OpenRevise

Flashcards · Maths

Ratio and Proportion

83 cards from 5 lessons

  1. What does a ratio of 3 : 5 tell you?

    For every 3 parts of the first quantity there are 5 parts of the second. It does not tell you the total.

  2. Why does the order of a ratio matter?

    Boys to girls 3 : 5 is not the same as girls to boys 3 : 5. Write it in the order the question asks.

  3. How do you simplify a ratio?

    Divide every part by the highest common factor, so \(12 : 18 = 2 : 3\).

  4. How do you simplify \(50\text{ cm} : 2\text{ m}\)?

    Change to the same units first: \(50 : 200 = 1 : 4\).

  5. How do you remove fractions from \(\dfrac{1}{2} : \dfrac{1}{3}\)?

    Multiply both parts by the common denominator, 6, to get \(3 : 2\).

  6. What is the form \(1 : n\)?

    A ratio with the first part 1, found by dividing both parts by the first part: \(4 : 10 = 1 : 2.5\).

  7. What are the three steps for sharing in a ratio?

    Add the parts, divide the total by the number of parts to find one part, then multiply.

  8. Share \(\pounds 60\) in the ratio \(2 : 3\).

    5 parts, one part is \(\pounds 12\), so \(\pounds 24\) and \(\pounds 36\).

  9. Share 240 in the ratio \(3 : 4 : 5\).

    12 parts, one part is 20, so 60, 80 and 100.

  10. In the ratio \(3 : 5\) the smaller part is \(\pounds 18\). What is the larger part?

    One part is \(\pounds 6\), so the larger part is \(\pounds 30\).

  11. In the ratio \(3 : 7\) the difference is \(\pounds 20\). What are the amounts?

    The difference is 4 parts, so one part is \(\pounds 5\) and the amounts are \(\pounds 15\) and \(\pounds 35\).

  12. What fraction of the whole is the first part of \(2 : 3\)?

    \(\dfrac{2}{5}\), because the whole is 5 parts.

  13. If \(\dfrac{1}{4}\) of a class walk, what is the ratio of walkers to the others?

    \(1 : 3\).

  14. What is the difference between a ratio and a fraction?

    A ratio compares part with part, but a fraction compares a part with the whole.

  15. How do you increase 40 in the ratio \(3 : 2\) (Higher tier)?

    Multiply by \(\dfrac{3}{2}\) to get 60.

  16. How do you combine \(a : b = 2 : 3\) and \(b : c = 4 : 5\) (Higher tier)?

    Make \(b\) match using 12: \(8 : 12\) and \(12 : 15\), so \(a : b : c = 8 : 12 : 15\).

  17. How do you check a ratio sharing answer?

    The shares must add up to the total and be in the original ratio.

  18. What does direct proportion mean?

    As one quantity increases, the other increases at the same rate, so doubling one doubles the other.

  19. What is the unitary method?

    Find the value of one unit, then multiply to find the value of the amount you need.

  20. 5 pens cost \(\pounds 3.50\). What do 8 pens cost?

    One pen costs 70p, so 8 pens cost \(\pounds 5.60\).

  21. What does a direct proportion graph look like?

    A straight line through the origin.

  22. How do you decide the better value between two packs?

    Compare the price of the same amount of each, or the amount per penny, and write a conclusion.

  23. Which is better value: 500 g for \(\pounds 1.20\), or 750 g for \(\pounds 1.65\)?

    750 g, at 22p per 100 g compared with 24p per 100 g.

  24. How do you use an exchange rate of \(\pounds 1 = \$1.25\)?

    Multiply by 1.25 to change pounds to dollars, and divide by 1.25 to change dollars to pounds.

  25. What does inverse proportion mean?

    As one quantity increases, the other decreases, and the product of the two stays the same.

  26. How do you solve an inverse proportion problem?

    Find the total (such as workers times days), then divide by the new quantity.

  27. 3 painters take 8 days. How long do 6 take?

    The total is 24 painter-days, so 6 painters take 4 days.

  28. What does an inverse proportion graph look like?

    A curve that falls and flattens and never touches the axes.

  29. How can you test whether a table shows direct proportion?

    Divide \(y\) by \(x\) for each pair. If the answer is always the same, it is direct proportion.

  30. Is a taxi fare of \(\pounds 3\) plus \(\pounds 2\) a mile in direct proportion to distance?

    No, because the fixed charge means the graph does not pass through the origin.

  31. What does \(y \propto x\) mean (Higher tier)?

    \(y\) is directly proportional to \(x\), which can be written \(y = kx\) for a constant \(k\).

  32. What does \(y \propto \dfrac{1}{x}\) mean (Higher tier)?

    \(y\) is inversely proportional to \(x\), which can be written \(y = \dfrac{k}{x}\).

  33. How do you find \(k\) (Higher tier)?

    Substitute a known pair of values into the equation, such as \(15 = k \times 3\) giving \(k = 5\).

