GCSEMathsEdexcelHigherFlashcards

Problem Solving with Ratios (Edexcel GCSE Maths)

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  • FrontRatios with Fractions, Decimals & Percentages

    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?

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  • 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.

1. Number
2. Algebra
3. Ratio, Proportion & Rates of Change
4. Geometry & Measures
5. Probability
6. Statistics