Whole Numbers. Whole Numbers. Solutions. Curriculum Ready.

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1 Whole Numbers Whole Numbers Solutions Curriulum Ready

2 Copyright 009 P Learning. All rights reserved. First edition printed 009 in Australia. A atalogue reord for this book is available from P Learning Ltd. ISBN Ownership of ontent The materials in this resoure, inluding without limitation all information, text, graphis, advertisements, names, logos and trade marks (Content) are proteted by opyright, trade mark and other intelletual property laws unless expressly indiated otherwise. You must not modify, opy, reprodue, republish or distribute this Content in any way exept as expressly provided for in these General Conditions or with our express prior written onsent. Copyright Copyright in this resoure is owned or liensed by us. Other than for the purposes of, and subjet to the onditions presribed under, the Copyright At 968 (Cth) and similar legislation whih applies in your loation, and exept as expressly authorised by these General Conditions, you may not in any form or by any means: adapt, reprodue, store, distribute, print, display, perform, publish or reate derivative works from any part of this resoure; or ommerialise any information, produts or servies obtained from any part of this resoure. Where opyright legislation in a loation inludes a remunerated sheme to permit eduational institutions to opy or print any part of the resoure, we will laim for remuneration under that sheme where worksheets are printed or photoopied by teahers for use by students, and where teahers diret students to print or photoopy worksheets for use by students at shool. A worksheet is a page of learning, designed for a student to write on using an ink pen or penil. This may lead to an inrease in the fees for eduational institutions to partiipate in the relevant sheme. Published P Learning Ltd For more opies of this book, ontat us at: Designed P Learning Ltd Although every preaution has been taken in the preparation of this book, the publisher and authors assume no responsibility for errors or omissions. Neither is any liability assumed for damages resulting from the use of this information ontained herein.

3 Page questions Plae values Write down the plae values for eah of these numbers a 6 b 60 Plae value of : 000 Plae value of : Plae value of : 0 Plae value of : d Plae value of : Plae value of 7: Plae value of 6: Plae value of 8: Write eah of these ordinary numbers in: (i) worded form (ii) expanded form a 60 (i) Two thousand, five hundred and sixty (ii) ( # 000) + ( # 00) + (6 # 0) b 06 (i) One million, three hundred and six thousand, two hundred and eleven (ii) ( # ) + ( # ) + (0 # 0 000) + (6 # 000) + ( # 00) + ( # 0) + ( # ) (i) Eight hundred and ninety one thousand, and twenty six (ii) (8 # ) + (9 # 0 000) + ( # 000) + (0 # 00) + ( # 0) + (6 # ) Mathletis Passport P Learning H SERIES TOPIC

4 Page questions Plae values d (i) Seven hundred and eight thousand, and two (ii) (7 # ) + (0 # 0 000) + (8 # 000) + (0 # 00) + (0 # 0) + ( # ) e (i) Nine million, eleven thousand, and sixty (ii) (9 # ) + (0 # ) + ( # 0 000) + ( # 000) + (0 # 00) + (6 # 0) + (0 # ) Write the ordinary number for eah of these: a Four hundred and thirty nine thousand, two hundred and six 9 06 b ( # ) + ( # ) + (0 # 0 000) + ( # 000) + (0 # 00) + ( # 0) + (0 # ) 0 00 Eighty one thousand and five 8 00 d (9 # 0 000) + (8 # 000) + (9 # 00) + (9 # 0) + (8 # ) e Any number whose plae values for, and are 000, and 00 Any number with the orret plae values for, and suh as:, 0, 6 9, 00 0 f Three million, thirty thousand and thirty H SERIES TOPIC Mathletis Passport P Learning

5 Page 9 questions Adding and subtrating large numbers Calulate eah of these addition questions showing all working. a b d e f Combo Time! Page 0 questions Adding and subtrating large numbers a 6 8 b Mathletis Passport P Learning H SERIES TOPIC

6 Page 0 questions Adding and subtrating large numbers d e f Page questions Long multipliation a Multiply 06 by Put a 0 in the ones olumn and multiply 06 by Add the olumns together b Multiply 8 by 9 Put a 0 in the ones olumn and multiply 8 by Add the olumns together H SERIES TOPIC Mathletis Passport P Learning

