Estimating Sums and Differences of Fractions Calculator

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Estimating Sums/Differences
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Rounding to:



Answer:
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About this Calculator

Estimates sums and differences for positive proper fractions, n/d, where n ≤ d and 0 ≤ n/d ≤ 1. Please read the notes below on Value of Estimating Fractions.

Estimating Fractions by Rounding:

This online calculator was originally set up to estimate by rounding fractions to the nearest 1/2.  Fractions are rounded to 0, 1/2 or 1.  For more precise estimating we added the ability to round fractions to the closest 1/4 or 1/8.  See section on "Value of Estimating Fractions".

  • Estimating sums and differences of fractions to the nearest 1/2
    • If the fraction < 1/4 it will be rounded down to 0.
    • If the fraction ≥ 1/4 and the fraction ≤ 3/4 it will be rounded to 1/2.
    • If the fraction is > 3/4 it will be rounded up to 1.
  • Estimating sums and differences of fractions to the nearest 1/4
    • If the fraction < 1/8 it will be rounded down to 0.
    • If the fraction ≥ 1/8 and the fraction < 3/8 it will be rounded to 2/8=1/4.
    • If the fraction ≥ 3/8 and the fraction < 5/8 it will be rounded to 4/8=2/4=1/2.
    • If the fraction ≥ 5/8 and the fraction < 7/8 it will be rounded to 6/8=3/4.
    • If the fraction ≥ 7/8 it will be rounded up to 8/8=4/4=1.
  • Estimating sums and differences of fractions to the nearest 1/8
    • If the fraction < 1/16 it will be rounded down to 0.
    • If the fraction ≥ 1/16 and the fraction < 3/16 it will be rounded to 2/16=1/8.
    • If the fraction ≥ 3/16 and the fraction < 5/16 it will be rounded to 4/16=2/8=1/4.
    • If the fraction ≥ 5/16 and the fraction < 7/16 it will be rounded to 6/16=3/8.
    • If the fraction ≥ 7/16 and the fraction < 9/16 it will be rounded to 8/16=4/8=1/2.
    • etc ......
    • If the fraction ≥ 15/16 it will be rounded up to 16/16=8/8=1

Fractions table for halves, quarters, eighths and sixteenths with decimal equivalents

0 0/2 0/4 0/8 0/16 0.00000
        1/16 0.06250
      1/8 2/16 0.12500
        3/16 0.18750
    1/4 2/8 4/16 0.25000
        5/16 0.31250
      3/8 6/16 0.37500
        7/16 0.43750
  1/2 2/4 4/8 8/16 0.50000
        9/16 0.56250
      5/8 10/16 0.62500
        11/16 0.68750
    3/4 6/8 12/16 0.75000
        13/16 0.81250
      7/8 14/16 0.87500
        15/16 0.93750
1 2/2 4/4 8/8 16/16 1.00000

 

See our expanded fractions table.

For these and some more basic methods of working with fractions see also Help With Fractions

Value of Estimating Fractions

First, always follow the guidelines your teacher gives you for estimating sums and differences of fractions.

Estimating operations on proper fractions in this way is sometimes more accurately done by a human than a calculator.  A calculator can certainly make an estimate based on defined parameters in a formula and there are many applications where estimating is done very well with calculators (or computers) however, in this case, a better estimate might be achieved by a human.

For example, the standard practice for estimating sums and differences of fractions for grammar school students seems to be rounding to the closest 1/2 as outlined above.  Or, rounding to 0, 1/2 or 1.  This works well through a calculator such as this if you are adding 3/8+11/16.  3/8 is closest to 1/2 and 11/16 is less than 3/4 so it is also closest to 1/2.  Estimating we have 1/2+1/2=1.  If we really add these terms 3/8+11/16, with a common denominator of 16 we have 6/16+11/16=17/16=1+1/16 which is really close to our estimate of 1.  If we now try 1/8+3/4, by the rules for rounding to the closest 1/2, 1/8 is closest to 0 and 3/4 is rounded to 1/2.  Estimating we get 0+1/2=1/2.  However, the real answer is 1/8+3/4=1/8+6/8=7/8.  This is much closer to 1 than it is to 1/2 so our estimate is not very accurate.  Keep in mind that an estimate, by definition, is a rough calculation.

If we try to add several fractions by the same method such as 1/8+1/16+2/8+3/16 we can end up with an estimate that is rougher than we want.  Therefore, you should use good judgment in your estimating process.

See also Ask Dr. Math - Estimating Fractions/Mixed Numbers

 

Cite this content, page or calculator as:

Furey, Edward "Estimating Sums and Differences of Fractions Calculator" From http://www.CalculatorSoup.com - Online Calculator Resource.