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Maths Gcse Aqa Higher

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  1. Scatter-Graphs-And-Correlation Aqa Higher
    2 主题
  2. Cumulative-Frequency-And-Box-Plots Aqa Higher
    4 主题
  3. Histograms Aqa Higher
    3 主题
  4. Statistical-Diagrams Aqa Higher
    5 主题
  5. Averages-Ranges-And-Data Aqa Higher
    7 主题
  6. Combined-And-Conditional-Probability Aqa Higher
    3 主题
  7. Tree-Diagrams Aqa Higher
    1 主题
  8. Simple-Probability-Diagrams Aqa Higher
    3 主题
  9. Transformations Aqa Higher
    5 主题
  10. Vectors Aqa Higher
    6 主题
  11. 3D-Pythagoras-And-Trigonometry Aqa Higher
    1 主题
  12. Sine-Cosine-Rule-And-Area-Of-Triangles Aqa Higher
    4 主题
  13. Pythagoras-And-Trigonometry Aqa Higher
    4 主题
  14. Area-And-Volume-Of-Similar-Shapes Aqa Higher
    1 主题
  15. Congruence-Similarity-And-Geometrical-Proof Aqa Higher
    5 主题
  16. Volume-And-Surface-Area Aqa Higher
    3 主题
  17. Circles-Arcs-And-Sectors Aqa Higher
    2 主题
  18. Area-And-Perimeter Aqa Higher
    4 主题
  19. Circle-Theorems Aqa Higher
    7 主题
  20. Bearings-Scale-Drawing-Constructions-And-Loci Aqa Higher
    5 主题
  21. Angles-In-Polygons-And-Parallel-Lines Aqa Higher
    3 主题
  22. Symmetry-And-Shapes Aqa Higher
    6 主题
  23. Exchange-Rates-And-Best-Buys Aqa Higher
    2 主题
  24. Standard-And-Compound-Units Aqa Higher
    5 主题
  25. Direct-And-Inverse-Proportion Aqa Higher
    2 主题
  26. Problem-Solving-With-Ratios Aqa Higher
    2 主题
  27. Ratios Aqa Higher
    3 主题
  28. Sequences Aqa Higher
    4 主题
  29. Transformations-Of-Graphs Aqa Higher
    2 主题
  30. Graphing-Inequalities Aqa Higher
    2 主题
  31. Solving-Inequalities Aqa Higher
    2 主题
  32. Real-Life-Graphs Aqa Higher
    4 主题
  33. Estimating-Gradients-And-Areas-Under-Graphs Aqa Higher
    2 主题
  34. Equation-Of-A-Circle Aqa Higher
    2 主题
  35. Functions Aqa Higher
    3 主题
  36. Forming-And-Solving-Equations Aqa Higher
    3 主题
  37. Graphs-Of-Functions Aqa Higher
    6 主题
  38. Linear-Graphs Aqa Higher
    4 主题
  39. Coordinate-Geometry Aqa Higher
    4 主题
  40. Iteration Aqa Higher
    1 主题
  41. Simultaneous-Equations Aqa Higher
    2 主题
  42. Quadratic-Equations Aqa Higher
    4 主题
  43. Linear-Equations Aqa Higher
    1 主题
  44. Algebraic-Proof Aqa Higher
    1 主题
  45. Rearranging-Formulas Aqa Higher
    2 主题
  46. Algebraic-Fractions Aqa Higher
    4 主题
  47. Completing-The-Square Aqa Higher
    1 主题
  48. Factorising Aqa Higher
    6 主题
  49. Expanding-Brackets Aqa Higher
    3 主题
  50. Algebraic-Roots-And-Indices Aqa Higher
    1 主题
  51. Using-A-Calculator Aqa Higher
    1 主题
  52. Surds Aqa Higher
    2 主题
  53. Rounding-Estimation-And-Bounds Aqa Higher
    2 主题
  54. Fractions-Decimals-And-Percentages Aqa Higher
    3 主题
  55. Introduction Aqa Higher
    7 主题
  56. Simple-And-Compound-Interest-Growth-And-Decay Aqa Higher
    4 主题
  57. Percentages Aqa Higher
    3 主题
  58. Fractions Aqa Higher
    4 主题
  59. Powers-Roots-And-Standard-Form Aqa Higher
    4 主题
  60. Prime-Factors-Hcf-And-Lcm Aqa Higher
    4 主题
  61. Number-Operations Aqa Higher
    10 主题
  1. Maths Gcse Aqa Higher
  2. Surds Aqa Higher
  3. Rationalising-Denominators Aqa Higher
课 52, 主题 1
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Rationalising-Denominators Aqa Higher

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Exam code:8300

Rationalising Denominators

What does rationalising the denominator mean?

  • If a fraction has a denominator containing a surd then it has an irrational denominator

    • E.g. fraction numerator 4 over denominator square root of 5 end fraction or square root of 2 over 3 end root equals fraction numerator square root of 2 over denominator square root of 3 end fraction

  • The fraction can be rewritten as an equivalent fraction, but with a rational denominator

    • E.g. fraction numerator 4 square root of 5 over denominator 5 end fraction or fraction numerator square root of 6 over denominator 3 end fraction

  • The numerator may contain a surd, but the denominator is rationalised

How do I rationalise denominators?

  • If the denominator is a surd:

    • Multiply the top and bottom of the fraction by the surd on the denominator

      • fraction numerator a over denominator square root of straight b end fraction equals blank fraction numerator a over denominator square root of straight b end fraction blank cross times blank fraction numerator square root of straight b over denominator square root of straight b end fraction

      • This is equivalent to multiplying by 1, so does not change the value of the fraction

      • <img alt=”square root of b space cross times space square root of b space equals space b” data-mathml='<math ><semantics><mrow><msqrt><mi>b</mi></msqrt><mo> </mo><mo>×</mo><mo> </mo><msqrt><mi>b</mi></msqrt><mo> </mo><mo>=</mo><mo> </mo><mi>b</mi></mrow><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“language”:”en”,”fontFamily”:”Times New Roman”,”fontSize”:”18″,”autoformat”:true}</annotation></semantics></math>’ height=”26″ role=”math” src=”data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml-extension%22%20height%3D%2226%22%20width%3D%22117%22%20wrs%3Abaseline%3D%2220%22%3E%3C!–MathML%3A%20%3Cmath%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsqrt%3E%3Cmi%3Eb%3C%2Fmi%3E%3C%2Fmsqrt%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmo%3E%26%23xD7%3B%3C%2Fmo%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmsqrt%3E%3Cmi%3Eb%3C%2Fmi%3E%3C%2Fmsqrt%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmi%3Eb%3C%2Fmi%3E%3C%2Fmath%3E–%3E%3Cdefs%3E%3Cstyle%20type%3D%22text%2Fcss%22%3E%40font-face%7Bfont-family%3A’math13d2dc549f508103e95d72be633’%3Bsrc%3Aurl(data%3Afont%2Ftruety

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