8: Advanced Proportional - Proportions and Ratios

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The farmer found that she had bred 70 lambs from her 42 ewes. What was her lambing percentage (100% would be one lamb for each ewe)?

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Student: Forty-two lambs would be one hundred percent. That leaves an extra twenty-eight lambs. Twenty-eight out of forty-two is the same as four sixths, and that’s two thirds. The decimal for two thirds is sixty-six point six recurring percent. So the farmer's lambing percentage is one hundred and sixty-six point six recurring percent.

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Students at the Advanced Proportional stage are learning to select from a repertoire of part-whole strategies to solve and estimate the answers to problems involving fractions, proportions, and ratios. These strategies are based on finding common factors and include strategies for the multiplication of decimals and the calculation of percentages.