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Sav [38]
3 years ago
9

Diya and Leo both write the decimal 2.15 repeating as a fraction. Diya's fraction: 97/45 Leo's fraction: 97/5 Who wrote the corr

ect fraction?
Mathematics
1 answer:
Ulleksa [173]3 years ago
8 0
We can solve this without counting too much, like this:

When we look st Diya's fraction: it's about 2 : you can see that the top number is about twice as big as the lower one (compare 90 and 40 for this, 90 is a little more than twice 40)

When we look at Leo's fraction: 97 is a lot more than twice 5!!! To simplify compare 90 and 5: it is definitely at least 10 times bigger (actually 18).

So even if we just "look at" the fractions; Leo's fraction seems too big to be 2.(15).

In fact, his fraction is equal to 19.4

Diya was right!

(and 97/45 is exactly 2.(15).
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First lap:
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Second lap:
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Third lap:
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These are the lengths of each strip.  They're 2-ft wide, so the area
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I expected to be able to see a pattern developing, but my brain cells
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lap, then add up all the areas and see how close he is:

Fourth lap:
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all the time, so each lap contributes less area than the last one did.

Hey ! Maybe that's the key to the approximate pattern !

Each lap around the yard mows a 2-ft strip along the length ... twice ...
and a 2-ft strip along the width ... twice.  (Approximately.)  So the area
that gets mowed around each lap is (2-ft) x (the perimeter of the rectangle),
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So now we have rectangles measuring

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and the areas of their rectangular strips are
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==> I see that the areas are decreasing by 32-ft² each lap.
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How much area do we have now:

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And there you are ... Somewhere during the 10th lap, he'll need to
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in front of the mower, and put down a yellow chalk-line exactly where
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There must still be an easier way to do it.  For now, however, I'll leave it
there, and go with my answer of:  During the 10th lap.

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