Math topic中文

Ratios rational

ratios involving rational numbers

Practice questions

  1. 1In the diagram, there are two right-angled triangles ΔABD and ΔCEB such that AD = 12 cm, BD = 15 cm and BE = 20 cm. Find…
  2. 2In triangle ABC, ∠ABC=90∘\angle ABC = 90^\circ, BX=2XCBX = 2XC and sin⁡∠AXC=35\sin \angle AXC = \dfrac{3}{5}. Express as a fraction in its…
  3. 3A cuboid has a volume of 250 cm^3, correct to the nearest cubic centimetre. The height of the cuboid is 8.4 cm, correct…
  4. 4The diagram below shows a gift souvenir formed by joining the plane face of a solid hemisphere of radius 3 cm and a soli…
  5. 5In the diagram, PQRS is a vertical rectangular wall of height 2.5 m and length 7.5 m. T is a point on level ground from…
  6. 6Triangle PQR is a right-angled triangle with PQ = 10 cm, QR = 6 cm and ∠PRQ = 90°. M is a point on PR such that MR = 5 P…
  7. 7In the Idol contest, 79\frac{7}{9} of the school's population decided to vote. There were 3 contestants and the votes fo…
  8. 8In the diagram, P, Q, R and S are points on a circle. PR and QS meet at T. Show that triangle PTS and triangle QTR are s…
  9. 9The acceleration, aa m/s2^2, of a particle is inversely proportional to the square of its distance xx metres from a f…
  10. 10ABCD is a square and AQ is perpendicular to PR. PQR and ADR are straight lines. DQ : DC = 1 : 2. Show that triangle DQR…
  11. 11John owns a cleaning company that cleans office blocks. The number of employees in his company and their salaries in 202…
  12. 12The diagram above shows a kite ABCD where angle BAC = 30°. EB, BD and DF are three sides of a regular polygon. ABE and A…
  13. 13A company divided a bonus among its employees A, B, and C in the ratio 2 : 3 : 7. C's bonus was X% more than the combine…
  14. 14Given x2−8xy+16y2=0x^2-8xy+16y^2=0, find the value of xy\dfrac{x}{y}. Answer ...
  15. 15CBEO is a parallelogram. The position vectors of C and E, relative to O, are a\mathbf{a} and b\mathbf{b} respectively.…
  16. 16Express the ratio 3233\frac{2}{3} kg : 450 g : 3×1023\times10^{2} g in its simplest form. Answer ... : ... : ...
  17. 17The number of blue, white and black masks Julian has is in the ratio 3 : 4 : 5. After exchanging 30 black masks for blue…
  18. 18A sheet of rectangular paper has length ll cm and breadth bb cm. If identical squares of side 3 cm are to be cut out f…
  19. 19The seating capacity of an auditorium is 300. The seats are categorised as 1, 2, 3 and 4. The costs of the tickets in th…
  20. 20Given 3x−yx+2y=13\dfrac{3x - y}{x + 2y} = \dfrac{1}{3}, find the ratio x : y. Answer x : y = ... Solve the inequality 2−3x3<2x−16\dfrac{2 - 3x}{3} < \dfrac{2x - 1}{6}…
  21. 21O is the centre of the equilateral triangle. The triangle ABC forms the base of a pyramid. The vertex, X is vertically a…
  22. 22In the diagram, ABCD is a rectangle and E and F are points on AD and BC respectively. The ratio of the area of triangle…
  23. 23PR is a diameter of the large circle, centre O. QS is a diameter of the small circle, centre O. PQ and RS are tangents t…
  24. 24ABC is a triangle. D is the point on BC such that 3BD = 2DC. Find AD in terms of m and n. Answer ... R is on AD produced…
  25. 25The diagram below shows three points, A, B and C on flat ground. AB = 80 m, AC = 100 m and BC = 90 m. C is due east of A…
  26. 26Underline the following ratios that are equivalent to the ratio a:ba : b. Answer 1b:1aa2:b33a:3ba+1:b+1\dfrac{1}{b} : \dfrac{1}{a} \quad a^{2} : b^{3} \quad 3a : 3b \quad a+1 : b+1…
  27. 27In the diagram, ABAB is the diameter of the circle. AED and ABC are straight lines. AE=12AE = 12 cm and EB=16EB = 16 cm. ∠ADC\angle ADC…
  28. 28In the diagram, BCD is a straight line and BC : CD = 3 : 5. Calculate the area of triangle ABC as a percentage of the ar…
  29. 29The scale of a map is 2 cm to 1 km. The actual length of a road is 8.5 km. Find the length of the road on the map in cm.…
  30. 30Albert and Chris have some savings in the ratio 5 : 3. They spent $30 each from their savings and the new ratio of thei…
