# Estimating Sums and Differences of Fractions Calculator

## Calculator Use

Estimate sums and differences for positive proper fractions, n/d (numerator/denominator), where n ≤ d and 0 ≤ n/d ≤ 1. Use rounding to estimate answers when adding or subtracting proper fractions.

## Estimating Fractions by Rounding

This online calculator was originally set up to estimate by rounding fractions to the nearest 1/2. Fractions were 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 the section on "Value of Estimating Fractions" below.

### Estimating sums and differences of fractions to the nearest 1/2

- Fractions < 1/4 are rounded down to 0
- Fractions ≥ 1/4 and ≤ 3/4 are rounded to 1/2
- Fractions > 3/4 are rounded up to 1

### Estimating sums and differences of fractions to the nearest 1/4

- Fractions < 1/8 are rounded down to 0
- Fractions ≥ 1/8 and < 3/8 are rounded to 2/8=1/4
- Fractions ≥ 3/8 and < 5/8 are rounded to 4/8=2/4=1/2
- Fractions ≥ 5/8 and < 7/8 are rounded to 6/8=3/4
- Fractions ≥ 7/8 are rounded up to 8/8=1

### Estimating sums and differences of fractions to the nearest 1/8

- Fractions < 1/16 are rounded down to 0
- Fractions ≥ 1/16 and < 3/16 are rounded to 2/16=1/8
- Fractions ≥ 3/16 and < 5/16 are rounded to 4/16=2/8=1/4
- Fractions ≥ 5/16 and < 7/16 are rounded to 6/16=3/8
- Fractions ≥ 7/16 and < 9/16 are rounded to 8/16=4/8=1/2
- Fractions ≥ 15/16 are rounded up to 16/16=8/8=1

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

See our expanded fractions table.

## 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). In this case however, 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 by rounding to 0, 1/2 or 1. This works well through a calculator such as 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 you try to add several fractions by the same method such as 1/8 + 1/16 + 2/8 + 3/16 you can end up with an estimate that is very rough. Therefore, you should use good judgment in your estimating process.

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