KS4 (2) - The Prescot...

Mathematics

Skill Booklet

KS4 (2)

Copyright: Math in English Page 8

Calculate and fill in the boxes

x 7

8 1 52

x 9

1 5 01

x 6

4 9 82

x 9

0 9 03

x 4

5 0 15

x 4

5 0 04

x 7

9 9 93

x 9

4 0 03

x 4

1 6 04

x 4

4 9 83

x 5

6 9 93

x 8

3 0 06

x 7

1 1 34

x 6

0 0 43

Multiplying 4 digits by 1 digit

, , ,

, ,,

, , ,

, , ,

, , ,

, , ,

, , ,

,,,

, ,

, ,

Rounding o� mix

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Complete the table

Round of the nearest:

Ten Hundred ThousandNumber

345

1,245

99

9,987

4,560

749

3,456

301

9

999

5,761

4,098

3,987

51

4,049

Mixed numbers and improper fractions

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Convert these mixed numbers into improper fractions.

4 2 5 = 5

1 6 = 9 3 1 = 5

3 2 =

6 1 2 = 5

1 3 = 3 3 5 = 8

2 4 =

8 2 1 = 5

2 2 = 5 2 3 = 5

2 5 =

4 1 2 = 3

2 5 = 8 2 3 = 9

2 1 =

4 2 9 = 3

2 7 = 3 1 5 = 8

2 4 =

6 2 2 = 7

2 1 = 7 1 1 = 6

2 4 =

6 2 5 = 3

2 1 = 2 1 3 = 6

4 3 =

7 7 5 = 5

2 4 = 6 2 2 =

5 1 2 = 4

1 3 = 2 1 1 =

Improper fractions and mixed numbers

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Convert these improper fractions into mixed numbers.

=

=

=

=

=

=

=

6 14

7 29

2 12

9 11

4 18

5 21

6 22

=

=

=

=

=

=

=

=

=

4 22

7 15

8 11

2 5

4 38

4 10

6 32

7 42

5 14

=

=

=

=

=

=

=

=

=

5 31

4 14

6 14

4 22

2 16

5 7

3 5

5 22

4 13

=

=

=

=

=

=

=

=

=

8 10

5 28

7 23

6 19

4 21

7 8

2 3

6 14

5 6

Conversion of Fractions into Decimals

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Convert these fractions into decimals

10012 = 10

3 = 4 3 = 10

7 =

5 3 = 4

2 = 10037 = 10

6 =

50 1 = 25

1 = 20 1 = 10

9 =

50 2 = 25

2 = 2010 = 25

5 =

10099 = 10

4 = 10065 = 25

9 =

200 2 = 50

7 = 10013 = 10

10 =

2 1 = 10

1 = 4 1 =

100 1 = 20

2 = 100 2 =

10010 = 5

1 = 100 50 = 10

4 =

Multiplying decimal numbers

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Multiply

8.4 x 3.4 = 2.6 x 1.3 = 5.5 x 4.2 =

2.9 x 1.9 = 3 x 3.6 = 9.1 x 4.8 =

9.5 x 2.2 = 2.3 x 2.6 = 2 x 4.7 =

7.5 x 2.5 = 9.5 x 4.1 = 8.5 x 5.2 =

5.7 x 1.5 = 3.8 x 1.4 = 7.5 x 2.9 =

0.7 x 0.5 = 5.1 x 1.5 = 2.8 x 2.3 =

2.4 x 5.2 = 6.2 x 7.7 =

5.5 x 2.8 = 7.1 x 3.7 =

9.2 x 8.2 = 7.2 x 2.4 = 4.1 x 2.5 =

Dividing decimal numbers

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Divide.

4.8 ÷ 8 = 4.5 ÷ 3 =

2.45 ÷ 7 = 6.4 ÷ 4 =

6.8 ÷ 2 = 3.08 ÷ 2 = 2.7 ÷ 3 =

4.62 ÷ 3 = 4.95 ÷ 9 = 6.3 ÷ 3 =

4.05 ÷ 3 = 9.6 ÷ 3 = 4.6 ÷ 4 =

0.9 ÷ 3 = 7.5 ÷ 6 = 6 ÷ 5 =

9.5 ÷ 2 = 0.9 ÷ 3 = 7.8 ÷ 6 =

2.4 ÷ 4 = 6.8 ÷ 4 = 2.4 ÷ 3 =

4.25 ÷ 5 = 4.8 ÷ 8 = 9 ÷ 4 =

Calculate these fractions of sets (round off to the nearest hundredth).