  31. 31The diagram shows a regular 12-sided polygon inscribed in a circle and a right-angled triangle PQR with length QR=6QR = 6…
  32. 32Javier and Stella are planning their exercise routines. Javier and Stella have a body mass of 70 kg and 60 kg respective…
  33. 33ABCD is a trapezium. F is a point on CD such that ABCF is a rhombus and 3AE=2EF3AE = 2EF. Show that triangles ABE and FDE are…
  34. 34In the diagram ABCD is a parallelogram. The diagonal AC and BD intersect at E. AF→=2p\overrightarrow{AF} = 2p and AB→=6p+4q\overrightarrow{AB} = 6p + 4q…
  35. 35The following diagram shows 2 geometrically similar boxes of cereals of the same brand. Show that the cost of the cereal…
  36. 36The ratio of the number of soccer balls and volleyballs in a sports shop was 11 : 7. After 126 soccer balls were added a…
  37. 37For a regular polygon with n sides, the ratio of the size of an interior angle to its exterior angle is 7 : 2. Find the…
  38. 38Matthew invests $20 000 into a fixed deposit at r%r\% per month, compounded monthly. After 24 months he will be able to…
  39. 39The diagram shows a circle BDEFG, centre O and diameter BE. The line AC is a tangent to the circle at B and ∠BOD=30∘\angle BOD = 30^\circ…
  40. 40The ratio of interior angle : exterior angle of a regular polygon is 5 : 1. Calculate the number of sides that the polyg…
  41. 4123 Jefferson and Victor were sent by their company to work in Washington D.C. and Beijing respectively. Jefferson rented…
  42. 42The length of a court is 0.028 km and the width of the court is 16 m. Express the ratio of the length to the width of th…
  43. 43The diagram shows two geometrically similar cup and saucer sets. The diameter of the smaller saucer is 5 cm. The diamete…
  44. 44Timmy wants to invest a sum of money in one of the following investment plans. | Plan | Description | |---|---| | Plan A…
  45. 45The point C lies on the line AB such AC:AB = 2:7. Write AC as a fraction of BC. Answer ... Given that AC is 24 cm, calcu…
  46. 46The sizes of four of the exterior angles of a decagon are in the ratio 1 : 2 : 2 : 3. The remaining exterior angles are…
  47. 47Given that 5a−3b2a=43\frac{5a-3b}{2a} = \frac{4}{3}, find the value of ab\frac{a}{b}. Answer ... Express x2−6x+1x^2 - 6x + 1 in the f…
  48. 48ABCD is a parallelogram and triangle CDE is isosceles. E and F are points on AD and BC respectively. AB, EF and CD are p…
  49. 49The figure shows ΔABC. May said that the line AC intersect the y axis at 3.2. Show how you would check if she is correct…
  50. 50In the diagram, ABC and AED are straight lines and BE is parallel to CD. Show that triangle ABE is similar to triangle A…
  51. 51A regular m-sided polygon and a regular n-sided polygon are joined together. Part of the polygons are shown below. ∠BCD:∠DCG=5:3\angle BCD : \angle DCG = 5 : 3…
  52. 52In a regular polygon, the ratio of an interior angle : exterior angle = 14 : 1. Find the number of sides of the polygon.…
  53. 53The diagram shows a container which consists of a cylinder of radius rr cm and height hh cm joined to a hemisphere of…
  54. 54Julian owns a fruit stall selling fruit juice. The tables below give information related to Julian's stall. (a) Calculat…
  55. 55ABCD is a parallelogram and G is a point on BD. The line BF produced meets DC at F and AD produced at E. GF is parallel…
  56. 56In the diagram, XYZ is a straight line. AY = 20 m, AZ = 12 m and YZ = 16 m. The ratio of XY : YZ is 1 : 4. Prove that tr…
  57. 57Ahmad, Simon and Bala share a sum of money in the ratio 3 : 2 : 5. If Bala has $900 more than Simon, what is the sum of…
  58. 58Ken divides his monthly salary into daily expenses, spending and saving in the ratio 3:4:5 respectively. Later he decide…
  59. 59OACB is a quadrilateral. OB is parallel to AC. D is the point on BC such that BD=13BCBD = \frac{1}{3} BC. The lines OB and AD…
  60. 60The employees of a company are offered an increase in salary. Employees have the option to choose from either Scheme A o…