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๐œ‹ - white rose mathsย ยท 2 5 รท 5 2 5 รท5 2 5 ร— ๐‘Ÿ 3 5 ร— ๐‘Ÿ 4 5 รท๐‘Ÿ 2 5 ร— ๐‘Ÿ 3๐‘Ÿ 5...

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Page 1: ๐œ‹ - White Rose Mathsย ยท 2 5 รท 5 2 5 รท5 2 5 ร— ๐‘Ÿ 3 5 ร— ๐‘Ÿ 4 5 รท๐‘Ÿ 2 5 ร— ๐‘Ÿ 3๐‘Ÿ 5 ร— 3๐‘Ÿ 5ร—4 5 รท๐‘Ÿ 2 5 ร— ๐‘Ÿ รท2 3๐‘Ÿ 5 ร—2 3๐‘Ÿ2 ร—1 5รท4 5 รท๐‘Ÿ a 2
Page 2: ๐œ‹ - White Rose Mathsย ยท 2 5 รท 5 2 5 รท5 2 5 ร— ๐‘Ÿ 3 5 ร— ๐‘Ÿ 4 5 รท๐‘Ÿ 2 5 ร— ๐‘Ÿ 3๐‘Ÿ 5 ร— 3๐‘Ÿ 5ร—4 5 รท๐‘Ÿ 2 5 ร— ๐‘Ÿ รท2 3๐‘Ÿ 5 ร—2 3๐‘Ÿ2 ร—1 5รท4 5 รท๐‘Ÿ a 2
Page 3: ๐œ‹ - White Rose Mathsย ยท 2 5 รท 5 2 5 รท5 2 5 ร— ๐‘Ÿ 3 5 ร— ๐‘Ÿ 4 5 รท๐‘Ÿ 2 5 ร— ๐‘Ÿ 3๐‘Ÿ 5 ร— 3๐‘Ÿ 5ร—4 5 รท๐‘Ÿ 2 5 ร— ๐‘Ÿ รท2 3๐‘Ÿ 5 ร—2 3๐‘Ÿ2 ร—1 5รท4 5 รท๐‘Ÿ a 2

โ€ข

โ€ข

โ€ข

โ€ข

โ€ข๐œ‹

โ€ข

โ€ข

โ€ข

โ€ข

โ€ข

โ€ข

โ€ข

โ€ข

Page 4: ๐œ‹ - White Rose Mathsย ยท 2 5 รท 5 2 5 รท5 2 5 ร— ๐‘Ÿ 3 5 ร— ๐‘Ÿ 4 5 รท๐‘Ÿ 2 5 ร— ๐‘Ÿ 3๐‘Ÿ 5 ร— 3๐‘Ÿ 5ร—4 5 รท๐‘Ÿ 2 5 ร— ๐‘Ÿ รท2 3๐‘Ÿ 5 ร—2 3๐‘Ÿ2 ร—1 5รท4 5 รท๐‘Ÿ a 2

โ€ข

โ€ข

โ€ข

โ€ข

โ€ข

โ€ข

Page 5: ๐œ‹ - White Rose Mathsย ยท 2 5 รท 5 2 5 รท5 2 5 ร— ๐‘Ÿ 3 5 ร— ๐‘Ÿ 4 5 รท๐‘Ÿ 2 5 ร— ๐‘Ÿ 3๐‘Ÿ 5 ร— 3๐‘Ÿ 5ร—4 5 รท๐‘Ÿ 2 5 ร— ๐‘Ÿ รท2 3๐‘Ÿ 5 ร—2 3๐‘Ÿ2 ร—1 5รท4 5 รท๐‘Ÿ a 2

