# math

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Anna and Julia each take a bicycle trip. Anna rides 20 miles in 1 1/3 hours. Julia rides 246 miles in 16 hours. Which has slower unit rate? By how much?

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recall that speed or rate is distance traveled over time, or:
speed, v = d/t

thus, you compare Anna's speed and Julia's speed:
Anna: v = 20/(1 1/3)
Julia: v = 246/(16)
*note: first convert mixed number to improper fraction before dividing.

hope this helps. :)

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so it would e 20/4 over 3? I don't get how I would divide that from 246/16

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it's 20/(4/3),, first simplify this,,

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how do you simifly that?

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when dividing a number by a fraction, first get the reciprocal of the fraction,,
*to get reciprocal: you just interchange the numerator and denominator, thus:
reciprocal of 4/3 = 3/4
now the operation becomes multiplication instead of division:
20 * (3/4)

i think you know how to do this. :)

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which is 12? Then do I divide 12 and 246/16?

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nope, it's not 12,,
remember that a whole number can be written to:
20 = 20/1
now,
20/1 * 3/4 = ?

..and we will not divide the answer by 246/16,, we will just compare them.

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Well 20 times 3 is 60
1 times 4 is 4
60/4

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you're on the right track,,
now, what is 60/4 ?

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15/1

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right~! :)
now, we simplify 246/16,,
since the numerator and denominator have a common factor 2, we can cancel it out:
(2*123)/(2*8) = 123/8
123/8 is in simplest form,, now change this to mixed number.

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15 3/8

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yes, that's right~! :)
now comparing the speed:
Anna: 15
Julia: 15 3/8

which of the two is slower (or has smaller speed)?
then, "by how much" means you will get the difference:
15 3/8 - 15 = ?

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3/8

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nope,, 15 3/8 is greater than 15,,
it's like you have 15 whole pizza plus 3 slices, while the other has only 15 whole pizzas, that's why,
15 3/8 > 15

then, "by how much" means you will get the difference:
15 3/8 - 15 = ?

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right. the difference is 3/8 m/s. :)

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the answer is obvious, do math