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Ratio Problem Solving (Edexcel IGCSE Maths A)

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  • FrontRatios & FDP

    True or False?

    A ratio can be expressed as a fraction.

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  • True or False?

    A ratio can be expressed as a fraction.

    True.

    A ratio can be expressed as a fraction (of the whole).

    For example, with a ratio of 2 colon 3, the first part is fraction numerator 2 over denominator 2 plus 3 end fraction equals 2 over 5 of the whole, and the other part is fraction numerator 3 over denominator 2 plus 3 end fraction equals 3 over 5 of the whole.

  • True or False?

    The ratio 1 colon 4 is equivalent to 1 fourth.

    False.

    A ratio of 1 colon 4 is not equivalent to 1 fourth.

    The two parts of that ratio are equivalent to fraction numerator 1 over denominator 1 plus 4 end fraction equals 1 fifth of the whole and fraction numerator 4 over denominator 1 plus 4 end fraction equals 4 over 5 of the whole.

  • If a ratio is X colon Y, write down a formula for the fraction of the whole belonging to X.

    If a ratio is X colon Y, then the fraction of the whole belonging to X is fraction numerator X over denominator X plus Y end fraction.

    Similarly, the fraction of the whole belonging to Y is fraction numerator Y over denominator X plus Y end fraction.

  • A bag contains blue and red marbles in the ratio 3 : 5.

    If 20% of blue marbles are cracked, what percentage of the bag of marbles are blue and cracked?

    The ratio 3 : 5 can be written as a fraction (there are 3 + 5 = 8 parts).

    So 3 over 8 of the bag are blue marbles.

    20% of blue marbles are cracked, so find 20% of 3 over 8, for example 20 over 100 cross times 3 over 8.

    This gives 3 over 40 equals 0.075 so 7.5% are blue are cracked.

  • A bag contains blue and red marbles in the ratio 3 : 5.

    If 4 over 25 of red marbles are cracked, find the fraction of the bag of marbles that are cracked red marbles.

    The ratio 3 : 5 can be written as a fraction (there are 3 + 5 = 8 parts).

    So 5 over 8 of the bag are red marbles.

    4 over 25 of red marbles are cracked, so find 4 over 25 of 5 over 8, for example 4 over 25 cross times 5 over 8.

    This gives 1 over 10 which is the fraction of the bag of marbles that are red and cracked.

  • True or False?

    If a ratio question wants a fraction or percentage answer, it is sometimes possible to pick your own value for the total number of items to help (e.g. assume there are 100 pupils in the school).

    True.

    If a ratio question wants a fraction or percentage answer, it is sometimes possible to pick your own value for the total number of items to help (e.g. assume there are 100 pupils in the school).

  • Given two, two-part ratios that share different amounts of a common quantity, how can they be combined into a single three -part ratio?

    E.g. if x space colon space y space equals space 1 space colon thin space 3 and y space colon thin space z space equals space 2 space colon thin space 5, what is the combined ratio x space colon thin space y space colon space z?

    To combine two, two-part ratios into a single three-part ratio:

    1. Find equivalent ratios so that the value for y is the same for both.

    2. Join the two ratios by their common quantity.

    E.g.
    x space colon space y space equals space 1 cross times 2 space colon thin space 3 cross times 2 space equals space 2 space colon space 6
    y space colon space z space equals space 2 cross times 3 space colon thin space 5 cross times 3 space equals space 6 space colon space 15

    So, x space colon space y space colon space z space equals space 2 space colon space 6 space colon space 15

  • True or False?

    If x space colon space y space equals space 1 space colon thin space 3 and x space colon thin space z space equals space 1 space colon thin space 2, then x space colon thin space y space colon space z equals 1 space colon space 3 space colon space 2.

    True.

    If x space colon space y space equals space 1 space colon thin space 3 and x space colon thin space z space equals space 1 space colon thin space 2, then x space colon thin space y space colon space z equals 1 space colon space 3 space colon space 2.

    In both original two-part ratios, the quantity x has the same value of 1, so no equivalent ratios need to be found.

    The three quantities can be written in the required order as a single three-part ratio.

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    1. Topic 1

      Number Toolkit

    2. Topic 2

      Set Notation & Venn Diagrams

    3. Topic 3

      Prime Factors, HCF & LCM

    4. Topic 4

      Powers, Roots & Standard Form

    5. Topic 5

      Fractions

    6. Topic 6

      Percentages

    7. Topic 7

      Compound Interest & Depreciation

    8. Topic 8

      Fractions, Decimals & Percentages

    9. Topic 9

      Rounding, Estimation & Bounds

    10. Topic 10

      Surds

    11. Topic 11

      Using a Calculator

    12. Topic 12

      Ratio Toolkit

    13. Topic 13

      Ratio Problem Solving

    14. Topic 14

      Exchange Rates & Best Buys

    15. Topic 15

      Direct & Inverse Proportion

    1. Topic 1

      Algebra Toolkit

    2. Topic 2

      Algebraic Roots & Indices

    3. Topic 3

      Expanding Brackets

    4. Topic 4

      Factorising

    5. Topic 5

      Completing the Square

    6. Topic 6

      Algebraic Fractions

    7. Topic 7

      Rearranging Formulas

    8. Topic 8

      Algebraic Proof

    9. Topic 9

      Solving Linear Equations

    10. Topic 10

      Solving Quadratic Equations

    11. Topic 11

      Solving Inequalities

    12. Topic 12

      Simultaneous Equations

    13. Topic 13

      Forming & Solving Equations

    1. Topic 1

      Sequences

    2. Topic 2

      Functions

    3. Topic 3

      Coordinate Geometry

    4. Topic 4

      Linear Graphs y = mx + c

    5. Topic 5

      Graphs of Functions

    6. Topic 6

      Estimating Gradients

    7. Topic 7

      Real-Life Graphs

    8. Topic 8

      Graphing Inequalities

    9. Topic 9

      Transformations of Graphs

    10. Topic 10

      Differentiation

    1. Topic 1

      Standard & Compound Units

    2. Topic 2

      Angles in Polygons & Parallel Lines

    3. Topic 3

      Bearings, Scale Drawing & Constructions

    4. Topic 4

      Circle Theorems

    5. Topic 5

      Area & Perimeter

    6. Topic 6

      Circles, Arcs & Sectors

    7. Topic 7

      Volume & Surface Area

    8. Topic 8

      Congruence, Similarity & Geometrical Proof

    9. Topic 9

      Area & Volume of Similar Shapes

    10. Topic 10

      Right-Angled Triangles - Pythagoras & Trigonometry

    11. Topic 11

      Sine, Cosine Rule & Area of Triangles

    12. Topic 12

      3D Pythagoras & Trigonometry

    1. Topic 1

      Vectors

    2. Topic 2

      Transformations

    1. Topic 1

      Statistics Toolkit

    2. Topic 2

      Histograms

    3. Topic 3

      Cumulative Frequency Diagrams

    4. Topic 4

      Probability Toolkit

    5. Topic 5

      Probability Diagrams - Venn & Tree Diagrams

    6. Topic 6

      Combined & Conditional Probability