# Proportional Reasoning

If your sample is random and large enough, you can use it to make a prediction.

For example, you have a population size of 56 and you randomly sample 8 of the 56 and get the same result for 7 of them. You can predict the result for the whole population by making a fraction 7/8 and finding an equivalent fraction with a denominator of 56 by multiplying the top and bottom by 7. Your estimate for the whole group would be 49.

Or you could cross-multiply and divide. (7 x 56)/8 = 49

All 2000 students at Anna’s school gets a special school jacket during spirit week. Anna has been asked to estimate how many of each size jacket should be purchased and then place the order. Without asking all 2000 students, how can she find out? Anna decided to survey 100 of the students. She chose them at random by picking every 20th student that left the school at the end of the day and asked them what size jacket they wore.

Of the 100 she asked, 30 said they wore a size medium. You can set up a fraction 30/100 and find an equivalent fraction by multiplying the top and bottom by 20.

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