 0⋅28
m 0⋅36 n 0⋅555 o 0⋅002 p 0⋅99 q 0⋅031 r 0⋅607

2 a --7--- b ----3---- c --5---3--- d ----9---- e --1---2---3--- f ----9---1----
100 100 100 1000 1000
10
g --1---3--- h --5---9--- i --5---6---3--- j --2---1--- k --3---0---3--- l --2---9---9---
100 1000 100 1000 1000
100
m --3--- n 2-- o 1-- p -1---6- q ----1---- r ----7----
5 4 25 200 500
50
b 0⋅71 c 0⋅3 d 0⋅83 e 0⋅51 f 0⋅12
3 a 0⋅7 h 0⋅3 i 0⋅43 j 0⋅92 k 0⋅68 l 0⋅5
g 0⋅63

4:02 Addition and Subtraction of Decimals

1 a 6⋅6 b 8⋅9 c 7⋅84 d 3⋅866 e 7⋅54 f 6⋅53 g 17⋅73 h 18⋅1
e 1⋅8 f 0⋅84 g 17⋅73 h 1⋅09
i 11⋅168 j 14⋅523 e 23⋅92 f 3⋅125 g 1⋅73 h 10⋅82

2 a 3⋅6 b 4⋅2 c 12⋅13 d 2⋅27

i 0⋅559 j 5⋅88

3 a 3⋅3 b 9⋅5 c 3⋅6 d 15⋅68

i 24⋅49 j 18⋅86

4:03 Multiplying a Decimal

1 a 0⋅6 b 4⋅2 c 1⋅77 d 23⋅55 e 28⋅8 f 69⋅2 g 92 h 61⋅2
l 0⋅063 e 10⋅5 f 10⋅83 g 9⋅52 h 66⋅5
i 23⋅4 j 22⋅47 k 0⋅32 e 35⋅4 f 370 g 1660 h 42
d 0⋅22
2 a 1⋅2 b 3⋅15 c 6⋅3 l 11⋅8

i 20⋅7 j 5⋅04 k 0⋅108 d 0⋅7
l 20
3a 6 b 52 c 40

i 414 j 810 k 0⋅32

4:04 Dividing a Decimal

1 a 0⋅4 b 0⋅1 c 0⋅2 d 0⋅01 e 0⋅01 f 0⋅01 g 0⋅3 h 0⋅03
d 0⋅11 e 0⋅13 f 0⋅13 g 0⋅03 h 0⋅03
i 0⋅02 j 0⋅2 d 1⋅1 e 4⋅3 f 1⋅8 g 1⋅2 h 3⋅1
d 4⋅13 e 1⋅15 f 0⋅41 g 0⋅42 h 1⋅12
2 a 0⋅23 b 0⋅12 c 0⋅09

i 0⋅16 j 0⋅31

3 a 0⋅5 b 2⋅1 c 1⋅7

i 2⋅3 j 2⋅2

4 a 1⋅02 b 2⋅12 c 1⋅01

i 1⋅03 j 1⋅04

4:05 Using Decimals b $6.72 c 43⋅8 cm d 41⋅1 L
f 5⋅4 t g 22⋅82 m h 2⋅72 g
1 a 0⋅6 kg j $25.36 k 0⋅24 l 75⋅6 L
e $16.24
i 15⋅21 h b $4.81 c $3.80 d 10 cm
f 0⋅975 kg g 4⋅241 kg h $10.61
2 a 1⋅1 m j 9⋅86 mL k $2.27 l 8⋅63 m
e 10⋅73 t
i 0⋅26 m b $0.47 c 1⋅57 m d 0⋅27 kg
f 2⋅32 mL g 0⋅041 m h 0⋅11 t
3 a 0⋅6 L j 0⋅081 g k $1.72 l 0⋅8 m
e $1.02
i 2⋅31 cm