  34. If \(y = kx^2\) and \(y = 20\) when \(x = 2\), what is \(y\) when \(x = 3\) (Higher tier)?

    \(k = 5\), so \(y = 5 \times 9 = 45\).

  35. What is the formula for speed?

    Speed \(=\) distance \(\div\) time.

  36. How do you find distance from speed and time?

    Distance \(=\) speed \(\times\) time.

  37. How do you find time from distance and speed?

    Time \(=\) distance \(\div\) speed.

  38. How many hours is 30 minutes, 45 minutes and 20 minutes?

    0.5 hours, 0.75 hours and \(\dfrac{1}{3}\) hour.

  39. How many hours is 1 hour 12 minutes?

    1.2 hours, because \(12 \div 60 = 0.2\).

  40. What is the common mistake with 2 hours 30 minutes?

    Writing it as 2.3 hours. It is 2.5 hours.

  41. A car travels 150 km in 2 hours 30 minutes. What is its speed?

    \(150 \div 2.5 = 60\) km/h.

  42. How long does 90 km take at 60 km/h?

    1.5 hours, which is 1 hour 30 minutes.

  43. What is average speed?

    Total distance divided by total time.

  44. Why is the average of 30 km/h and 60 km/h not always 45 km/h?

    The time spent at each speed may differ. For equal distances the average speed is 40 km/h.

  45. What does the gradient of a distance-time graph show?

    The speed.

  46. What does a flat section of a distance-time graph mean?

    The object is stationary.

  47. What does a downward section of a distance-time graph mean?

    The object is returning towards the start.

  48. What is the formula for density?

    Density \(=\) mass \(\div\) volume.

  49. A metal has density 8 g/cm\(^3\). What is the mass of 25 cm\(^3\)?

    \(8 \times 25 = 200\) g.

  50. What is the formula for pressure (Higher tier)?

    Pressure \(=\) force \(\div\) area.

  51. How do you change 72 km/h to m/s (Higher tier)?

    Multiply by 1000 and divide by 3600, which gives 20 m/s.

  52. How many millimetres are in a centimetre?

    10.

  53. How many centimetres are in a metre?

    100.

  54. How many metres are in a kilometre?

    1000.

  55. How many grams are in a kilogram, and kilograms in a tonne?

    1000 in each case.

  56. How many millilitres are in a litre?

    1000.

  57. What is 1 cm\(^3\) in millilitres?

    1 ml.

  58. When you convert from a big unit to a small unit, do you multiply or divide?

    Multiply, because there are more small units.

  59. Change 3.6 km to metres.

    \(3.6 \times 1000 = 3600\) m.

  60. Change 2450 g to kilograms.

    \(2450 \div 1000 = 2.45\) kg.

  61. How many minutes are in 1.5 hours?

    90 minutes.

  62. What does a map scale of \(1 : 25\,000\) mean?

    1 cm on the map is 25 000 cm in real life, which is 250 m.

  63. A drawing has a scale of 1 cm to 2 m. What is the real length of a 6 cm line?

    \(6 \times 2 = 12\) m.

  64. How do you find the length on a drawing from a real length?

    Divide the real length by the scale.

  65. How many square centimetres are in 1 m\(^2\) (Higher tier)?

    \(100 \times 100 = 10\,000\) cm\(^2\).

  66. How many cubic centimetres are in 1 m\(^3\) (Higher tier)?

    \(100^3 = 1\,000\,000\) cm\(^3\).

  67. How many square millimetres are in 1 cm\(^2\) (Higher tier)?

    \(10 \times 10 = 100\) mm\(^2\).

  68. What is the multiplier for a 15% increase?

    1.15.

  69. What is the multiplier for a 15% decrease?

    0.85.

  70. What is the multiplier for a 5% increase?

    1.05.

  71. What is the multiplier for a 2% decrease?

    0.98.

  72. How do you apply the same percentage change 3 times?

    Multiply by the multiplier cubed, or multiplier\(^3\).

  73. What is compound interest?

    Interest paid on the original amount plus the interest already earned.

  74. What is simple interest?

    Interest paid on the original amount only, so the same amount is added each year.

  75. Which gives more after 5 years, simple or compound interest?

    Compound interest.

  76. What is \(1.1^2\)?

    1.21.

  77. Why is two 10% increases not a 20% increase?

    The second 10% is taken from the larger amount, so the total increase is 21%.

  78. £1000 grows by 10% each year. What is it worth after 2 years?

    \(1000 \times 1.1^2 = \pounds 1210\).

  79. A car worth £12 000 loses 20% of its value each year. What is it worth after 2 years?

    \(12\,000 \times 0.8^2 = \pounds 7680\).

  80. What is depreciation?

    A fall in the value of something over time.

  81. What do you do to a final amount to find the original after a percentage increase (Higher tier)?

    Divide it by the multiplier.

  82. After a 25% increase a price is £150 000. What was the original (Higher tier)?

    \(150\,000 \div 1.25 = \pounds 120\,000\).

  83. How many decimal places should a money answer have?

    2, such as £163.20.