Video: Solving Word Problems Involving Fractions

Charlotte spends 8 hours of her day sleeping and 2 hours working. Determine the fraction of the day during which Charlotte is neither sleeping nor working.

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Video Transcript

Charlotte spends eight hours of her day sleeping and two hours working. Determine the fraction of the day during which Charlotte is neither sleeping nor working.

We’re told in the question that Charlotte spends eight hours of her day sleeping and two hours working. This means that the total amount of time she spends sleeping or working could be calculated by adding eight and two. Eight plus two is equal to 10. Therefore, Charlotte spends 10 hours per day either sleeping or working.

We know that there are 24 hours in one day. This means that to calculate the amount of time that Charlotte is not sleeping or working, we need to subtract 10 from 24. This is equal to 14. Charlotte is neither sleeping nor working for 14 hours out of 24 hours in a day. This can be written as a fraction, 14 over 24.

As both of these numbers are even, we can divide the numerator and denominator by two. Remember, when simplifying fractions, whatever you do to the top, you must do to the bottom. 14 divided by two is equal to seven. 24 divided by two is equal to 12. This means that the fraction of the day during which Charlotte is neither sleeping nor working, in its simplest form, is seven over 12, or seven twelfths.

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