1

3

1

3

1

3

1

3

1

3

1

3

๐Ÿ

๐Ÿ‘

๐Ÿ

๐Ÿ‘

๐Ÿ

๐Ÿ‘

๐Ÿ

๐Ÿ‘

1

3

1

1

2

1

2

1

6

1

6

1

6

1

6

1

6

1

6

1

3

1

3

1

3

1

4

1

4

1

4

1

4

1

8

1

8

1

8

1

8

1

8

1

8

1

8

1

8

Page 6: ๐œ‹ - White Rose Mathsย ยท 2 5 รท 5 2 5 รท5 2 5 ร— ๐‘Ÿ 3 5 ร— ๐‘Ÿ 4 5 รท๐‘Ÿ 2 5 ร— ๐‘Ÿ 3๐‘Ÿ 5 ร— 3๐‘Ÿ 5ร—4 5 รท๐‘Ÿ 2 5 ร— ๐‘Ÿ รท2 3๐‘Ÿ 5 ร—2 3๐‘Ÿ2 ร—1 5รท4 5 รท๐‘Ÿ a 2
Page 7: ๐œ‹ - White Rose Mathsย ยท 2 5 รท 5 2 5 รท5 2 5 ร— ๐‘Ÿ 3 5 ร— ๐‘Ÿ 4 5 รท๐‘Ÿ 2 5 ร— ๐‘Ÿ 3๐‘Ÿ 5 ร— 3๐‘Ÿ 5ร—4 5 รท๐‘Ÿ 2 5 ร— ๐‘Ÿ รท2 3๐‘Ÿ 5 ร—2 3๐‘Ÿ2 ร—1 5รท4 5 รท๐‘Ÿ a 2
Page 8: ๐œ‹ - White Rose Mathsย ยท 2 5 รท 5 2 5 รท5 2 5 ร— ๐‘Ÿ 3 5 ร— ๐‘Ÿ 4 5 รท๐‘Ÿ 2 5 ร— ๐‘Ÿ 3๐‘Ÿ 5 ร— 3๐‘Ÿ 5ร—4 5 รท๐‘Ÿ 2 5 ร— ๐‘Ÿ รท2 3๐‘Ÿ 5 ร—2 3๐‘Ÿ2 ร—1 5รท4 5 รท๐‘Ÿ a 2

3

12

1

4+

1

4+

1

43 ร—

1

4

7 ร—2

3

๐Ÿ

๐Ÿ‘

๐Ÿ

๐Ÿ‘

๐Ÿ

๐Ÿ‘

๐Ÿ

๐Ÿ‘

1

1

7

Page 9: ๐œ‹ - White Rose Mathsย ยท 2 5 รท 5 2 5 รท5 2 5 ร— ๐‘Ÿ 3 5 ร— ๐‘Ÿ 4 5 รท๐‘Ÿ 2 5 ร— ๐‘Ÿ 3๐‘Ÿ 5 ร— 3๐‘Ÿ 5ร—4 5 รท๐‘Ÿ 2 5 ร— ๐‘Ÿ รท2 3๐‘Ÿ 5 ร—2 3๐‘Ÿ2 ร—1 5รท4 5 รท๐‘Ÿ a 2

3 ร—2

7

4 ร—2

3=

8

3

8

3= 2

2

3

2

7

2

7

2

7

3ร—2

7

๐Ÿ

๐Ÿ‘

๐Ÿ

๐Ÿ‘

๐Ÿ

๐Ÿ‘

๐Ÿ

๐Ÿ‘

3 ร—2

38 ร—

2

3

2

3ร— 5 1.5 ร—

4

3

3 ร—2

52 ร—

3

53 ร—

2

53 ร—

2

73 ร—

2

56 ร—

1

5

Page 10: ๐œ‹ - White Rose Mathsย ยท 2 5 รท 5 2 5 รท5 2 5 ร— ๐‘Ÿ 3 5 ร— ๐‘Ÿ 4 5 รท๐‘Ÿ 2 5 ร— ๐‘Ÿ 3๐‘Ÿ 5 ร— 3๐‘Ÿ 5ร—4 5 รท๐‘Ÿ 2 5 ร— ๐‘Ÿ รท2 3๐‘Ÿ 5 ร—2 3๐‘Ÿ2 ร—1 5รท4 5 รท๐‘Ÿ a 2

1

3ร—

1

5=

1

15

1

3ร—

1

2

1

3รท 5

1

5รท 3

1

3

1

5ร—1

6=1

?

1

3ร—1

?=

1

30

1

?ร—1

?=

1

30

Page 11: ๐œ‹ - White Rose Mathsย ยท 2 5 รท 5 2 5 รท5 2 5 ร— ๐‘Ÿ 3 5 ร— ๐‘Ÿ 4 5 รท๐‘Ÿ 2 5 ร— ๐‘Ÿ 3๐‘Ÿ 5 ร— 3๐‘Ÿ 5ร—4 5 รท๐‘Ÿ 2 5 ร— ๐‘Ÿ รท2 3๐‘Ÿ 5 ร—2 3๐‘Ÿ2 ร—1 5รท4 5 รท๐‘Ÿ a 2

