How do compare ratios then simplify to find the answer

"Compare ratios" covers a lot of territory. If all you want to do is find which one is larger, you can subtract or divide.

(a/b) - (c/d) > 0 . . . . means a/b is larger

(a/b) / (c/d) > 1 . . . . means a/b is larger

These operations with fractions are done using the methods of arithmetic with fractions that you have been taught.

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"Simplify" when applied to ratios usually means common factors are removed from each of the terms.

For example, the ratio 2:12 is a ratio of even numbers, so we know both numbers have a factor of 2. (2 is a factor common to both numbers.) When we divide them both by 2, we have the reduced ratio 1:6. That is, 2:12 simplifies to become 1:6.

(It is helpful to have a good working knowledge of multiplication tables when you approach problems in simplifying ratios.)

= = = = = = = = = =

In "quick and dirty" terms, you can do the subtraction ...

That is, you really only need to find out if (ad) > (bc) to determine if (a/b) > (c/d). A similar result is obtained when you consider division ...

This will be greater than 1 if (ad) > (bc), signifying that (a/b) > (c/d).

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Here's an example with numbers.

... Compare 6/7 to 43/50.

... The relationship of interest will be revealed by the products 6·50 = 300 and 7·43 = 301.

... Since 300 < 301, these tell us 6/7 < 43/50.

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We say the above methods are "quick and dirty" because the results may need to be simplified when you're done.

For example, subtracting 1/6 from 1/2 gives

... 1/2 - 1/6 = (1·6 - 2·1)/(2·6) = 4/12

Here, numerator and denominator have a common factor of 4. Removing that gives 4/12 = 1/3.

Even if you do this by the method of common denominators, you still need to reduce the result.

... 1/2 - 1/6 = 3/6 - 1/6 = (3-1)/6 = 2/6

This must be reduced to 1/3 by removing a common factor of 2 from numerator and denominator.

the results from a pre-test for students for the year 2000 and the year 2010 are illustrated in the box plot. what do these results tell us about how students performed on the 29 question pre-test for the two years?

if we compare only the lowest and highest scores between the two years, we might conclude that the students in 2010 did better than the students in 2010. this conclusion seems to follow since the lowest score of 8 in 2010 is greater in value than the lowest score of 6 in 2000. also, the highest score of 28 in 2010 is greater in value than the highest score of 27 in 2000.

but the box portion of the illustration gives us more detailed information. the middle bar in each box shows us that the median score of 20 in 2000 is greater in value than the median score of 17 in 2010. further, we note that the box and whiskers divide the illustration into four pieces. each of these four pieces represents the same portion of students. so, the upper half of the students in 2000 scored in the same score range as the upper one-fourth of the students in 2010, see the illustration at a score of 20.

by considering the upper one-fourth, upper half, and upper three-fourths instead of just the lowest and highest scores, we would conclude that the students as a whole did much better in 2000 than in 2010. we would conclude that as a whole the students in 2010 are less prepared than the students in 2000.

in this section, we discuss box-and-whisker plots and the five key values used in constructing a box-and-whisker plot. the key values are called a five-number summary, which consists of the minimum, first quartile, median, third quartile, and maximum.

step-by-step explanation: