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Keep It 1.2.3 – Store notes, web links, and documents in one place. February 1, 2018 Keep It is for writing notes, saving web links, storing documents, and finding them again. Windows 7: System Restore Windows 8 or Windows 8.1: How to refresh, reset, or restore your PC If you could not uninstall the program or driver via System Restore, you may be able to identify the faulty software by performing the clean boot troubleshooting steps listed in the following Knowledge Base article.
Unit fractions (fractions which have numerators of 1) can be written as the sum of two different unit fractions.
For example
$frac{1}{2} = frac{1}{3} + frac{1}{6}$
Charlie thought he'd spotted a rule and made up some more examples.
$frac{1}{2} = frac{1}{10} + frac{1}{20}$
$frac{1}{3} = frac{1}{4} + frac{1}{12}$
$frac{1}{3} = frac{1}{7} + frac{1}{21}$
$frac{1}{4} = frac{1}{5} + frac{1}{20}$
Are all his examples correct?
What do you notice about the sums that are correct?
Find some other correct examples..
How would you explain to Charlie how to generate lots of correct examples?
Alison started playing around with $frac{1}{6}$ and was surprised to find that there wasn't just one way of doing this.
She found:
$frac{1}{6} = frac{1}{7} + frac{1}{42}$
$frac{1}{6} = frac{1}{8} + frac{1}{24}$
$frac{1}{6} = frac{1}{9} + frac{1}{18}$
$frac{1}{6} = frac{1}{10} + frac{1}{15}$
$frac{1}{6} = frac{1}{12} + frac{1}{12}$ (BUT she realised this one didn't count because they were not different.)
Charlie tried to do the same with $frac{1}{8}$. Can you finish Charlie's calculations to see which ones work?
$frac{1}{8} = frac{1}{9} + ?$
$frac{1}{8} = frac{1}{10} + ?$
$frac{1}{8} = frac{1}{11} + ?$
..........
Can all unit fractions be made in more than one way like this?
Choose different unit fractions of your own to test out your theories.
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Jan 04, 2018 Keep It is for writing notes, saving web links, storing documents, and finding them again. Available on Mac, and as a separate app for iPhone and iPad, changes are automatically made available across all your devices with iCloud. Keep It is the destination for all those things you want to put somewhere, confident you will find them again later. Windows 7: System Restore Windows 8 or Windows 8.1: How to refresh, reset, or restore your PC If you could not uninstall the program or driver via System Restore, you may be able to identify the faulty software by performing the clean boot troubleshooting steps. Question: 'What does it mean that love always protects (1 Corinthians 13:7)?' Answer: The “love chapter,” 1 Corinthians 13, mentions four specific attributes of love that are “always” put into action. The first of these is that love “always protects” (NIV) or “love bears all things” (ESV and NKJV).