4:06 Multiplying Decimals

1 a 0⋅82 b 0⋅81 c 8⋅4 d 18⋅5 e 1⋅17 f 29⋅05 g 1⋅66 h 0⋅036
l 0⋅76 e 0⋅4 f 3⋅6 g 0⋅027 h 0⋅0048
i 0⋅375 j 24⋅4 k 21⋅28 e 0⋅427 f 0⋅066 g 0⋅52 h 0⋅0052
d 0⋅05
2 a 0⋅28 b 0⋅06 c 0⋅035 l 0⋅006

i 0⋅09 j 0⋅25 k 0⋅0032 d 0⋅136
l 0⋅24
3 a 2⋅16 b 1⋅25 c 0⋅72

i 0⋅000 84 j 0⋅146 k 2⋅37

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4:09 Rounding Off

1 a 85c b 8c c 61c d 19c e 40c f 53c g 3c h 46c
k 88c l 14c m 10c n 40c o 71c p 18c
i 27c j 30c d $4 e $2 f $2 g $8 h $9
c $4 l $2 m $4 n $10 o $5 p $10
q 60c r 6c k $6
d $91 e $25 f $67 g $13 h $3
2 a $8 b $9 d 40c e 60c f 10c g 65c h 25c
d $5.60 e $3.10 f $7.60 g $2.95 h $3.35
i $12 j $6

q $7 r $4

4:10 Application of Decimals

1 a $106 b $90 c $4

i $7 j $40

2 a 75c b 85c c 30c

i 95c j 5c

3 a $4 b $4.25 c $1.70

i $8.10 j $2.35

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5:10 Division of Directed Numbers

1 a −4 b −4 c −2 d −3 e −3 f −1 g −4 h −2
i −2 j −3 h −2
d −1 e −10 f4 g −7 h −12
2 a −6 b2 c2 l −4 m −5 n9 o 13
d −6 e −1 f2 g6 h −35
i 5 j 8 k8 l −2 m4 n −10 o −11 h −15

3 a −5 b5 c3 g 11

i −9 j −7 k −6 g 28

5:11 Using Directed Numbers

1 a −2 b −1 c9 d −1 e −7 f −7

i −21 j6 k2 l −23

2a 8 b5 c −14 d0 e −1 f8
i9 j −12 k −9 l −18

3 a −2, −3, −4 b −12, −15, −18 c −5, −10, −15
d 5, 8, 11 e 50, −60, 70 f −4, 0, 4

INTERNATIONAL MATHEMATICS 1 FOUNDATION WORKSHEETS 6 © Pearson Education Australia 2007.
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6:04 Addition and Subtraction of Fractions

1 a --5--- = -1- b --9--- 2 a 5-- b --8--- = 2-- 3 a 2-- b -4-
10 2 11 12 3 9
8 5
e -2- h --2---7---
4 a -3- b -1- c --3--- d 1----9- 5 f -1---1- g --7--- 100
8 10 20 15 11
8 m 1----4- p --2---
i 3-- j 7-- k -1---0- l -1---7- 25 n -1---1- o --7--- 15
8 13 25 20 10
5 u --5--- = -1- x --5--- = -1-
q --3---7--- r -2---9- s -1---1- t --8---3--- 10 2 v --4--- = 1-- w --4--- = 1-- 20 4
40 12 100 16 4 12 3
100 h 6 1----2-
y -6- = -3- 25

84 h 8 --7---
12
6:05 Addition and Subtraction of Mixed Numbers
h 3 -7-
1 a 1 -3- b 5 --1--- c 2 5-- d 7 1----3- e 3 -7- f 4 1----1- g 10 4-- 9
10 9 20 8 12 5
4 h 4 -1---5-
i 1 --1---1--- j 5 5-- 16
6
100 h --7---
10
2 a 3 -1- b 5 -1- c 9 -5- d 6 --3--- e 8 1-- f 10 -2- g 9 1----7-
4 8 10 9 5 20 h --3---
2 16
i 2 --8--- j 5 --3--- c 2 -5- d 3 -5- e 1 --7--- f 2 --7--- g 1----7-
10 6 8 10 12 20 h --1---
15 16
b 1 -3-
3 a 1-- 4 b3
b4
2 j 9 -1- h3
i 2 --3--- 5 p3

16 f $3
l $60
4 a 2 1-- b 2 3-- c 1 2-- d 2 7-- e 2 1-- f 1 1----7- g 1 --8---
4 3 8 5 20 15 h 333 min
2 p 15 cm
i --4---7--- j 8--
9
100

