Multiplying fractions

Mark scheme and answers · Total marks: 42

Question 1 [1 mark]

314

Mark scheme
  • A [1] — cao 3⁄14

Accept algebraically equivalent correct forms.

Question 2 [1 mark]

16

Mark scheme
  • A [1] — cao 1⁄6

Accept algebraically equivalent correct forms.

Question 3 [1 mark]

445

Mark scheme
  • A [1] — cao 4⁄45

Accept algebraically equivalent correct forms.

Question 4 [1 mark]

110

Mark scheme
  • A [1] — cao 1⁄10

Accept algebraically equivalent correct forms.

Question 5 [1 mark]

112

Mark scheme
  • A [1] — cao 1⁄12

Accept algebraically equivalent correct forms.

Question 6 [1 mark]

49

Mark scheme
  • A [1] — cao 4⁄9

Accept algebraically equivalent correct forms.

Question 7 [1 mark]

27125

Mark scheme
  • A [1] — cao 27⁄125

Accept algebraically equivalent correct forms.

Question 8 [1 mark]

3 13 m

Mark scheme
  • A [1] — cao 3 1⁄3 m

Accept algebraically equivalent correct forms.

Question 9 [1 mark]

159 14 miles

Mark scheme
  • A [1] — cao 159 1⁄4 miles

Accept algebraically equivalent correct forms.

Question 10 [1 mark]

215

Mark scheme
  • A [1] — cao 2⁄15

Accept algebraically equivalent correct forms.

Question 11 [1 mark]

x = 1

Mark scheme
  • A [1] — cao x = 1

Accept algebraically equivalent correct forms.

Question 12 [1 mark]

x = 3

Mark scheme
  • A [1] — cao x = 3

Accept algebraically equivalent correct forms.

Question 13 [1 mark]

16

Mark scheme
  • A [1] — cao 1⁄6

Accept algebraically equivalent correct forms.

Question 14 [1 mark]

12

Mark scheme
  • A [1] — cao 1⁄2

Accept algebraically equivalent correct forms.

Question 15 [1 mark]

1 14

Mark scheme
  • A [1] — cao 1 1⁄4

Accept algebraically equivalent correct forms.

Question 16 [1 mark]

34

Mark scheme
  • A [1] — cao 3⁄4

Accept algebraically equivalent correct forms.

Question 17 [1 mark]

58

Mark scheme
  • A [1] — cao 5⁄8

Accept algebraically equivalent correct forms.

Question 18 [1 mark]

14

Mark scheme
  • A [1] — cao 1⁄4

Accept algebraically equivalent correct forms.

Question 19 [1 mark]

23

Mark scheme
  • A [1] — cao 2⁄3

Accept algebraically equivalent correct forms.

Question 20 [1 mark]

5 17

Mark scheme
  • A [1] — cao 5 1⁄7

Accept algebraically equivalent correct forms.

Question 21 [2 marks]

1 34

Mark scheme
  • A [2] — cao 1 3⁄4

Accept algebraically equivalent correct forms.

Question 22 [2 marks]

2x

Mark scheme
  • A [2] — cao 2x

Accept algebraically equivalent correct forms.

Question 23 [2 marks]

536

Mark scheme
  • A [2] — cao 5⁄36

Accept algebraically equivalent correct forms.

Question 24 [2 marks]

1514

Mark scheme
  • A [2] — cao 15⁄14

Accept algebraically equivalent correct forms.

Question 25 [2 marks]

160 litres

Mark scheme
  • A [2] — cao 160 litres

Accept algebraically equivalent correct forms.

Question 26 [2 marks]

2150 m²

Mark scheme
  • A [2] — cao 21⁄50 m²

Accept algebraically equivalent correct forms.

Question 27 [2 marks]

8

Mark scheme
  • A [2] — cao 8

Accept algebraically equivalent correct forms.

Question 28 [2 marks]

12 cup

Mark scheme
  • A [2] — cao 1⁄2 cup

Accept algebraically equivalent correct forms.

Question 29 [2 marks]

14

Mark scheme
  • A [2] — cao 1⁄4

Accept algebraically equivalent correct forms.

Question 30 [4 marks]

Proof: Let 0 < ab < 1 and 0 < cd < 1. Then (ab) × (cd) = (ac)(bd). Since a < b and c < d, ac < bd, so (ac)(bd) < 1. Also, (ac)(bd) < ab because cd < 1, and similarly < cd.

Mark scheme
  • A [4] — cao Proof: Let 0 < a/b < 1 and 0 < c/d < 1. Then (a/b) × (c/d) = (ac)/(bd). Since a < b and c < d, ac < bd, so (ac)/(bd) < 1. Also, (ac)/(bd) < a/b because c/d < 1, and similarly < c/d.

Accept algebraically equivalent correct forms.

© Maths Vault · mathsvault.uk