We have prepared two pitchers of lemonade for a birthday.[br]As each one contains different amounts of lemon and water, their lemon flavor is not the same. Which has a stronger flavor?

Once you are confident that you can always work out which mixture is stronger, here are some questions to consider:[br][br]How might you use fractions to help you to work out which mixture is stronger?[br]How might you use ratios?[br]How about a graphical approach?[br][br]Do you always use the same strategy?[br]Describe some occasions when one strategy might be more efficient than another.[br][br]In the original example, the first glass had 200ml of lemon juice and 300ml of water, and the second glass had 100ml of lemon juice and 200ml of water.[br]If I mix the two glasses of lemonade together, the mixture is weaker than the first glass was, but stronger than the second glass.[br]Try the same with some other mixtures.[br]Is the strength of the combined mixture always between the strengths of the originals? Can you justify your findings?  [br][br]If we combine the two jars into one, how will its lemon flavor be compared to the other two? (major, minor, between the other two, ...)[br][br]Try to relate it to this property of fractions:[br]❝If we have two fractions and we add their numerators on the one hand and their denominators on the other, the value of the fraction obtained is between the two of them❞

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