6:06 Multiplication of Fractions

1 a 1-- b 1-- c 1----1- d 1----1- e 2-- f -1- g 3--
2 2 20 20 3 4 4

i 5-- j 7-- k 1----9- l 8-- m -1- n 1----3- o --8---
6 8 20 9 5 15 11

2 a 1-- b 2-- c -1- d --3--- e --2--- f --3--- g --1---
5 4 10 11 10 10
4
i --4--- j --5--- k -3- l -1- m --3--- n --4--- o ----7----
18 8 8 25 31 100
45
f --1--- g ----1----
3 a 1-- b --1--- c --1--- d --1--- e --1--- 32 100
12 70 20 15
6
i --1--- j ----1----
100
30

6:07 Division Involving Fractions

1a 8 b4 2a9 b2 3 a2
6a3
4a 4 b2 5a2 b7
g3
7a 3 b 5 c 2 d5 e 5 f5 o2
n 11
i 7 j 1 k 3 l 3 m6

q9 r 1 s4 t 2

6:08 Fractions of Quantities

1 a 10 min b 3 kg c $5 d 30 m e 7 mm
j 15 kg k 18 L
g $50 h 9 km i 11 t p 111 min

m 22 mm n 120 t o 12 h

2 a 10 b 20 c 30

3 a $8 b $24 c $56

4 a $6 b $12 b $18

5 a $15 b 21 mm c $15 d $350 e 28 t f 30 kg g $120
m 18 m n $48 o $57
i 20 cm j 35 L k 15 kg l 12 h

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6:09 Review of Percentage

1 a 34% b 66% c --3---4--- = -1---7- d --6---6--- = 3----3-
100 50 100 50

2 a 65% b 35% c --6---5--- = 1----3- d --3---5--- = --7---
100 20 100 20

3 a ----3---- = 0⋅03 b --1---7--- = 0⋅17 c --6---3--- = 0⋅63 d --9---9--- = 0⋅99
100 100 100
100

e --2---7--- = 0⋅27 f --2---0--- = 1-- = 0⋅2 g ----5---- = --1--- = 0⋅05 h ----6---- = --3--- = 0⋅06
100 100 5 100 20 100 50

i --1---5--- = --3--- = 0⋅15 j --4---4--- = -1---1- = 0⋅44 k --2---5--- = 1-- = 0⋅25 l --5---0--- = 1-- = 0⋅5
100 20 100 25 100 4 100 2

m --1---8--- = --9--- = 0⋅18 n --6---2--- = 3----1- = 0⋅62 o --5---5--- = 1----1- = 0⋅55 p --3---6--- = --9--- = 0⋅36
100 50 100 50 100 20 100 25

q --8---3--- = 0⋅83 r --4---6--- = 2----3- = 0⋅46 s --7---7--- = 0⋅77 t ----1---- = 0⋅01
100 100 50 100 100

4 a 7% b 7% c 23% d 78% e 52% f 20%

g 39% h 75% i 90% j 16% k 35% l 45%

m 2% n 58% o 50% p 47% q 61% r 28%

6:10 Changing Fractions and Decimals to Percentages

1 a 15% b 2% c 47% d 93% e 72% f 6% g 25% h 20%
n 45% o 24% p 50%
i 1% j 33% k 5% l 84% m 90% v 82% w 70% x 95%

q 22% r 75% s 48% t 10% u 77% f 31% g 30% h 85%
n 23% o 1% p 29%
y 19%

2 a 14% b 7% c 64% d 99% e 2%

i 80% j 18% k 44% l 40% m 53%

q 71% r 90% s 25% t 58%

6:12 Finding a Percentage of a Quantity

1 a $15 b 8g c 10 kg d 30 m e4 f 9L g $20 h 15 cm
m 25 h n 211 t o 30 kg p $45
i 14 t j 12 g k9 l 22 m
e 160 m f 54 g g 60 h 24 s
2 a $4 b $35 c 18 t d 35 kg m 240 m n 54 cm o 160 g p $200

