Fractions, Number Lines, and Order

Number Sense with Fractions

One way of estimating solutions to problems involving fractions is to use 0, , and 1 as key points or anchors to help us visualize the relative size of fractions between 0 and 1. These are good reference points or landmarks to keep in mind when estimating solutions.

Example:  Is  closer to 0, , or 1?

Solution:  First we notice that  is equivalent to one-half, so  is greater in value than . Next we notice that the numerator 5, is as close as we can get to the denominator 6, without reaching .  So we conclude that is closer to one.

 

Example:  Is closer to 0, , or 1?

Solution: First we notice that is equivalent to .   We conclude that  is slightly larger than one-half.

 

Example:  Estimate the value of the sum for .

 Solution: We estimate the value of the sum to be 3, since  .

Note that the symbol, ≈, means approximately equal to. The symbol should be used anytime an estimate or approximation is made during a computation.

 

Joke or Quote

Order is Heaven's first law.
An Essay on Man IV - Pope, Alexander (1688-1744)

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