# approximation fractions

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which math fraction is greater through approximation:
10/21 or 15/28?

• approximation fractions -

One way to answer would be to convert to common denominators.
10/21 = 40/84
15/28 = 45/84
so 15/28 is quite a bit larger.

Here is another way:
10/21 is 0.5/21 or 1/42 larger than 1/2
15/28 is 1/28 larger than 1/2.
Since 1/28 > 1/42, 15/28 is larger

• approximation fractions -

increase the first by a factor of 28/21 or 4/3 or 1.3

10/21 * 1.3/1.3= 13/28

Which means 15/28 is the larger.

• approximation fractions -

here is yet another "very old-fashioned" way:

write the fractions side by side, and take the product of the "diagonals"

10/21 vs 15/28

diagonal leaning left = 10x28 = 280
diagonal leaning right = 21x15 = 315

since 280 < 315
10/21 < 15/28

• approximation fractions -

My second method contained an error but got the right answer.
10/21 is 1/42 LESS than 1/2, not greater.
15/28 is greater than 1/2.
I should have seen that right away.

• approximation fractions -

http://www.echalk.co.uk/tasters/taster2/taster.html

A nice Texas estimating fractions exercise (Texas=UK)

• approximation fractions -

nice!

(probably better than some of the "methods" used these days to teach fractions)

• approximation fractions -

Cool game !

• approximation fractions -

OH,MY Goodness

http://www.echalk.co.uk/

The Blob Game is hilarious.
Catch what happens to the blob when you pick the wrong one.

• approximation fractions -

15/56 8/35

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