Whole Numbers WHOLE NUMBERS.

Whole Numbers WHOLE NUMBERS www.mathletics.co.uk

How does it wk? Solutions Whole Numbers Page questions Place values Write down the place values f each of these numbers a 6 b 60 Place value of : 000 Place value of : Place value of : 0 Place value of : 0 000 c 60 d 7 80 6 Place value of : 00 000 Place value of 7: 7 000 000 Place value of 6: 60 000 Place value of 8: 80 000 Write each of these dinary numbers in: (i) wded fm (ii) partitioned fm 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) ( # 000 000) + ( # 00 000) + (0 # 0 000) + (6 # 000) + ( # 00) + ( # 0) + ( # ) c 89 06 (i) Eight hundred and ninety one thousand, and twenty six (ii) (8 # 00 000) + (9 # 0 000) + ( # 000) + (0 # 00) + ( # 0) + (6 # ) Mathletics Passpt P Learning H SERIES TOPIC

How does it wk? Solutions Whole Numbers Page questions Place values d 708 00 (i) Seven hundred and eight thousand, and two (ii) (7 # 00 000) + (0 # 0 000) + (8 # 000) + (0 # 00) + (0 # 0) + ( # ) e 9 0 060 (i) Nine million, eleven thousand, and sixty (ii) (9 # 000 000) + (0 # 00 000) + ( # 0 000) + ( # 000) + (0 # 00) + (6 # 0) + (0 # ) Write the dinary number f each of these: a Four hundred and thirty nine thousand, two hundred and six 9 06 b ( # 000 000) + ( # 00 000) + (0 # 0 000) + ( # 000) + (0 # 00) + ( # 0) + (0 # ) 0 00 c Eighty one thousand and five 8 00 d (9 # 0 000) + (8 # 000) + (9 # 00) + (9 # 0) + (8 # ) 98 998 e Any number whose place values f, and are 000, and 00 Any number with the crect place values f, and such as:, 0, 6 9, 00 0 f Three million, thirty thousand and thirty 00 00 H SERIES TOPIC Mathletics Passpt P Learning

How does it wk? Solutions Whole Numbers Page 9 questions Adding and subtracting large numbers Calculate each of these addition questions showing all wking. a 6 0 8 8 0 6 9 6 9 + b 7 0 0 + 0 8 0 9 0 8 6 0 c 9 9 + d 8 + 9 8 6 6 0 6 0 6 7 0 e 6 9 9 9 7 6 0 9 9 6 + f 8 7 6 8 9 0 8 7 6 + Combo Time! 0 9 8 7 9 6 6 0 0 + Page 0 questions Adding and subtracting large numbers a 6 8 b 7 6 0 9 6 9 6 Mathletics Passpt P Learning H SERIES TOPIC

How does it wk? Solutions Whole Numbers Page 0 questions Adding and subtracting large numbers c 6 6 8 0 8 7 8 6 d 9 7 6 e 0 0 0 0 0 9 8 7 f 7 0 0 0 0 6 7 8 9 7 0 7 9 8 7 7 9 6 Page questions Long multiplication a 0 6 0 6 + 6 0 0 6 6 Multiply 06 by Put a 0 in the ones column and multiply 06 by Add the columns together b 8 9 + +7 8 9 8 0 + + 9 0 9 Multiply 8 by 9 Put a 0 in the ones column and multiply 8 by Add the columns together H SERIES TOPIC Mathletics Passpt P Learning

How does it wk? Solutions Whole Numbers Page questions Long multiplication c 9 7 0 6 + + 7 0 + + 0 0 0 + + 6 0 9 0 Multiply 970 by Put a 0 in the ones column and multiply 970 by 6 Add the columns together d 8 7 6 + + + 0 0 + + + 8 0 + + + 7 0 Multiply 876 by Put a 0 in the ones column and multiply 876 by Add the columns together e 0 7 + 7 0 7 0 6 0 + 7 Multiply 0 by 7 Put a 0 in the ones column and multiply 0 by Add the columns together f 0 0 + + 0 0 0 0 0 0 0 0 0 0 0 Multiply 0 0 by Put a 0 in the ones column and multiply 0 0 by Add the columns together Page questions Long multiplication a 0 0 0 6 Multiply by Put a 0 in the ones column and multiply by Put 0s in the ones and tens columns and multiply by Add the columns together Mathletics Passpt P Learning H SERIES TOPIC

How does it wk? Solutions Whole Numbers Page questions Long multiplication b 8 0 + + 0 0 0 0 0 0 + + 8 0 0 0 + 0 9 0 Multiply 8 by Put a 0 in the ones column and multiply 8 by 0 Put 0s in the ones and tens columns and multiply 8 by Add the columns together c 9 0 8 0 9 +7 8 0 0 0 0 0 + 8 0 6 0 0 8 9 7 7 Multiply 908 by 9 Put a 0 in the ones column and multiply 908 by 0 Put 0s in the ones and tens columns and multiply 908 by Add the columns together d 8 6 + + 0 0 0 + + 6 0 + + 8 0 0 + + 9 8 0 8 0 Multiply 86 by Put a 0 in the ones column and multiply 86 by Put 0s in the ones and tens columns and multiply 86 by Add the columns together e 7 + + + 7 + 9 6 0 + + 8 0 0 0 + + + 7 9 0 Multiply by 7 Put a 0 in the ones column and multiply by Put 0s in the ones and tens columns and multiply by Add the columns together f 6 8 + + + 8 + + 8 6 0 0 6 8 0 0 + + 7 9 7 6 Multiply 68 by Put a 0 in the ones column and multiply 68 by Put 0s in the ones and tens columns and multiply 68 by Add the columns together 6 H SERIES TOPIC Mathletics Passpt P Learning

How does it wk? Solutions Whole Numbers Page 6 questions Sht division a 767 89 b 680 6 8 9 6 g 7 6 7 g 6 8 0 c 69 78 d 0 6 009 7 8 0 0 0 9 g 6 9 6g 0 a 896 7 80 7 b 879 99 8 0 r 7 7g 8 9 6 9 9 r g 8 7 9 c 96 8 7 8 7 d 80 6 966 6 g 7 7 r 8 6 8 9 6 g 0 9 6 6 r 6 6 8 0 Mathletics Passpt P Learning H SERIES TOPIC 7

How does it wk? Solutions Whole Numbers Page 7 questions Long division a 7 g 8 0 8 7 0 0 0 b 8 9 g 8 9 7 6 9 0 8 0 7 0 7 0 ` 8 ' 7 ` 897 ' 89 c 6 g 8 8 8 d 7 7 g 7 8 7 8 7 8 8 7 ` 8 ' 6 ` 78 ' 7 7 8 H SERIES TOPIC Mathletics Passpt P Learning

How does it wk? Solutions Whole Numbers Page 9 questions Divisibility Tests,,, 0 60,, 8 6,,, 6, 8 96 9,, 9 07,, 8 6,,, 6 88 8,, 6, 9 78 00 00 9,,, 6 76 0,,,, 6, 8, 9, 0 860 None of them 87,, 6, 9, 0 600 Mathletics Passpt P Learning H SERIES TOPIC 9

How does it wk? Solutions Whole Numbers Page questions Index notation f numbers a # b # # c # # # # d # # # 6 e 7 # 7 # 7 # 7 # 7 # 7 7 f # # # # # # # 8 a # # # # # 8 # 6 8 b # # # # # 6 00 c 6 # 6 # 6 # 6 # 7 # 7 # 7 6 # 7 96 # 8 d # # # # # # 8 8 e # 8 # 8 # # 8 # 8 # 8 # 8 # 768 07 f # # # # # # # # # 8 # 7 # 6 6 a # # b 8 8 # 8 # 8 # 8 6 6 6 6 6 c 6 # # # # 7 d # # # # # # e # 7 # # # 7 # 7 f # # # # # # g 7 # 7 # 7 # 7 # 7 # 7 # # # # h # # # # # # # # # 0 H SERIES TOPIC Mathletics Passpt P Learning

How does it wk? Solutions Whole Numbers Page questions Puzzle Time 6 6 Area expression Area expression Area # + + # + # + # 6 Area ( + 6) # ( + + 6) If you went further and calculated the area, you would get: + 9+ + 0 + 7 units # units 6 units 6 units Page questions Square roots and cube roots a means 'because' a a # # b 6 a # 6 6 # c a # # d 9 a 7 # 7 9 9 7 # 7 7 7 Mathletics Passpt P Learning H SERIES TOPIC

How does it wk? Solutions Whole Numbers Page questions Square roots and cube roots a means 'because' e 8 9 a 9 # 9 8 8 9 # 9 9 9 f a # # a 7 a # # 7 7 # # b 6 a # # 6 6 # # c 6 6 a 6 # 6 # 6 6 6 6 # 6 # 6 6 6 d 8 a 8 # 8 # 8 8 # 8 # 8 8 8 a 9 a # 9 # 9 ` 9 b 8 6 a 8 # 8 6 8 8 # 8 6 ` 8 6 c 6 6 a 6 # 6 6 6 6 # 6 6 ` 6 6 d a # ` # a a # # # # ` b 8 a # # 8 ` # # 8 8 c a # # # # ` d 7 a 7 # 7 # 7 7 7 # 7 # 7 ` 7 H SERIES TOPIC Mathletics Passpt P Learning