7 Page questions Long multipliation Multiply 970 by Put a 0 in the ones olumn and multiply 970 by 6 Add the olumns together d Multiply 876 by Put a 0 in the ones olumn and multiply 876 by Add the olumns together e Multiply 0 by 7 Put a 0 in the ones olumn and multiply 0 by Add the olumns together f Multiply 0 0 by Put a 0 in the ones olumn and multiply 0 0 by Add the olumns together Page questions Long multipliation a Multiply by Put a 0 in the ones olumn and multiply by Put 0s in the ones and tens olumns and multiply by Add the olumns together Mathletis Passport P Learning H SERIES TOPIC

8 Page questions Long multipliation b Multiply 8 by Put a 0 in the ones olumn and multiply 8 by 0 Put 0s in the ones and tens olumns and multiply 8 by Add the olumns together Multiply 908 by 9 Put a 0 in the ones olumn and multiply 908 by 0 Put 0s in the ones and tens olumns and multiply 908 by Add the olumns together d Multiply 86 by Put a 0 in the ones olumn and multiply 86 by Put 0s in the ones and tens olumns and multiply 86 by Add the olumns together e Multiply by 7 Put a 0 in the ones olumn and multiply by Put 0s in the ones and tens olumns and multiply by Add the olumns together f Multiply 68 by Put a 0 in the ones olumn and multiply 68 by Put 0s in the ones and tens olumns and multiply 68 by Add the olumns together 6 H SERIES TOPIC Mathletis Passport P Learning

9 Page 6 questions Short division a b g g d g 6 9 6g 0 a b r 7 7g r g d g 7 7 r g r Mathletis Passport P Learning H SERIES TOPIC 7

10 Page 7 questions Long division a 7 g b 8 9 g ` 8 ' 7 ` 897 ' 89 6 g d 7 7 g ` 8 ' 6 ` 78 ' H SERIES TOPIC Mathletis Passport P Learning

11 Page 9 questions Commutative laws a Two rows of four b Four olumns of two Four rows of two d Two olumns of four # # # # e Four olumns of one f Three rows of six g Two rows of seven h Four rows of one # # 6 # 7 # a b # # 6 # # d # # 6 # # 6 8 Mathletis Passport P Learning H SERIES TOPIC 9

12 Page 0 questions Commutative laws Here are two of the many possibilities # 6 6 # # 6 6 # To obtain an answer of, these whole number multipliations are possible: # 6 # 8 # # 6 # 8 # # # # 6 6 # 8 # # 8 # # # # 0 H SERIES TOPIC Mathletis Passport P Learning

13 Page questions Assoiative laws a b d Mathletis Passport P Learning H SERIES TOPIC

14 Page questions Assoiative laws a b d e f H SERIES TOPIC Mathletis Passport P Learning

15 Page questions Assoiative laws a # # 6 # # # # # 6 # 6 b # # 0 # # # # 8 # # 0 0 # # 68 8 # # 7 8 # # 7 # 7 8 # 68 d # # 6 # # 0 6 # # 0 6 # 0 8 # 0 80 Mathletis Passport P Learning H SERIES TOPIC

16 Page questions Assoiative laws a # # # ( # ) ( # ) # b # # # ( # 6) ( # ) # 6 # # # ( # ) ( # ) # d # # # ( # ) ( # ) # 0 a # 8 # 0 # 0 # 8 b # 0 # 7 # 0 # 7 00 # # # 9 # 7 # 7 # 9 d # # # # 00 # 9 80 # H SERIES TOPIC Mathletis Passport P Learning

17 Page 6 questions Assoiative laws 6 a ( ' ) ' ' ( ' ) True False b ( ' 0) ' ' (0 ' ) True False (0 - ) ( - ) True False d (0 ' 6) ' 0 ' (6 ' ) True False e (0 - ) ( - 0) True False f ( ' ) ' ' ( ' ) True False g (0 ' ) ' 0 ' ( ' ) True False h (8-0) (0 - ) True False i ( - ) - - ( - ) True False j (0 - ) ( - 0) True False 7 a ( + 8) + ( + + ) ( + 8) + ( + + ) Numbers were grouped that added to a multiple of 0 to make it easier to add together. b # # # ( # ) # ( # ) 6 # 0 60 ( # ) # ( # ) 60 # ( + 7) + ( + 6) + ( + 9) a # b # # # # # # # # # # 7 # # # 7 0 # 0 0 # 00 0 Mathletis Passport P Learning H SERIES TOPIC