i $40 j 24 km k 54 d l $18

q 33 t r $28 s 300 L t 30

6:13 One Quantity as a Percentage of Another

1 a 1-- b 1-- c ----7---- d -1- e -1- f 1-- g --3---3--- h -1-
5 100 2 4 5 100 2
2
i -3- j --9--- k 4-- l -1- m 2-- n -1- o --7--- p --5---
10 5 2 3 3 10 12
5
b 20% c 7% d 50% e 25% f 20% g 33% h 50%
2 a 50% m 70% n 32% o 89% p 2%

i 60% j 90% k 80% l 50%
q 16% r 18% s 25% t 75%

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8:03 Patterns and Rules

1 a 20, 25 b 10, 12 c 14, 12 d 24, 48 e 50, 60 f 16, 32
c 20 d3 e 18 f3
2a 8 b 14 c7 d 10 e6 f1
c5 d3 e b=t×3 f b=t+2
3a 6 b1

4a 2 b 10

INTERNATIONAL MATHEMATICS 1 FOUNDATION WORKSHEETS 9 © Pearson Education Australia 2007.
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9:02 Making Sense of Algebra

1 a x+2 b y+3 c 3x d6 e a+8 f 4y + 3 g 2x + 3 h y + 5

i 3a + 3 j 5y + 3

2 a 2y + 1 b 2x + y c x+y d 3x + 2y
g 2a + 3b h 3x + 4
e a + 3b f 2x + 3 k 2x + y + 2 l a + 3b + 2
i 5x + 2y j 4y + 5 o m+n+4

m 3a + 2b + 1 n x + 2y + 3

9:03 Substitution

1 a 36 b 40 c 11 d3 e9 f 15 g0 h 63
k 17 l 24 m1 n6 o4 p5
i 8 j 36
c 20 d 16 e −3 f8 g 19 h 20
2a 2 b8 k 24 l 48 m −8 n −8 o7 p 52
s 28 t 30 u3
i3 j 124
q −3 r 12

9:05 Simplifying Algebraic Expressions

1 a 2x + 5 b 2a + 4 c 4x + 3 d x + 3y e a+8
d 6f e 11k
2 a 5x b 4a c 14p j 16t k 15w f 9m
p 6y q 2f l 5x
g 2y h 7y ix r 22c
d 15 + 4h e 4c + 1
m 7d n0 o 14p j 2x + 4y k 7m + 2n f 10t + 5
s 24c t 12ab p 9b + 3c q 5t + 6u l 11 + 7a
r 11w + 9
3 a 5a + 7 b 6x + 3y c 7a + 6b e 10m + 50
k 18 − 6x f 4y + 32
g 9m + 7 h 10 + 4c i 6 + 2x q y+8 l 4y + 20
m 15x + 3y n 13x + 2y o 7b + 5c r 10x − 70
s 7x + 4 t 12 + 3y e 20p + 90
k 24c − 15 f 7x − 8
9:05 Grouping Symbols q 21 − 15x l 11 − 44c
r 15x + 50
1 a 2x + 6 b 5a − 20 c 3p + 6 d 8c − 8 e 15
i 5x + 30 j 36 − 9b f 16
g 14 − 7h h 8 + 2d o 20a + 100 p 20 − 2x e −10
k4 f −4
m 21 + 7t n 11c − 33 c 21 + 14x d 12x + 4 l −5
i 16 − 56a j 6 − 14a e3
s 3c − 12 t 6f + 54 o 12d + 4 p 42y + 24 k −4 f 10
l −5
2 a 15m − 3 b 4x + 10 e5
f −6
g 20x − 35 h 12x + 6 e −4
k4 f −12a
m 18y + 27 n 36 + 20t l −36b
s 22p − 4 t 16x − 48 e −10h
k 5t f 10c
9:08 Directed Numbers l 2d

1 a 14 b 10 c4 d 10
i1 j 34
g 0 h 25 d5
c −5 j −1
2 a −1 b1 i −10
o5 d −6
g −7 h −6 j0
m −6 n 10 c −10
i −5
3a 6 b 10 o −48

g −16 h −8
m 12 n −20

9:09 Simplifying Expressions With Directed Numbers

1 a −5 b −4 c 11 d −5

g −14 h5 i −1 j −14

2 a −20 b −6x c 12 d 35x

g −5y h −20k i −3t j −21m
m −30n n 3y o −40x

3 a −3x b −5y c −a d 3m

g −4y h 11p i −6x j −6x

m0 n 3x o −2y

INTERNATIONAL MATHEMATICS 1 FOUNDATION WORKSHEETS 10 © Pearson Education Australia 2007.
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9:10 Algebraic Sentences

