How do negatives work?

The sign applies to the whole quantity, so minus two and three quarters is minus eleven over four. Treating only the whole part as negative gives minus five over four, which is a different number.

Math & Statisticsfractions

Mixed Number Calculator

A mixed number as an improper fraction and a decimal. The conversion is one multiplication and one addition, and getting the sign right on a negative whole part is where it goes wrong.

Also called: mixed to improper fraction.

As an improper fraction

11/4

2 and 3/4 is 11/4, or 2.75 as a decimal. Converting multiplies the whole part by the denominator before adding the numerator.

As a decimal

2.75

Improper numerator

Simplified

11/4

As a percentage

275%

How this is calculated

Method and background

How this is calculated

Multiply the whole part by the denominator and add the numerator, keeping the same denominator. With a negative whole part the fractional part is also negative, so minus two and three quarters is minus eleven quarters rather than minus five quarters, which is the mistake that shows up in the sign.

improper numerator = whole part * denominator + numerator

w: Whole part
n: Numerator
d: Denominator

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

two and three quarters

Whole part: 2
Numerator: 3
Denominator: 4

As an improper fraction11/4

2 * 4 + 3

Open this example

a negative carries the sign through

Whole part: -2
Numerator: 3
Denominator: 4

As an improper fraction-11/4

boundary: the sign error this page warns about

Open this example

Method and limits

What it assumes

A non-negative fractional part, with the sign carried by the whole part.

What it deliberately does not model

Improper mixed numbers, where the numerator exceeds the denominator, are converted as given.

Formula version 1.0.0 · definition 1.0.0 · United States · Report a problem with this calculator

Frequently asked questions

How do negatives work?: The sign applies to the whole quantity, so minus two and three quarters is minus eleven over four. Treating only the whole part as negative gives minus five over four, which is a different number.