18 Page 8 questions Distributive law a # + 6 # + # 6 b 7 # 8-7 # 8-7 # 6 # + 6 # 9 6 # + 9 d # 7 - # 0 # 7-0 e # # f # a a) # 8 + # 8 + # b) # + 6 # + # b The sum of the terms inside both brakets are equal. So is multiplied by the same value in both expressions. # # + 9 # + 7 # + The sum of the terms inside the brakets must equal 0. a 6 # 6 # 0 + b 8 # 98 8 # 00-6 # # 8 # 00-8 # # # 0 + d # 9 # 0 - # 0 + # # 0 - # H SERIES TOPIC Mathletis Passport P Learning

19 Page 9 questions Distributive law a # 7 b # 8 # 7 # (0 - ) # 0 - # # 0 - # 8 # (80 + ) # 80 + # # (0 + ) # 0-0 # 0 + # (0 + ) # # 80 + # # 7 d # # 7 7 # (0 + ) 7 # # 7 # # # (00 + ) # 00 + # 00 + # (70 + ) # # 0 + # (0 + ) # # + # e 8 # f 0 # 08 # 8 # (80 + ) # 80 + # # # 08 0 # (0 - ) 0 # 0-0 # 0 # 0-0 (0 + ) # # 80 + # (00 + 0) # # # Mathletis Passport P Learning H SERIES TOPIC 7

20 Page questions Divisibility Tests,,, 0 60,, 8 6,,, 6, ,, 9 07,, 8 6,,, ,, 6, ,,, ,,,, 6, 8, 9, None of them 87,, 6, 9, H SERIES TOPIC Mathletis Passport P Learning

21 Page questions Index notation for numbers a # b # # # # # # d # # # 6 e 7 # 7 # 7 # 7 # 7 # 7 7 f # # # # # # # 8 a # # # # # 8 # 6 8 b # # # # # # 6 # 6 # 6 # 7 # 7 # 7 6 # 7 96 # 8 d # # # # # # 8 8 e # 8 # 8 # # 8 # 8 # 8 # 8 # f # # # # # # # # # 8 # 7 # 6 6 a # # b 8 8 # 8 # 8 # # # # # 7 d # # # # # # e # 7 # # # 7 # 7 f # # # # # # g 7 # 7 # 7 # 7 # 7 # 7 # # # # h # # # # # # # # # Mathletis Passport P Learning H SERIES TOPIC 9

22 Page questions Puzzle Time 6 6 Area expression Area expression Area # + + # + # + # 6 Area ( + 6) # ( + + 6) If you went further and alulated the area, you would get: units # units 6 units 6 units Page questions Square roots and ube roots a means 'beause' a or a # # b 6 a # 6 or 6 # a # or # d 9 a 7 # 7 9 or 9 7 # H SERIES TOPIC Mathletis Passport P Learning

23 Page 6 questions Square roots and ube roots a means 'beause' e 8 9 a 9 # 9 8 or 8 9 # f a # or # a 7 a # # 7 or 7 # # b 6 or 6 # # a # # a 6 # 6 # 6 6 or 6 6 # 6 # d 8 or a 8 # 8 # 8 8 # 8 # a 9 a # 9 or # 9 ` 9 b 8 6 or 8 8 # 8 a 8 # ` a 6 # 6 6 or 6 6 # 6 6 ` 6 6 d or a # ` # a a # # or # # ` b 8 or # # a # # 8 8 ` 8 a # # or # # ` d 7 or a 7 # 7 # # 7 # 7 ` 7 Mathletis Passport P Learning H SERIES TOPIC

24 Where does it work? Solutions Whole Numbers Page 9 questions Fator Trees 8 9 ` # 8 ` # ` 6 # 7 ` ` 8 # # 7 ` 8 7 H SERIES TOPIC Mathletis Passport P Learning

25 Where does it work? Solutions Whole Numbers Page 0 questions Fator Trees 8 a b 0 ` 8 ` 0 # d ` # ` 60 # # e 96 f 8 ` # ` 96 # Mathletis Passport P Learning H SERIES TOPIC

