Math topic中文

Simplest form

writing a ratio in its simplest form

Practice questions

  1. 1把20克糖放入200克水中，糖与糖水的质量比是多少？
  2. 2A bag contains 2 gold balls, rr red balls and ss silver balls where r×sr \times s is prime number and r<sr < s. The tota…
  3. 3The diagram shows two circles that touch at C. A, B and C are points on the small circle, centre P. C, D and E are point…
  4. 4Triangle 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…
  5. 5The diagram shows a semi-circle BAC, with diameter BC = 34 cm. AD and BCD are straight lines. Given that cos⁡∠ABC=817\cos\angle ABC = \dfrac{8}{17}…
  6. 6Jane had a box filled with 8 red pens, 4 blue pens and 6 green pens. She took out two pens at random, one after the othe…
  7. 7走一段路，甲用1515分钟，乙用1010分钟，甲和乙速度的最简整数比是 ___，若甲、乙在路的两端同时相向而行，___分钟相遇。
  8. 8In the diagram, BDCE is a straight line. BD = 4 cm, AC = 10 cm and AB = AD. Given that the area of triangle ABD is 16 cm…
  9. 9A bag contains 8 red balls, 5 green balls and 7 yellow balls. A ball is chosen at random and then replaced. What is the…
  10. 10In the diagram, OA‾=12 AP‾\overline{OA}=\tfrac{1}{2}\,\overline{AP} and OB‾=14 OQ‾\overline{OB}=\tfrac{1}{4}\,\overline{OQ}. M is the mi…
  11. 11甲数除以乙数的商是1.5，甲数和乙数的比是___：___．
  12. 12CBEO is a parallelogram. The position vectors of C and E, relative to O, are a\mathbf{a} and b\mathbf{b} respectively.…
  13. 13聪聪从家到学校步行需要1515分钟，如果骑自行车只需要99分钟，步行与骑自行车速度的最简整数比是 ：。
  14. 14Express the ratio 3233\frac{2}{3} kg : 450 g : 3×1023\times10^{2} g in its simplest form. Answer ... : ... : ...
  15. 15OABC is a trapezium. OA→=a\overrightarrow{OA}=a, OC→=2c\overrightarrow{OC}=2c and CB→=2a\overrightarrow{CB}=2a. OP:PB=1:3OP : PB = 1 : 3.…
  16. 16Given 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}…
  17. 17In the diagram, ABCD is a rectangle and E and F are points on AD and BC respectively. The ratio of the area of triangle…
  18. 18一项工程，甲单独做要8天完成，乙单独做要10天完成，甲、乙所用工作时间的比是 ，甲、乙工作效率的比是 。
  19. 19OBC, ADC, AEB and OED are straight lines. OA→=a\overrightarrow{OA}=a and OB→=b\overrightarrow{OB}=b. OB=13OCOB=\dfrac{1}{3}OC, AE:EB=3:2AE:EB=3:2…
  20. 20A manufacturer sells drinks in bottles of two sizes that are geometrically similar. Some specifications for the bottles…
  21. 21The scale of a map is 8 cm : 2 km. Write this scale in the form 1 : n. Answer 1 : ... The actual area of a lake is 90 00…
  22. 22把一个棱长12厘米的正方体表面染成红色，然后切成棱长2厘米的小正方体若干个，三面染色的块数与一面染色的块数之比是 ．
  23. 23The diagram shows a solid ornament in the shape of a cylinder with an upright cone cut out at one end and a hemisphere a…
  24. 24ABCD 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…
  25. 25In 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…
  26. 26The scale of a map is 4 cm : 1 km. Write this scale in the form 1 : n. Answer 1 : ... The distance between two cities on…
  27. 27A manufacturing company produces electronic components for various devices. They are analyzing the production data for t…
  28. 28John flipped a coin five times and obtained five successive heads. Is it conclusive that the coin is biased? Explain you…
  29. 29The 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…
  30. 30Triangle ABC is equilateral. CAD and ABE are straight lines and AD = BE. Show that triangle ABD and triangle BCE are con…
  31. 31AB→=(−39), BC→=(25), CD→=(d4).\overrightarrow{AB}=\begin{pmatrix}-3\\9\end{pmatrix},\ \overrightarrow{BC}=\begin{pmatrix}2\\5\end{pmatrix},\ \overrightarrow{CD}=\begin{pmatrix}d\\4\end{pmatrix}.…
  32. 32The diagram shows a lucky draw spinner at a departmental store. The pointer is equally likely to stop at any of the sect…
  33. 33A box has 20 pots of plants. There are 5 pink pots, 9 blue pots and the remaining pots are green. (i) Two pots are taken…
  34. 34Given that x is 35% of y, find the value of 2x5y\dfrac{2x}{5y}, expressing your answer as a fraction in its lowest terms.…
  35. 35The scale of a map is 2 cm : 1 km. Write this scale in the form 1 : n . The area of a park is represented by an area of…
  36. 36A 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…
  37. 37如果线段m=3cmm=3cm，n=12cmn=12cm，那么mm：nn的值是()(\quad) A. 11：44 B. 33：11 C. 1212：11 D. 33：1212
  38. 38A map is drawn to a scale of 1 : n. The actual distance between two points X and Y is 2.8 km. On the map, they are 4 cm…
  39. 39小明的妈妈身高160cm160cm，她照了一张照片，照片上的她身高4cm4cm，这张照片是按___：___的比例拍摄的．
  40. 40In 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…
  41. 41Ken divides his monthly salary into daily expenses, spending and saving in the ratio 3:4:5 respectively. Later he decide…
  42. 42A drawer contains 2 blue socks and 6 white socks. Two socks are taken from the drawer at random without replacement. If…
  43. 43OACB 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…
  44. 44A length of 5 cm on a map represents an actual distance of 2.5 km. Find the actual distance represented by 20 cm on the…
  45. 45从A地到B地共600千米，甲车要10小时，乙车要15小时．甲乙两车的速度比是 ，按照这样的速度，从A地到B地，甲乙两车所用时间比是 ．
  46. 46把2525克盐溶解在100100克水中，盐和盐水的最简整数比是11：44。 ___((判断对错))
  47. 47There are 12 girls and 9 boys in a group. Find, in its simplest form, the probability of selecting a boy randomly from t…