2

3ร—

3

5

2 ร— 3

3 ร— 5=

6

15=2

5

3

5

2 ร— 3

3 ร— 5=2 ร— 3

5 ร— 3=2

5

2 ร— 3 ร—1

3ร—1

5

2

33

5

1

5ร—3

8

2

5ร—3

8โˆ’

1

15ร—

9

16

2

15ร—15

16

3

5

2

0.2 ร—40

81

2

3ร—

3

4ร—

32

56

3

8ร—8

7

5

7ร—

3

11

3

4+

4

10

Page 12: ๐œ‹ - White Rose Mathsย ยท 2 5 รท 5 2 5 รท5 2 5 ร— ๐‘Ÿ 3 5 ร— ๐‘Ÿ 4 5 รท๐‘Ÿ 2 5 ร— ๐‘Ÿ 3๐‘Ÿ 5 ร— 3๐‘Ÿ 5ร—4 5 รท๐‘Ÿ 2 5 ร— ๐‘Ÿ รท2 3๐‘Ÿ 5 ร—2 3๐‘Ÿ2 ร—1 5รท4 5 รท๐‘Ÿ a 2

1

3

1

3

1

3

1 รท1

3= 4 รท

1

3= 40 รท

1

3= 1 รท

1

?= 6 ? รท

1

6= 30 ? รท

1

6= 15

4 รท1

24 รท

1

34 รท

1

44 รท

1

5

4 รท1

138 รท

1

138 รท

1

๐‘›๐‘Ž รท

1

๐‘›

1

2

1

2

1

2

1

2

1

2

1

2

1

2

1

2

4

4 รท1

2=

4 รท 8 =

2 รท1

2=

1 รท1

2=

Page 13: ๐œ‹ - White Rose Mathsย ยท 2 5 รท 5 2 5 รท5 2 5 ร— ๐‘Ÿ 3 5 ร— ๐‘Ÿ 4 5 รท๐‘Ÿ 2 5 ร— ๐‘Ÿ 3๐‘Ÿ 5 ร— 3๐‘Ÿ 5ร—4 5 รท๐‘Ÿ 2 5 ร— ๐‘Ÿ รท2 3๐‘Ÿ 5 ร—2 3๐‘Ÿ2 ร—1 5รท4 5 รท๐‘Ÿ a 2

3

4รท

1

4

3

8รท

1

8

1

2รท

1

6

1

3รท

1

6

< > =

3

4รท

1

8

3

8

1

8

1

8

1

8

1

4

1

4

1

4

1

8

1

8

1

8

1

8

1

8

1

8

1

2

1

2

1

6

1

6

1

6

1

6

1

6

1

6

1

3

1

3

1

3

1

2รท

1

3=

3

2

3

5รท1

5

3

5รท1

6

1

2รท1

5

1

4รท1

5

1

5รท1

3

3

5รท1

9

Page 14: ๐œ‹ - White Rose Mathsย ยท 2 5 รท 5 2 5 รท5 2 5 ร— ๐‘Ÿ 3 5 ร— ๐‘Ÿ 4 5 รท๐‘Ÿ 2 5 ร— ๐‘Ÿ 3๐‘Ÿ 5 ร— 3๐‘Ÿ 5ร—4 5 รท๐‘Ÿ 2 5 ร— ๐‘Ÿ รท2 3๐‘Ÿ 5 ร—2 3๐‘Ÿ2 ร—1 5รท4 5 รท๐‘Ÿ a 2

1

5ร— 5

1

4รท

7

8

1

4รท

7

8

2

7

1

4รท

7

81

4ร—

8

7?

21

2

2

50.4 ๐‘Ž

2

๐‘Ž

3 รท1

4

3 ร— 4

3 รท 4

3 ร—1

4

8 รท1

5

8 ร— 5

8 รท 5

8 ร—1

5

1

4

1

4

1

4

1

4

1

8

1

8

1

8

1

8

1

8

1

8

1

8

1

8

2 รท1

52 รท

2

5

3

5รท2

5

3

10รท2

5

1

5รท 2 0.4 รท

1

2

Page 15: ๐œ‹ - White Rose Mathsย ยท 2 5 รท 5 2 5 รท5 2 5 ร— ๐‘Ÿ 3 5 ร— ๐‘Ÿ 4 5 รท๐‘Ÿ 2 5 ร— ๐‘Ÿ 3๐‘Ÿ 5 ร— 3๐‘Ÿ 5ร—4 5 รท๐‘Ÿ 2 5 ร— ๐‘Ÿ รท2 3๐‘Ÿ 5 ร—2 3๐‘Ÿ2 ร—1 5รท4 5 รท๐‘Ÿ a 2

