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What is the triangle proportionality therom
1 answer:
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"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.)
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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 right fraction represents the percentage; 42 over 100 (100 is the total), or 0.42.
The left fraction is the part number over the whole number. The whole number is unknown, so we use 'x'.
Your answer is 75.