1a 7 b5 c2 d4 e7 f6
i9 j9 k3 l7
g4 h 5 o 21 p 22 q 27 r6

m1 n 8 c 48 d 19 e 31 f 11
i7 j 30 k 18 l 20
s9 t 1 o 63 p 30 q 30 r 20

2a 9 b 18 d 18 e7 f 18

g 8 h 15 d 22 e5 f 25
j 23 k9 l 17
m 23 n 48

s 16 t7

9:11 Solving Problems Using Algebra

1a 1 b6 c 15

g 8 h 8 i 60

2a 9 b6 c 12

g $14.90 h $46 i $132

m 16 n $36

INTERNATIONAL MATHEMATICS 1 FOUNDATION WORKSHEETS 11 © Pearson Education Australia 2007.
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11:04 Finding the Size of an Angle

a 40 b 60 c 28 d 111 e 125 f 123 g 50 h 81
l 107 m 43 n 90 o 36 p 258
i 60 j 28 k 60 t 58

q 80 r 40 s 22

INTERNATIONAL MATHEMATICS 1 FOUNDATION WORKSHEETS 12 © Pearson Education Australia 2007.
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12:01 Measuring Instruments

1 a 5 cm b 3 cm c 2 cm d 8 cm
g 1 cm h 7 cm
e 4 cm f 10 cm
c half-past three d 2 minutes past 11 pm
i 6 cm g 12 o’clock h 29 past 1 am
k 20 past 3 am l 6 o’clock
2 a 5 o’clock b 9 o’clock

e 10 to 2 f 10 past 10 am

i 1 minute past 7 pm j quarter to 6

12:02 Units of Length

1 a 2 cm b 3 cm c 6 cm d 9 cm e 9 cm f 12 cm
d8 e 7000 f 900
2 a 80 b3 c9 l 11 000 m5 n 10 000 g 3000 h 120
t 6000 o8 p6
i5 j 15 k 2000 d 10
l 420
q 12 r 200 s 62
d 2 cm
3 a 180 b 120 c2 e 300 f8 g 1440 h5
d 25 mm m 720 n 600 o 240 p -1-
i 1200 j -1- k 15
2 4

12:03 Measuring Length

1 a 5 cm b 4 cm c 2 cm e 7 cm f 4 cm g 5 cm h 3 cm

i 8 cm j 2 cm

2 a 32 mm b 8 mm c 35 mm e 51 mm f 18 mm g 63 mm h 74 mm

12:05 Perimeter c 24 cm d 64 cm e 56 m f 32 m g 23 m h 45 m
k 40 mm l 64 m m 52 cm n 22⋅6 m o 30 mm p 50 cm
1 a 9 cm b 31 cm c 200 m d 6 cm e 134 mm f 14⋅4 cm g 440 m h 8⋅4 cm
i 16⋅4 cm j 48⋅5 m

2 a 40 cm b 42 m
i 77 cm j 60⋅2 m

12:06 The Calendar and Dates

1 a 14 b3 c 1095 d8 e 56 f 48 g 70 h 12
l6 g 66
i 52 j 120 k 40 d 22

2a 7 b 23 c 22 e 28 (or 29 in leap year) f 91

h 28 i 61 j 25

12:07 Clocks and Times

1 a 60 b 120 c 600 d 1440 e 30 f 90 g 300 h 330

i 15 j 135 k 660 l 420

2 a 5 minutes to 9 b 20 minutes to 4 c 10 minutes past 12 d 20 minutes past 3
g 10 minutes to 4 h 20 minutes to 1
e 15 minutes past 6 f 25 minutes to 1 k 25 minutes past 9 l 25 minutes to 5

i 30 minutes past 12 j 15 minutes past 11

12:08 Operating With Time

1 a 7 h 30 min b 7 h 20 min c 6 h 35 min d 5 h 40 min
g 13 h 30 min
e 10 h 55 min f 14 h 5 min k 2 h 46 min h 4 h 53 min

i 10 h 26 min j 4 h 42 min d 7h l 5 h 14 min
j 5h
2 a 3h b 4h c 6h e 11 h f 11 h
c 30 min
g 7h h 5h i 12 h g 2 h 30 min k 12 h l 9h
k 1 h 5 min
3 a 15 min b 22 min d 25 min

e 1 h 20 min f 1 h 20 min h 3 h 15 min

i 34 min j 2 h 20 min l 23 min

INTERNATIONAL MATHEMATICS 1 FOUNDATION WORKSHEETS 13 © Pearson Education Australia 2007.
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13:01 The Definition of Area e 6 cm2 f 12 cm2 g 8 cm2 h 8 cm2
1 a 4 cm2 b 5 cm2 c 7 cm2 d 12 cm2
e 10 u2 h 16 u2
i 10 cm2 j 5 cm2 e 28 u2 h 7u2
2 Various possibilities—check with teacher. h 64 cm2
e 45 cm2
13:02 Area of a Rectangle f 32 cm2
d 4 cm2 l 45 cm2
1 a 12 u2 b 4 u2 c 6 u2 d 6 u2 d 15 cm2 f 21 u2 g 15 u2
d 25 u2 j 21 cm2 f 16 u2 g 30 u2 f 36 cm3
2 a 18 u2 b 8 u2 c 14 u2
d 32 cm2 d 27 cm3 f 6000
i 24 u2 d 80 cm3 l 20
f 25 000
3 a 40 cm2 b 28 cm2 c 100 cm2 d 11 f 33 cm2 g 36 cm2 l4
j 8000 f 8000
i 100 cm2 j 30 cm2 d6 l 1⋅5
j 400
13:03 Area of a Triangle d4
j5
1 a 3 cm2 b 5 cm2 c 4 -1- cm2
2
2 a 6 cm2 b 8 cm2 e 14 cm2
g 25 cm2 h 70 cm2 c 24 cm2 k 120 cm2

i 35 cm2 e 10 cm3

13:06 Volume of a Rectangular Prism e3
k 500
1 a 8 cm3 b 12 cm3 c 20 cm3 e5
k 0⋅7
2 a 48 cm3 b 72 cm3 c 32 cm3 e 400
k 3000
g 84 cm3 h 64 cm3 i 180 cm3

13:07 Capacity

1 a 2000 b 7000 c4
i 10 000
g 5 h 14 c 9000
i 500
2 a 3000 b2 c 100
i 100
g 7000 h 10

3a 3 b 15

g 500 h 750

INTERNATIONAL MATHEMATICS 1 FOUNDATION WORKSHEETS 14 © Pearson Education Australia 2007.
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Challenge
Extension 1:09 Solving Puzzles

1 a 6 32 18 44 30 b 23 6 19 2 15 c 3 10 17 19 26
40 16 42 28 4 10 18 1 14 22 22 24 6 8 15
14 50 26 2 38 17 5 13 21 9 11 13 20 27 4
48 24 10 36 12 4 12 25 8 16 25 7 9 16 18
22 8 34 20 46 11 24 7 20 3 14 21 23 5 12

2 5 cuts → 15 minutes
3 F is opposite A, E is opposite B, C is opposite D
45

42

16 3

Extension 3:06 HCF and LCM by Prime Factors

1 HCF = 8, LCM = 48 2 6, 72 3 4, 900 4 20, 560 5 27, 324 6 24, 144
10 12, 420 11 25, 150 12 14, 490
7 15, 150 8 18, 108 9 45, 270

Extension 8:02 Describing Number Patterns

1 a number = h (h + 1) b5 6 7 8
2 a 10, 15, 20 30 42 56 72

b 25, 30

3 a Number of sides (s) 3 4 5 6 7 8 9 10

Number of diagonals (d) 0 1 2 3 4 5 6 7

b The number of diagonals is 3 less than the number of sides.
c d=s−3

4 a B = T2, 100 b B = 12 − T, 2

5 a 21, 25 b 0⋅5, 0⋅25 c 0, −5 d 4 000 000, 40 000 000
d 6, 9, 14, 21
6 a 5, 8, 11, 14 b 5, 4, 3, 2 c −5, −3, −1, 1

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