2 1 of 135 = 3

1 of 80 =

3 1 of 50 = 4

1 of 30 =

2 1 of 105 = 3

1 of 170 =

2 1 of 93 = 2

1 of 191 = 2 1 of 176 =

5 1 of 153 = 3

1 of 95 = 3 1 of 190 =

6 1 of 110 = 10

1 of 155 = 2 1 of 165 =

4 1 of 225 = 8

1 of 140 = 3 1 of 125 =

4 1 of 174 = 9

1 of 70 = 4 1 of 124 =

6 1 of 60 = 8

1 of 180 = 9 1 of 99 =

7 1 of 147 = 4

1 of 244 = 6 1 of 104 =

9 1 of 50 = 6

1 of 150 = 5 1 of 110 =

8 1 of 190 = 3

1 of 200 = 7 1 of 200 =

Fractions of a set

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Addition of Mixed Numbers

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Calculate and show your answers in the lowest terms

2 1 + 5

3 = 2 1 4 3 + 7

1 = 3 2

4 3 + 6

4 = 1 1 5 4 + 3

1 = 4 1

7 3 + 6

1 = 5 1 8 1 + 9

2 = 1 1

8 1 + 6

2 = 3 1 9 1 + 6

1 = 5 1 4 2 + 9

6 = 3 2

5 4 + 6

1 = 3 2 4 1 + 6

5 = 3 1 4 1 + 6

5 = 2 6

4 2 + 6

1 = 4 1 4 3 + 6

2 = 1 4 4 1 + 7

6 = 7 1

3 2 + 2

1 = 4 1 3 1 + 6

5 = 4 4 8 7 + 6

1 = 2 4

3 1 + 4

3 = 2 3 4 2 + 6

5 = 3 2 5 1 + 2

1 = 3 2

2 1 + 6

4 = 2 2 8 1 + 9

8 = 1 1 4 3 + 6

2 = 5 1

Dividing Fractions

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Divide and express your answers in the lowest possible terms

= 4 ÷ 3 1 = 3 ÷ 5

4

= 5 ÷ 4 2 = 4 ÷ 3

1

= 4 ÷ 3 3 = 4 ÷ 7

2 = 7 ÷ 8 1

= 5 ÷ 5 1 = 8 ÷ 6

2 = 5 ÷ 6 5

= 3 ÷ 2 1 = 5 ÷ 7

2 = 8 ÷ 6 1

= 3 ÷ 5 1 = 9 ÷ 5

1 = 3 ÷ 9 4

= 9 ÷ 8 3 = 4 ÷ 2

3 = 2 ÷ 5 4

= 6 ÷ 3 1 = 3 ÷ 5

4 = 4 ÷ 4 3

= 2 ÷ 7 2 = 8 ÷ 9

1 = 4 ÷ 4 5

Multiplying Fractions

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Multiply and express your answers in mixed numbers

= 4 x 3 1 = 8 x 5

2

= 5 x 4 2 = 9 x 7

2

= 9 x 7 1 = 7 x 3

1 = 9 x 2 1

= 4 x 5 2 = 5 x 4

1 = 8 x 3 1

= 4 x 3 4 = 5 x 2

1 = 5 x 3 1

=11 x 3 2 = 8 x 6

1 = 4 x 3 5

= 9 x 5 1 = 9 x 7

1 = 4 x 8 3

= 4 x 7 2 = 9 x 6

1 =24 x 5 1

=39 x 4 1 = 4 x 7

6 = 4 x 5 4

Fractions and Percents

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Convert the following fractions into percents (round off to the nearest hundredth)