26 Where does it work? Solutions Whole Numbers Page questions Highest ommon fator (HCF) Find the highest ommon fator for these pairs of numbers. a 8 and Fators of 8:,,, 8 Fators of :,,,, 6, ` The HCF for 8 and is: b 6 and Fators of 6:,,, 6 Fators of :,,, ` The HCF for 6 and is: 0 and 8 Fators of 0:,,, 0 Fators of 8:,,, 6, 9, 8 ` The HCF for 0 and 8 is: d 8 and Fators of 8:,,, 6, 9, 8 Fators of :,,,, 6, 8,, ` The HCF for 8 and is: 6 e and 8 Fators of :,, 7, Fators of 8:,,, 7,, 8 ` The HCF for and 8 is: f 6 and 6 Fators of 6:,,, 8, 6 Fators of 6:,,,, 6, 9,, 8, 6 ` The HCF for 6 and 6 is: H SERIES TOPIC Mathletis Passport P Learning

27 Where does it work? Solutions Whole Numbers Page questions Highest ommon fator (HCF) Use the prime fators to find the HCF for these larger numbers. a and 8 Prime fators of :,,,, Prime fators of 8:,,, 7 ` The HCF for and 8 is: # # b 9 and 7 Prime fators of 9:,, Prime fators of 7:,,,, ` The HCF for 9 and 7 is: # 80 and 90 Prime fators of 80:,,,, 7 Prime fators of 90:,, 7, 7 ` The HCF for 80 and 90 is: 7 70 # # d 6 and 60 Prime fators of 6:,,,,,,, Prime fators of 60:,,,,,,, ` The HCF for 6 and 60 is: 8 # # # # # # Mathletis Passport P Learning H SERIES TOPIC

28 Where does it work? Solutions Whole Numbers Page questions Lowest ommon multiple (LCM) Find the lowest ommon multiple for these pairs of numbers. a and 9 Multiples of :, 6, 9,,... Multiples of 9: 9, 8,... ` The LCM for and 9 is: 9 b and 0 Multiples of :, 0,,... Multiples of 0: 0, 0,... ` The LCM for and 0 is: 0 and 6 Multiples of :, 8,, 6,... Multiples of 6: 6,, 8,... ` The LCM for and 6 is: d and 6 Multiples of :, 0,, 0,, 0,... Multiples of 6: 6,, 8,, 0,... ` The LCM for and 6 is: 0 e 6 and 7 Multiples of 6: 6,, 8,, 0, 6,, 8,... Multiples of 7: 7,,, 8,,,... ` The LCM for 6 and 7 is: f and 6 Multiples of :,, 6, 8, 60, 7,... Multiples of 6: 6,, 8, 6,... ` The LCM for and 6 is: 8 6 H SERIES TOPIC Mathletis Passport P Learning

29 Where does it work? Solutions Whole Numbers Page questions Lowest ommon multiple (LCM) Use the prime fators to find the LCM for these larger numbers. Steps taken l List all the prime fators for both numbers l Cirle all the different fators in the smaller number l Multiply the larger number by the different fator a 60 and 08 Prime fators of 60:,,, Prime fators of 08:,,,, ` The LCM for 60 and 08 is: 08 0 # b and 0 Prime fators of :,, 7 Prime fators of 0:,,, ` The LCM for and 0 is: # 68 and 80 Prime fators of 68:,,,, 7 Prime fators of 80:,,,, ` The LCM for 68 and 80 is: # # d 0 and 8 Prime fators of 0:,,, 7 Prime fators of 8:, 7, ` The LCM for 0 and 8 is: 8 0 # # Mathletis Passport P Learning H SERIES TOPIC 7

30 What else an you do? Solutions Whole Numbers Page 7 questions Pasal's Triangle Page 9 questions Appliations of Pasal's Triangle A B C D 0 E 8 F 6 A B C D E F 8 H SERIES TOPIC Mathletis Passport P Learning

Appliations of Pasal's Triangle Start Start

Path Path 6 Page 0 questions Appliations of

number of different pathways the ant an travel

31 What else an you do? Solutions Whole Numbers Page 9 questions Appliations of Pasal's Triangle Start Start Start Path Path Path Start Start Start Path Path Path 6 Page 0 questions Appliations of Pasal's Triangle Main Chamber The total number of different pathways the ant an travel downwards to the main hamber Mathletis Passport P Learning H SERIES TOPIC 9

32 Whole Numbers

Whole Numbers. Whole Numbers. Solutions. Curriculum Ready.

Whole Numbers. Whole Numbers. Solutions. Curriculum Ready. Whole Numbers Whole Numbers Solutions Curriulum Ready www.mathletis.om Page questions Plae values Write down the plae values for eah of these numbers a 6 b 60 Plae value of : 000 Plae value of : Plae