2

5รท

3

4

2

5รท3

4

=8

20รท15

20

=8

15

2

5รท3

4

=2

5ร—4

3

=8

15

2

5รท3

4

=0.4

0.75

=40

75

=8

15

2

5รท3

4= ๐‘ฅ

2

5=3

4๐‘ฅ

2

5ร— 4

= 3๐‘ฅ

8

5รท 3 = ๐‘ฅ

8

15= ๐‘ฅ

8

9รท 0.9 4

100

63

35

70

175

5

6๐‘ฆ =

35

48

Page 16: ๐œ‹ - White Rose Mathsย ยท 2 5 รท 5 2 5 รท5 2 5 ร— ๐‘Ÿ 3 5 ร— ๐‘Ÿ 4 5 รท๐‘Ÿ 2 5 ร— ๐‘Ÿ 3๐‘Ÿ 5 ร— 3๐‘Ÿ 5ร—4 5 รท๐‘Ÿ 2 5 ร— ๐‘Ÿ รท2 3๐‘Ÿ 5 ร—2 3๐‘Ÿ2 ร—1 5รท4 5 รท๐‘Ÿ a 2

64

5รท 2

2

5.

๐Ÿ

๐Ÿ‘

๐Ÿ

๐Ÿ‘

๐Ÿ

๐Ÿ‘

๐Ÿ

๐Ÿ‘

21

4ร— 3 2

1

4ร— 4 5 ร— 2

1

4

55

8ร— 1

7

955

8ร— 1

5

955

8ร— 1

5

7

1 รท2

51 รท 2

2

52 รท 2.4

43

8รท 2

1

721

7รท 4

3

8

22

7รท 4.375

Page 17: ๐œ‹ - White Rose Mathsย ยท 2 5 รท 5 2 5 รท5 2 5 ร— ๐‘Ÿ 3 5 ร— ๐‘Ÿ 4 5 รท๐‘Ÿ 2 5 ร— ๐‘Ÿ 3๐‘Ÿ 5 ร— 3๐‘Ÿ 5ร—4 5 รท๐‘Ÿ 2 5 ร— ๐‘Ÿ รท2 3๐‘Ÿ 5 ร—2 3๐‘Ÿ2 ร—1 5รท4 5 รท๐‘Ÿ a 2

๐‘ฅ

2๐‘ฅ

5รท

๐‘ฅ

5

2๐‘ฅ

5รท

5

๐‘ฅ

2

5ร—

๐‘ค

๐‘Ÿ

3

5๐‘คร—

๐‘ค

๐‘Ÿ

4

5๐‘ครท

๐‘Ÿ

๐‘ค

2๐‘ค

5ร—

๐‘ค

๐‘Ÿ

3๐‘Ÿ

5๐‘คร—

๐‘ค

3๐‘Ÿ

5 ร—4

5๐‘ครท

๐‘Ÿ

๐‘ค

2๐‘ค

5ร—

๐‘ค

๐‘Ÿรท 2

3๐‘Ÿ

5๐‘คร—

2๐‘ค

3๐‘Ÿ2ร—

1

๐‘š

5 รท4

5๐‘ครท

๐‘Ÿ

๐‘ค

a

2ร—4๐‘Ž

3

2

๐‘Žร—4๐‘Ž

3

3

๐‘รท

๐‘

5

๐‘

3รท๐‘

5

๐‘2

4

๐‘

4

2

(๐‘‘ + 5) รท 2๐‘‘ (๐‘‘ + 5) รท2

๐‘‘


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Data Structures and Algorithms 2...4 ็›ฎๅฝ•้กต Ming Zhangโ€Data Structures and Algorithms โ€œ Linear structure โ€ข Tuple ๐ต=๐พ,๐‘…๐พ={๐‘Ž0,๐‘Ž1,โ€ฆ,๐‘Ž๐‘›โˆ’1}๐‘…={๐‘Ÿ}

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Which number sentence is true? A. (4 + 5) + 2 = 2 + (4 + 5) B. (5 - 4) + 2 = 5 + (4 - 2) C. (5 - 4) + 2 = (4 -2) + 5) D. (5 + 4) + 2 = 5 - (4 - 2)

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