14 3 = %

7 1 = %

3 4 = %

6 2 = %

8 5 = %

17 3 = %

75 1 = %

6 1 = %

3 2 = %

7 3 = %

11 1 = %

9 5 = %

8 6 = %

7 6 = %

9 9 = %

3 9 = %

25 1 = %

3 1 = %

7 2 = %

9 1 = %

8 1 = %

13 2 = %

3 1 = %

2 1 = %

5 4 = %

7 8 = %

2 8 = %

50 1 = %

6 4 = %

Percentage of numbers

Copyright: Math in English Page 20

Calculate the following percentages

25% of 150 = 40% of 180 =

15% of 170 = 10% of 160 =

35% of 150 = 60% of 145 =

42% of 200 = 50% of 198 = 61% of 450 =

48% of 325 = 90% of 400 = 72% of 250 =

65% of 190 = 75% of 150 = 60% of 153 =

80% of 110 = 95% of 160 = 15% of 500 =

15% of 320 = 75% of 170 = 18% of 150 =

30% of 100 = 37% of 150 = 25% of 270 =

92% of 250 = 49% of 250 = 33% of 200 =

Dividing Fractions by Fractions

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Divide and express your answers in mixed numbers if possible

1⁄4 ÷ 1⁄3 = 3⁄4 ÷ 5⁄6 =

2⁄4 ÷ 1⁄3 = 2⁄11 ÷ 1⁄8 =

3⁄11 ÷ 1⁄3 = 1⁄5 ÷ 1⁄7 =

2⁄4 ÷ 1⁄9 = 1⁄3 ÷ 2⁄7 = 1⁄4 ÷ 1⁄9 =

1⁄2 ÷ 1⁄6 = 2⁄4 ÷ 6⁄3 = 1⁄2 ÷ 2⁄8 =

1⁄4 ÷ 1⁄10 = 2⁄6 ÷ 1⁄9 = 1⁄3 ÷ 2⁄9 =

2⁄3 ÷ 1⁄9 = 1⁄4 ÷ 8⁄3 = 1⁄3 ÷ 4⁄3 =

3⁄7 ÷ 1⁄6 = 3⁄4 ÷ 3⁄4 = 4⁄6 ÷ 1⁄6 =

3⁄2 ÷ 1⁄4 = 1⁄4 ÷ 1⁄8 = 1⁄2 ÷ 1⁄5 =

2⁄9 ÷ 1⁄4 = 6⁄8 ÷ 7⁄6 = 1⁄4 ÷ 1⁄9 =

3⁄3 ÷ 1⁄9 = 3⁄2 ÷ 1⁄4 = 1⁄8 ÷ 1⁄9 =

Dividing Mixed Numbers

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Divide and express your answers in mixed numbers if possible

÷ =1⁄22 1⁄31 ÷ =1⁄34 1⁄72

÷ =3⁄41 1⁄31 ÷ =1⁄61 1⁄23

÷ =1⁄32 4⁄51 ÷ =3⁄81 1⁄42

÷ =1⁄33 4⁄51 ÷ =1⁄42 1⁄51 ÷ =1⁄72 1⁄27

÷ =1⁄72 3⁄42 ÷ =3⁄51 3⁄81 ÷ =1⁄27 3⁄43

÷ =1⁄51 4⁄61 ÷ =1⁄21 1⁄91 ÷ =1⁄61 8⁄91

÷ =1⁄44 1⁄23 ÷ =1⁄54 3⁄41 ÷ =1⁄25 1⁄31

÷ =3⁄41 1⁄22 ÷ =1⁄28 2⁄31 ÷ =1⁄84 1⁄32

÷ =5⁄61 1⁄31 ÷ =1⁄26 1⁄81 ÷ =1⁄33 1⁄72

÷ =1⁄27 1⁄26 ÷ =1⁄34 1⁄62 ÷ =1⁄24 1⁄49

Greatest Common Factors

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Find the greatest common factors of the following sets of numbers.

12 and 20 = 13 and 65 =

35 and 18 = 12 and 21 =

24 and 96 = 15 and 75 =

12 and 56 = 14 and 77 = 11 and 78 =

12 and 28 = 17 and 68 = 18 and 28 =

19 and 95 = 12 and 23 = 14 and 84 =

12 and 66 = 19 and 48 = 17 and 68 =

14 and 87 = 12 and 26 = 30 and 45 =

21 and 33 = 15 and 95 = 15 and 90 =

16 and 64 = 12 and 30 = 24 and 30 =

Lowest Common Multiple

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Find the lowest common multiple of the following sets of numbers.