Where does it wk? Solutions Whole Numbers Page 7 questions Fact Trees 8 9 ` # 8 ` # 6 8 7 ` 6 # 7 ` 8 8 7 6 6 6 ` 8 # # 7 ` 8 7 Mathletics Passpt P Learning H SERIES TOPIC

Where does it wk? Solutions Whole Numbers Page 8 questions Fact Trees 8 a b 0 ` 8 ` 0 # c d 60 8 0 ` # ` 60 # # e 96 f 8 ` # ` 96 # H SERIES TOPIC Mathletics Passpt P Learning

Where does it wk? Solutions Whole Numbers Page 0 questions Highest common fact (HCF) Find the highest common fact f these pairs of numbers. a 8 and Facts of 8:,,, 8 Facts of :,,,, 6, ` The HCF f 8 and is: b 6 and Facts of 6:,,, 6 Facts of :,,, ` The HCF f 6 and is: c 0 and 8 Facts of 0:,,, 0 Facts of 8:,,, 6, 9, 8 ` The HCF f 0 and 8 is: d 8 and Facts of 8:,,, 6, 9, 8 Facts of :,,,, 6, 8,, ` The HCF f 8 and is: 6 e and 8 Facts of :,, 7, Facts of 8:,,, 7,, 8 ` The HCF f and 8 is: f 6 and 6 Facts of 6:,,, 8, 6 Facts of 6:,,,, 6, 9,, 8, 6 ` The HCF f 6 and 6 is: Mathletics Passpt P Learning H SERIES TOPIC

Where does it wk? Solutions Whole Numbers Page 0 questions Highest common fact (HCF) Use the prime facts to find the HCF f these larger numbers. a and 8 Prime facts of :,,,, Prime facts of 8:,,, 7 ` The HCF f and 8 is: # # b 9 and 7 Prime facts of 9:,, Prime facts of 7:,,,, ` The HCF f 9 and 7 is: # c 80 and 90 Prime facts of 80:,,,, 7 Prime facts of 90:,, 7, 7 ` The HCF f 80 and 90 is: 7 70 # # d 6 and 60 Prime facts of 6:,,,,,,, Prime facts of 60:,,,,,,, ` The HCF f 6 and 60 is: 8 # # # # # # 6 H SERIES TOPIC Mathletics Passpt P Learning

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

Where does it wk? Solutions Whole Numbers Page questions Lowest common multiple (LCM) Use the prime facts to find the LCM f these larger numbers. Steps taken l List all the prime facts f both numbers l Circle all the different facts in the smaller number l Multiply the larger number by the different fact a 60 and 08 Prime facts of 60:,,, Prime facts of 08:,,,, ` The LCM f 60 and 08 is: 08 0 # b and 0 Prime facts of :,, 7 Prime facts of 0:,,, ` The LCM f and 0 is: 0 7 00 # c 68 and 80 Prime facts of 68:,,,, 7 Prime facts of 80:,,,, ` The LCM f 68 and 80 is: 80 7 0 # # d 0 and 8 Prime facts of 0:,,, 7 Prime facts of 8:, 7, ` The LCM f 0 and 8 is: 8 0 # # 8 H SERIES TOPIC Mathletics Passpt P Learning

What else can you do? Solutions Whole Numbers Page questions Pascal's Triangle 6 0 0 6 0 6 7 7 8 8 6 70 6 8 8 9 6 8 6 6 8 6 9 0 0 0 0 0 0 6 0 6 6 0 6 0 66 0 9 79 9 79 9 0 66 78 86 7 87 76 76 87 7 86 78 9 6 00 00 00 00 00 00 6 9 0 6 00 00 6 6 00 00 6 0 Page 7 questions Applications of Pascal's Triangle A B C D 0 E 8 F 6 A B C D E F Mathletics Passpt P Learning H SERIES TOPIC 9

What else can you do? Solutions Whole Numbers Page 7 questions Applications of Pascal's Triangle Start Start Start Path Path Path Start Start Start Path Path Path 6 Page 8 questions Applications of Pascal's Triangle 6 0 0 Main Chamber The total number of different pathways the ant can travel downwards to the main chamber + + 0 + 0 + + 0 H SERIES TOPIC Mathletics Passpt P Learning

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