Math CentralQuandaries & Queries


Question from jonecia, a student:

write this ratio as a fraction in lowest terms 707days of 112days?

Hello Jonecia,

There are a few ways to think of this question, here is an example...
'of' is a division word and fractions are a more precise way to represent a number (instead of a decimal).
If a family has a pie to share, they cut it into 6 pieces and eat 4,
then they have eaten 4 of 6 pieces or 4/6.
If we wrote this as a ratio (eaten to noneaten pie) we would write 4 to 6.
Let's try a similar example to your question.

Write this ratio as a fraction in lowest terms; 322 days of 112 days,
$322 = 2 \times 7 \times 23$ and $112 = 2^4 \times 7$ and hence

\[\frac{322}{112} = \frac{2 \times 7 \times 23}{2^4 \times 7} = \frac{23}{2^3} = \frac{23}{8}.\]

Good luck.


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