14 and 20 = 13 and 65 =

24 and 18 = 14 and 21 =

12 and 96 = 15 and 75 =

12 and 56 = 17 and 77 = 12 and 78 =

14 and 28 = 15 and 72 = 7 and 28 =

19 and 95 = 12 and 30 = 14 and 84 =

12 and 64 = 18 and 48 = 17 and 68 =

17 and 68 = 12 and 26 = 30 and 45 =

21 and 33 = 15 and 95 = 15 and 80 =

16 and 64 = 15 and 30 = 24 and 30 =

Percents

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Calculate the percents of each number (round off to nearest tenth)

14 is 12 % of

25 is 3 % of

35 is 15 % of

20 is 17 % of 25 is 22 % of

18 is 28 % of 90 is 15 % of

15 is 35 % of 16 is 64 % of

21 is 20 % of 13 is 60 % of

45 is 12 % of 36 is 40 % of

88 is 15 % of 82 is 25 % of

75 is 25 % of 67 is 23 % of

22 is 30 % of 72 is 12 % of

98 is 50 % of 12 is 16 % of

32 is 34 % of 18 is 80 % of

24 is 12 % of 26 is 45 % of

Multiplying fractions by decimals

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Calculate and round your answers off to the nearest tenth

= 2.4 x 4 1 = 3.5 x 9

2

= 5.8 x 7 2 = 8.3 x 7

6

= 3.3 x 7 4 = 9.5 x 7

1 = 9.1 x 8 1

= 4.4 x 9 2 = 7.1 x 6

1 = 8.4 x 3 2

= 4.9 x 3 8 = 8.5 x 7

1 = 5.7 x 9 1

=15.3 x 9 2 = 7.2 x 6

3 = 4.3 x 7 9

= 7.9 x 5 3 = 3.2 x 7

4 = 8.3 x 8 7

= 4.9 x 9 2 = 9.2 x 7

1 =24.2 x 8 2

=25.4 x 4 3 = 8.2 x 7

3 = 3.7 x 3 4

Divisibility rules of 4, 6, 7 and 9

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Are the following numbers divisible by 4, 6, 7 and 9 (no remainders or decimals)? Complete the tables with yes or no.

385By 4By 6By 7By 9

284By 4By 6By 7By 9

3,424By 4By 6By 7By 9

999By 4By 6By 7By 9

440By 4By 6By 7By 9

738By 4By 6By 7By 9

256By 4By 6By 7By 9

642By 4By 6By 7By 9

264By 4By 6By 7By 9

450By 4By 6By 7By 9

9,448By 4By 6By 7By 9

Square roots

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Between which 2 whole numbers are the following square roots?

110 is between and

150 is between and

40 is between and 10 is between and

200 is between and 550 is between and

70 is between and 30 is between and

230 is between and 270 is between and

50 is between and 500 is between and

122 is between and 85 is between and

60 is between and 190 is between and

300 is between and 424 is between and

Prime factorization

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Prime factorize of the following numbers.

64 =

210 =

250 = 375 =

125 = 250 =

350 = 98 =

295 = 140 =

100 = 175 =

200 = 525 =

364 = 230 =

88 = 110 =

Calculations with 3 Integers

Copyright: Math in English Page 16

Calculate

-13 x 5 x -11 =

25 + -3 x -20 =

15 + 8 x -20 = -18 x 2 x -22 =

-25 x -3 x -11 = -35 x 3 + -12 =

-34 x -3 + -62 = -15 + 3 - -19 =

-14 x -3 x 8 = -17 x 2 x -15 =

-11 x 4 - -33 = 22 x 2 + -12 =

10 - 4 x 12 = -20 + 4 + -22 =

-22 x -3 - -23 = -12 x 3 x -15 =

-10 + 4 x -10 = 25 + -3 x -14 =

-11 - 8 x -12 = -15 x 2 x -11 =

45 + 8 x - 5 = -25 x -2 + 99 =